Le Risque de Valeur Résiduelle Trois études quantitatives - Portail ...
Le Risque de Valeur Résiduelle Trois études quantitatives - Portail ...
Le Risque de Valeur Résiduelle Trois études quantitatives - Portail ...
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Mme Sandrine Lardic,<br />
UNIVERSITÉ PARIS OUEST - NANTERRE LA DÉFENSE<br />
T H È S E<br />
pour obtenir le gra<strong>de</strong> <strong>de</strong><br />
Docteur <strong>de</strong> l’Université<br />
<strong>de</strong> Paris Ouest - Nanterre La Défense<br />
Discipline : Sciences Économiques<br />
présentée et soutenue publiquement par<br />
Sylvain Prado<br />
<strong>Le</strong> 21 juin 2010<br />
<strong>Le</strong> <strong>Risque</strong> <strong>de</strong> <strong>Valeur</strong> <strong>Résiduelle</strong><br />
<strong>Trois</strong> étu<strong>de</strong>s <strong>quantitatives</strong><br />
Directrice <strong>de</strong> thèse : Mme Valérie Mignon<br />
Jury :<br />
Maître <strong>de</strong> conférences à l’Université Paris Ouest - Nanterre La Défense<br />
Mr Jean-François <strong>Le</strong>mettre,<br />
Professeur à l’Université Paris Sud (Rapporteur)<br />
Mme Valérie Mignon,<br />
Professeur à l’Université <strong>de</strong> Paris Ouest - Nanterre La Défense<br />
Mr Jamel Trabelsi,<br />
Maître <strong>de</strong> Conférences à l’Université <strong>de</strong> Strasbourg (Rapporteur)
ii<br />
L’Université <strong>de</strong> Paris Ouest-Nanterre La Défense n’entend donner aucune approbation ni<br />
improbation aux opinions émises dans les thèses ; ces opinions doivent être considérées comme<br />
propres à leurs auteurs.
Remerciements<br />
Je tiens à remercier :<br />
Valérie Mignon pour sa compréhension, pour avoir encadré mon travail avec beaucoup <strong>de</strong><br />
compétences, pour m’avoir donné les moyens <strong>de</strong> réaliser et <strong>de</strong> mener à bout cette thèse.<br />
Evguenia pour son appui, ses conseils, et l’ai<strong>de</strong> indispensable fournie dans la réalisation <strong>de</strong><br />
cette thèse.<br />
Jean-François <strong>Le</strong>mettre et Jamel Trabelsi pour avoir accepté <strong>de</strong> rédiger les rappors sur cette<br />
thèse, ainsi que Sandrine Lardic pour sa participation au jury.<br />
Christophe Bourgoin et Hacène Ouzia pour l’ai<strong>de</strong> sur LaTeX et grâce à qui le lecteur a entre<br />
ses mains un travail bien plus lisible que lors <strong>de</strong> ma première mise en page.<br />
L’intérêt <strong>de</strong> l’entreprise GE Capital à l’égard <strong>de</strong> mon travail, et plus particulièrement Pierre<br />
Olivier Bard, qui a contribué à un climat favorable à ma démarche intellectuelle.<br />
Tous ceux avec qui j’ai eu le plaisir <strong>de</strong> collaborer au sein <strong>de</strong> GE : les équipes AMO mon<strong>de</strong>,<br />
Europe, alleman<strong>de</strong>s, espagnoles, francaises, italiennes et britanniques.<br />
Tous ceux qui m’ont fourni un retour constructif sur mon travail : Kamel Mathout pour la<br />
relecture <strong>de</strong> mes premiers travaux, le laboratoire Economix lors du séminaire lunch, l’université<br />
<strong>de</strong> Brunel à Londres lors <strong>de</strong> la conférence QASS, l’université <strong>de</strong> Limerick lors <strong>de</strong> la Irish Society<br />
of New Economists Annual Conference.<br />
iii
iv REMERCIEMENTS
Résumé<br />
Malgré son poids économique et ses avantages, l’activité <strong>de</strong> leasing reste méconnue. <strong>Le</strong> lea-<br />
sing fait l’objet d’un nombre limité <strong>de</strong> travaux académiques, notamment sur une problématique<br />
qui lui est propre, le risque <strong>de</strong> valeur résiduelle. Dans l’activité <strong>de</strong> leasing, le bailleur prend le<br />
risque <strong>de</strong> ne pas récupérer su¢ samment <strong>de</strong> capital lors <strong>de</strong> la revente <strong>de</strong> l’actif. <strong>Le</strong> risque <strong>de</strong><br />
perte à la revente à la …n <strong>de</strong> la pério<strong>de</strong> contractuelle, ainsi que la tari…cation sont fortement<br />
impactés par le prix estimé <strong>de</strong> revente <strong>de</strong> l’actif (la valeur résiduelle). La thèse vise à fournir une<br />
contribution académique aux professionnels en charge <strong>de</strong> la gestion <strong>de</strong> ce risque dans le secteur<br />
du leasing. <strong>Trois</strong> thèmes sont abordés : la valorisation <strong>de</strong>s actifs, la couverture <strong>de</strong>s risques <strong>de</strong><br />
valeur résiduelle, et la dimension macro-économique.<br />
Dans le premier chapitre, nous appliquons la métho<strong>de</strong> <strong>de</strong>s prix hédoniques à un por-<br />
tefeuille européen <strong>de</strong> leasing, a…n d’estimer la distribution <strong>de</strong>s prix <strong>de</strong> revente d’automobiles.<br />
L’approche hédonique estime le prix d’un bien par la valorisation <strong>de</strong> ses attributs. Suite à une<br />
discussion sur les prix hédoniques, nous proposons un modèle opérationnel pour le marché <strong>de</strong><br />
l’automobile d’occasion. <strong>Le</strong> modèle est appliqué à quatre pays européens (l’Allemagne, l’Es-<br />
pagne, la France et la Gran<strong>de</strong>-Bretagne), et les distributions sont calculées sur <strong>de</strong>ux modèles<br />
<strong>de</strong> véhicules (Audi A4 et Ford Focus) permettant la comparaison <strong>de</strong>s pro…ls <strong>de</strong> dépréciation et<br />
<strong>de</strong>s risques <strong>de</strong> valeur résiduelle.<br />
Mots-clés : modèles hédoniques, valeur résiduelle, marché automobile. Classi…cation<br />
JEL : C51, G12, G32, D12.<br />
Dans le <strong>de</strong>uxième chapitre, nous proposons un modèle statistique pour couvrir le risque<br />
<strong>de</strong> valeur résiduelle en utilisant la technique <strong>de</strong>s copules gaussiens. A la suite d’une discussion<br />
sur la problématique du risque <strong>de</strong> valeur résiduelle et <strong>de</strong>s modèles <strong>de</strong> risque <strong>de</strong> crédit existants,<br />
un nouveau produit dérivé est proposé et analysé : le Collateralized Residual Value (CRV).<br />
v
vi RÉSUMÉ<br />
<strong>Le</strong> modèle est appliqué à un portefeuille européen <strong>de</strong> location longue durée d’automobiles. Nos<br />
résultats indiquent que ce produit …nancier est facile à adapter et à mettre en œuvre en fonction<br />
<strong>de</strong>s caractéristiques du contrat et <strong>de</strong> la corrélation entre les actifs le composant.<br />
Mots-clés : risque <strong>de</strong> valeur résiduelle, risque <strong>de</strong> crédit, produits dérivés <strong>de</strong> crédit, modèle<br />
factoriel, copules. Classi…cation JEL : C10, G13.<br />
<strong>Le</strong> <strong>de</strong>rnier chapitre répond à <strong>de</strong>ux questions cruciales dans le secteur du leasing automo-<br />
bile : Quelles sont les interactions entre les automobiles neuves et d’occasion ? Pouvons-nous<br />
utiliser ces interactions a…n d’estimer le prix <strong>de</strong> revente <strong>de</strong>s véhicules ? <strong>Le</strong>s voitures neuves<br />
d’aujourd’hui seront les voitures d’occasion <strong>de</strong> <strong>de</strong>main, et l’on suppose une forme <strong>de</strong> compé-<br />
tition entre le marché du neuf et le marché <strong>de</strong> l’occasion. C’est pourquoi il existe quelques<br />
idées préconçues et <strong>de</strong> nombreuses théories sur les interactions entre le premier marché et le<br />
second marché. Nous proposons <strong>de</strong> développer la ré‡exion par une analyse macro-économique<br />
<strong>de</strong>s marchés automobiles Français, Britanniques et Nord-Américains. <strong>Le</strong>s di¤érents concepts<br />
sont répertoriés et statistiquement contrôlés. Nos résultats indiquent que les relations entre les<br />
di¤érents marchés semblent limitées en France et au Royaume-Uni, alors que le marché Nord-<br />
Américain est confronté à un mécanisme dit <strong>de</strong> ‘Scitovscky’. Dans tous les cas, les relations ne<br />
sont pas assez fortes pour expliquer complètement les comportements <strong>de</strong>s marchés.<br />
Mots-clés : Second marché, marché automobile, prix, causalité, corrélation cycliques, VAR.<br />
Classi…cation JEL : C32, E31, E37.
Summary<br />
<strong>Le</strong>asing, by its volume and its attributes, constitutes a signi…cant mean of …nancing in the<br />
world. <strong>Le</strong>asing, however, sparked o¤ a limited aca<strong>de</strong>mic interest, many of its features have been<br />
unexplored and particularly on a critical point, the residual value risk. In the leasing industry<br />
the lessor faces a risk, at the end of the contract, in not recovering su¢ cient capital value from<br />
resale of the asset. The risk of loss on sales at the end of the contract term, as well as pricing,<br />
are critically impacted by the forecasted resale price of the asset (residual value). The thesis<br />
aims to provi<strong>de</strong> an aca<strong>de</strong>mic contribution directed at asset analysts in charge of residual value<br />
in the leasing industry. Three topics are discussed : asset valuation, residual value risk hedging,<br />
and macro economy perspective.<br />
In the …rst chapter, we apply the Hedonic methodology to European auto lease portfolios,<br />
in or<strong>de</strong>r to estimate the resale price distribution. The Hedonic approach estimates the price<br />
of a good through the valuation of its attributes. Following a discussion on Hedonic prices,<br />
we propose an operational mo<strong>de</strong>l for the automobile resale market. The mo<strong>de</strong>l is applied to<br />
four European countries (France, Germany, Spain and Great Britain), and distributions are<br />
calculated on two vehicle versions (Audi A4 and Ford Focus) allowing a comparison of market<br />
<strong>de</strong>preciation patterns and residual value risks.<br />
Keywords : Hedonic mo<strong>de</strong>l, residual value, automotive market. JEL Classi…cation :<br />
C51, G12, G32, D12.<br />
In the second chapter, we propose a mo<strong>de</strong>l to hedge residual value risk using the Gaussian<br />
copula methodology. After discussing residual value risk and credit risk mo<strong>de</strong>lization, a new<br />
<strong>de</strong>rivative product is introduced and analyzed ; the Collateralized Residual Values (CRV). The<br />
mo<strong>de</strong>l is applied to an European auto lease portfolio of operating lease contracts pertaining to<br />
a major company. Our results indicate that the …nancial product is easy to customize, and to<br />
implement through the contract characteristics and the level of correlation.<br />
vii
viii SUMMARY<br />
Keywords : residual value risk, credit risk, credit <strong>de</strong>rivatives, factor mo<strong>de</strong>ling, copula. JEL<br />
Classi…cation : C10, G13.<br />
In the third chapter, we aim at answering two critical questions of the Auto lease industry.<br />
What are the interactions between the new and the second-hand car markets ? Can we use the<br />
interactions to estimate the car prices of tomorrow ? Everybody knows that the new cars of<br />
today are used cars of tomorrow and some people assume a competition between new and<br />
used markets. There are numerous, preconceived i<strong>de</strong>as and aca<strong>de</strong>mic theories regarding the<br />
interactions between primary and secondary markets. To investigate the relations, we provi<strong>de</strong><br />
a macroeconomic analysis of the French, the British and the US car markets. Our results<br />
indicate that the relations appear limited for France and the UK, whereas the US market faces<br />
a Scitovscky mechanism. Furthermore, they illustrate that the interrelations are not strong<br />
enough to fully explain and forecast market patterns.<br />
Keywords : second-hand market, automotive market, prices, causality, cyclical correlations,<br />
VAR. JEL Classi…cation : C32, E31, E37.
Table <strong>de</strong>s matières<br />
Remerciements iii<br />
Résumé v<br />
Summary vii<br />
Introduction Générale xiii<br />
General Introduction xxiii<br />
1 The European used-car market at a glance 1<br />
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2<br />
1.2 The Hedonic theory un<strong>de</strong>rlies our mo<strong>de</strong>l . . . . . . . . . . . . . . . . . . . . . . 4<br />
1.2.1 Goods attributes constitute the Hedonic theory. . . . . . . . . . . . . . . 4<br />
1.2.2 An i<strong>de</strong>nti…cation problem appears in Hedonic mo<strong>de</strong>ls. . . . . . . . . . . . 5<br />
1.2.3 Used cars are durable commodities. . . . . . . . . . . . . . . . . . . . . . 7<br />
1.3 Some characteristics of the mo<strong>de</strong>l are discussed. . . . . . . . . . . . . . . . . . . 8<br />
1.3.1 Coe¢ cients interpretation <strong>de</strong>pends on used market substitution to new<br />
market. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8<br />
1.3.2 Others products interact with price. . . . . . . . . . . . . . . . . . . . . . 9<br />
1.3.3 Multicollinearity is a main issue in Hedonic mo<strong>de</strong>ls. . . . . . . . . . . . . 10<br />
1.3.4 Which functional form ? . . . . . . . . . . . . . . . . . . . . . . . . . . . 10<br />
1.3.5 Unobserved tastes create heteroscedasticity. . . . . . . . . . . . . . . . . 11<br />
1.4 We use the Hedonic mo<strong>de</strong>l to estimate the distribution of resale price. . . . . . . 12<br />
1.4.1 Ohta and Griliches have an empirical approach. . . . . . . . . . . . . . . 12<br />
1.4.2 Statistical mo<strong>de</strong>ls are slightly di¤erent by country. . . . . . . . . . . . . . 13<br />
ix
x TABLE DES MATIÈRES<br />
1.4.3 We estimate the distribution of resale price. . . . . . . . . . . . . . . . . 14<br />
1.4.4 An adjustment removes uncertain variables e¤ects. . . . . . . . . . . . . 14<br />
1.5 We apply the methodology to four European countries. . . . . . . . . . . . . . . 15<br />
1.5.1 Mo<strong>de</strong>ls are created according to the information usually available in the<br />
leasing industry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15<br />
1.5.2 The regression provi<strong>de</strong>s a Hedonic price assessment of the European mar-<br />
kets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16<br />
1.5.3 The analysis on Ford focus and Audi A4 give additional informations. . . 16<br />
1.6 Conclusion and extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18<br />
1.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19<br />
1.7.1 Appendix A : Methodological aspects. . . . . . . . . . . . . . . . . . . . 19<br />
1.7.2 Appendix B : Regression equations and notations . . . . . . . . . . . . . 22<br />
1.7.3 Appendix C : Regression results . . . . . . . . . . . . . . . . . . . . . . . 25<br />
1.7.4 Appendix D : Pivot Point results . . . . . . . . . . . . . . . . . . . . . . 27<br />
1.7.5 Appendix E : Graphical analysis : . . . . . . . . . . . . . . . . . . . . . . 28<br />
2 Hedging residual value risk using <strong>de</strong>rivatives 37<br />
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38<br />
2.2 <strong>Le</strong>asing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42<br />
2.2.1 Main characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42<br />
2.2.2 Residual value risk versus competitiveness . . . . . . . . . . . . . . . . . 44<br />
2.3 Mo<strong>de</strong>l pre requisites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47<br />
2.3.1 CDO are a subclass of ABS . . . . . . . . . . . . . . . . . . . . . . . . . 47<br />
2.3.2 Default, <strong>de</strong>fault, <strong>de</strong>fault.... . . . . . . . . . . . . . . . . . . . . . . . . . . 48<br />
2.3.3 Basic elements on Copulas . . . . . . . . . . . . . . . . . . . . . . . . . . 49<br />
2.3.4 Speci…c pre requisites, the Gaussian copula . . . . . . . . . . . . . . . . . 51<br />
2.3.5 The initial one factor mo<strong>de</strong>l is used for CDO pricing . . . . . . . . . . . 52<br />
2.4 A modi…ed mo<strong>de</strong>l : The leasing mo<strong>de</strong>l . . . . . . . . . . . . . . . . . . . . . . . 55<br />
2.4.1 There is a similarity between credit risk and residual value risk. But there<br />
are also dissimilarities and speci…cally in Auto <strong>Le</strong>ase. . . . . . . . . . . . 56<br />
2.4.2 Homogeneous equipment type mo<strong>de</strong>l . . . . . . . . . . . . . . . . . . . . 58<br />
2.4.3 Heterogeneous equipment type mo<strong>de</strong>l : a portfolio of three di¤erent assets 60<br />
2.4.4 Collateralized Residual Values . . . . . . . . . . . . . . . . . . . . . . . . 62
TABLE DES MATIÈRES xi<br />
2.5 Empirical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66<br />
2.5.1 Correlation to the one sector factor . . . . . . . . . . . . . . . . . . . . . 66<br />
2.5.2 Fair Market Value and Residual Value setting . . . . . . . . . . . . . . . 71<br />
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76<br />
2.7 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77<br />
3 A Family Hitch 81<br />
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82<br />
3.2 Aca<strong>de</strong>mic researches in the second-hand market are legion. . . . . . . . . . . . . 82<br />
3.2.1 Why secondary markets exist ? . . . . . . . . . . . . . . . . . . . . . . . 83<br />
3.2.2 The Akerlof e¤ect and the car durability are linked. . . . . . . . . . . . . 85<br />
3.2.3 Optimal durability and Time inconsistency are two areas of research. . . 87<br />
3.2.4 Scitovsky’s mechanisms are part of a Keynesian framework. . . . . . . . 88<br />
3.2.5 There are implied mechanisms behind the aca<strong>de</strong>mic theories. . . . . . . . 90<br />
3.3 The macroeconomic times series need clari…cations. . . . . . . . . . . . . . . . . 91<br />
3.3.1 Three countries are compared through four time series. . . . . . . . . . . 91<br />
3.3.2 How to connect the aca<strong>de</strong>mic literature with a time series analysis ? . . . 93<br />
3.3.3 We work on macroeconomic time series, a limited information. . . . . . . 96<br />
3.3.4 What do the series look like ? . . . . . . . . . . . . . . . . . . . . . . . . 98<br />
3.4 The econometric analysis shows di¤erent results by country. . . . . . . . . . . . 99<br />
3.4.1 The unit root tests un<strong>de</strong>rmine the advanced mechanisms. . . . . . . . . . 100<br />
3.4.2 The correlation analysis provi<strong>de</strong>s a one-month period perspective. . . . . 102<br />
3.4.3 The Granger causality tests elaborate the assessments of the correlation<br />
analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102<br />
3.4.4 The Hodrick-Prescott …lter reveals economic cycles. . . . . . . . . . . . . 104<br />
3.4.5 Vector Autoregressive (VAR) mo<strong>de</strong>ls clarify the previous results. . . . . . 106<br />
3.5 To conclu<strong>de</strong>, an inter<strong>de</strong>pen<strong>de</strong>nce ? . . . . . . . . . . . . . . . . . . . . . . . . . . 108<br />
3.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111<br />
3.6.1 Appendix 1 : Data sources . . . . . . . . . . . . . . . . . . . . . . . . . . 111<br />
3.6.2 Appendix 2 : Median Age and Average Sales price in the US . . . . . . . 112<br />
3.6.3 Appendix 3 : Raw data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113<br />
3.6.4 Appendix 4 : Growth rate and seasonally adjusted times series . . . . . . 115<br />
3.6.5 Appendix 5 : Granger Test . . . . . . . . . . . . . . . . . . . . . . . . . . 118
xii TABLE DES MATIÈRES<br />
3.6.6 Appendix 6 : Correlation Analysis . . . . . . . . . . . . . . . . . . . . . . 120<br />
3.6.7 Appendix 7 : Hodrick-Prescott Filter, cycles and trends . . . . . . . . . . 121<br />
3.6.8 Appendix 8 : Hodrick-Prescott Cycles Correlations . . . . . . . . . . . . 124<br />
Conclusion Générale 133<br />
Bibliographie 137
Introduction Générale<br />
"(. . . ) le principe véritable <strong>de</strong> la fécondité irremplaçable <strong>de</strong> la recherche empi-<br />
rique : Faire sans savoir complètement ce que l’on fait, c’est se donner une chance<br />
<strong>de</strong> découvrir dans ce que l’on a fait quelque chose que l’on ne savait pas."<br />
P. Bourdieu, Homo Aca<strong>de</strong>micus, <strong>Le</strong>s Editions <strong>de</strong> Minuit, 1984, p17.<br />
L’activité <strong>de</strong> leasing est peu connue bien qu’elle constitue une part importante <strong>de</strong> l’économie<br />
mondiale.<br />
L’International Accounting Standard for <strong>Le</strong>ase, ou IAS17 1 dé…nit un contrat <strong>de</strong> leasing<br />
comme «un accord par lequel le bailleur cè<strong>de</strong> au locataire, en échange d’un paiement ou une série<br />
<strong>de</strong> paiements, le droit d’utiliser un actif pendant une pério<strong>de</strong> <strong>de</strong> temps convenue» . Cependant,<br />
la législation peut être di¤érente selon les pays, les contrats peuvent être adaptés pour répondre<br />
aux besoins d’un client et tout type d’équipement peut, en théorie, faire l’objet <strong>de</strong> leasing. Ainsi<br />
le mot ‘lease’comprend un large éventail <strong>de</strong> contrats.<br />
Dans l’ensemble, le leasing est un instrument …nancier pour l’achat <strong>de</strong> matériel. Dans un<br />
contrat <strong>de</strong> leasing, le bailleur fournit un équipement qui doit être utilisé par un locataire sur une<br />
pério<strong>de</strong> dé…nie en échange <strong>de</strong> paiements spéci…és. <strong>Le</strong> bien loué peut être tout type <strong>de</strong> matériel<br />
(imprimante, scanner, camions, avions...) utilisé par le locataire à <strong>de</strong>s …ns commerciales. <strong>Le</strong><br />
bailleur achète l’équipement et il est le propriétaire légal <strong>de</strong> l’actif. Pour utiliser l’équipement,<br />
le locataire verse <strong>de</strong>s paiements périodiques au bailleur tout au long <strong>de</strong> la pério<strong>de</strong> du contrat.<br />
1 Au sein <strong>de</strong> l’Union européenne, toutes les sociétés cotées sont tenues d’adopter l’IAS17. La norme équivalente<br />
aux USA est le SAF13.<br />
xiii
xiv INTRODUCTION GÉNÉRALE<br />
L’ensemble du marché du leasing mondial 2 a été estimé à plus <strong>de</strong> 633 milliards <strong>de</strong> dollars<br />
en 2006. L’Europe et L’Amérique du Nord ont représenté 41% et 38% du marché mondial.<br />
<strong>Le</strong> ‘World <strong>Le</strong>asing Yearbook 2009’ a rapporté un montant global d’équipement en leasing<br />
<strong>de</strong> plus <strong>de</strong> 760 milliards <strong>de</strong> dollars pour 2007. <strong>Le</strong>s associations européennes <strong>de</strong> leasing ont<br />
enregistré un volume <strong>de</strong> crédit-bail neuf au-<strong>de</strong>ssus <strong>de</strong> 330 milliards d’Euros et une contribution<br />
au …nancement, en moyenne, <strong>de</strong> 18% du total <strong>de</strong>s investissements européens pour 2008. Par<br />
ailleurs, le leasing a impliqué plus <strong>de</strong> 16 millions d’automobiles en Europe 3 .<br />
D’une manière générale, les contributions aca<strong>de</strong>miques traitant du sujet sont quasiment<br />
toutes liées à la comparaison entre le leasing et l’acquisition d’un équipement par le crédit.<br />
Certains papiers analysent les avantages …scaux résultant du choix entre un contrat <strong>de</strong> leasing<br />
et le recours à un emprunt 4 . Un <strong>de</strong>uxième groupe d’articles académiques discutent du ‘<strong>Le</strong>a-<br />
sing Puzzle’. <strong>Le</strong>s théories en …nance et en economie suggèrent que les contrats <strong>de</strong> leasing et<br />
les emprunts sont <strong>de</strong>s substituts. Ainsi, une augmentation du leasing <strong>de</strong>vrait conduire à une<br />
diminution <strong>de</strong> la <strong>de</strong>tte. De plus, les théories …nancières standard gèrent les ‡ux <strong>de</strong> trésorerie<br />
provenant <strong>de</strong>s contrats <strong>de</strong> leasing <strong>de</strong> la même manière que ceux provenant <strong>de</strong>s crédits. Mais<br />
Ang et Peterson (1984) ont constaté empiriquement que le leasing et la <strong>de</strong>tte apparaissent, en<br />
fait, comme <strong>de</strong>s compléments pour les entreprises. Un accroissement du leasing est associé à un<br />
accroissement <strong>de</strong> la <strong>de</strong>tte. Ne pouvant avancer une explication concluante, ils quali…èrent leur<br />
découverte d’énigme non résolue <strong>de</strong> la …nance ou <strong>de</strong> ’<strong>Le</strong>asing Puzzle’. À la suite <strong>de</strong> leur article<br />
fondateur, plusieurs recherches académiques ont tenté <strong>de</strong> reproduire et <strong>de</strong> véri…er les résultats 5 .<br />
<strong>Le</strong> ‘Puzzle’nous amène au troisième domaine <strong>de</strong> recherche qui couvre tous les articles liés<br />
aux incitations au leasing et à ses avantages. Lasfer et Lévis (1998), par exemple, ont reformulé<br />
le problème. En théorie, le leasing ne procure aucune valeur ajoutée par rapport à l’achat d’un<br />
équipement au travers d’un crédit : les <strong>de</strong>ux moyens <strong>de</strong> …nancement sont associés à un même<br />
taux d’intérêt, ont un statut …scal similaire et prévoient le même prix <strong>de</strong> revente <strong>de</strong> l’actif.<br />
Toutefois, dans la pratique, ces conditions ne sont pas toujours satisfaites et il existe plusieurs<br />
2 White Clarke Global <strong>Le</strong>asing Report (2008).<br />
3 <strong>Le</strong>aseurope Association Website.<br />
4 Voir Smith et Wakeman (1985), Brick, Fung et Subrahmanyam (1987), Mackie-Mason (1990), Goodacre<br />
(2002).<br />
5 Voir Marston et Harris (1988), <strong>Le</strong>wis et Schallheim (1992), Krishnan et Moyer (1994), Branson (1995),<br />
Beattie, Goodacre et Thomson (1999), Yan (2006).
motifs pour le leasing 6 . Pour les gran<strong>de</strong>s entreprises, leur étu<strong>de</strong> révèle que les responsables<br />
…nanciers utilisent le leasing comme un instrument pour minimiser le coût après impôt du<br />
capital. Pour les petites entreprises, le leasing apparaît comme une opportunité <strong>de</strong> croissance et<br />
<strong>de</strong> survie. <strong>Le</strong>s petites entreprises ont <strong>de</strong>s di¢ cultés pour accé<strong>de</strong>r au marché du crédit. De ce fait,<br />
le leasing facilite le …nancement <strong>de</strong> la formation <strong>de</strong> capital …xe. En d’autres termes, les petites<br />
entreprises à fort potentiel <strong>de</strong> croissance ou avec <strong>de</strong> faibles béné…ces sont plus susceptibles <strong>de</strong><br />
faire appel à ce mo<strong>de</strong> <strong>de</strong> …nancement. En conséquence, sans le leasing <strong>de</strong> nombreux projets<br />
n’auraient jamais pu voir le jour.<br />
Drakos et Goulas (2008) avancent que l’incertitu<strong>de</strong> d’un investissement pour une entreprise<br />
est exacerbée par l’irréversibilité du capital. En permettant la séparation <strong>de</strong> l’utilisation d’un<br />
équipement avec les engagements associés à son acquisition 7 , le leasing facilite le désengage-<br />
ment <strong>de</strong> projets infructueux. Schmitt et Stuyck (2002) 8 , Schmitt (2003) 9 et Schmitt (2004) ont<br />
démontré que le leasing est une activité relativement peu risquée et que les recommandations <strong>de</strong><br />
Bâle 2 pour le montant <strong>de</strong>s réserves en capital <strong>de</strong>vrait être réduit pour les entreprises <strong>de</strong> leasing.<br />
Au total, le leasing apparaît comme un instrument …nancier sûr. En outre, le fait <strong>de</strong> louer <strong>de</strong>s<br />
biens plutôt que <strong>de</strong> les vendre peut contribuer à réduire les problèmes environnementaux 10 . La<br />
pratique du leasing limite la production <strong>de</strong> déchets et incite à la création d’un schéma d’utilisa-<br />
tion du matériel en boucle fermée. Pour certains équipements et certains types <strong>de</strong> contrats, les<br />
fabricants peuvent prendre conscience <strong>de</strong>s problèmes opérationnels, ainsi que <strong>de</strong>s coûts associés<br />
à la gestion <strong>de</strong>s produits en …n <strong>de</strong> vie. Ainsi, ils peuvent re<strong>de</strong>ssiner les produits en conséquences<br />
a…n <strong>de</strong> limiter les externalités négatives en …n <strong>de</strong> vie. En restant dans le circuit commercial, les<br />
équipements sont moins susceptibles d’être jetés aux ordures ou stockés quand ils <strong>de</strong>viennent<br />
6 Lasfer et <strong>Le</strong>wis ont énuméré trois principales motivations pour la location. D’abord, la location peut réduire<br />
les taxes …nancières. Deuxièmement, le leasing pourrait être avantageux …nancièrement pour les entreprises en<br />
di¢ culté a…n d’obtenir un accord et l’accès aux équipements, car les bailleurs ont <strong>de</strong>s créances <strong>de</strong> premier rang<br />
sur l’actif. En…n, le leasing peut réduire le coût d’agence parce qu’il ne constitue pas un investissement complet<br />
pour le locataire.<br />
7 L ’hétérogénéité du capital et les di¤érents <strong>de</strong>grés d’irréversibilité associés expliqueraient ainsi les divers<br />
recours au leasing par les entreprises.<br />
8 Schmitt et Stuyck ont analysé <strong>de</strong>s contrats <strong>de</strong> leasing en défaut sur une pério<strong>de</strong> <strong>de</strong> 1976 à 2000 dans six pays<br />
d’Europe au sein <strong>de</strong> douze gran<strong>de</strong>s entreprises. Ils ont constaté que le taux <strong>de</strong> recouvrement était comparables<br />
à celui <strong>de</strong>s obligations <strong>de</strong> premier rang.<br />
9 L’estimation <strong>de</strong> la fonction <strong>de</strong> distribution <strong>de</strong>s pertes et la Value at Risk dans le secteur du leasing révèlent<br />
que l’activité présente un risque relativement faible. Voir aussi Pirotte et Vaessen (2008).<br />
10 Voir Fishbein, McGarry et Dillon (2000).<br />
xv
xvi INTRODUCTION GÉNÉRALE<br />
obsolescents.<br />
Malgré le peu d’étu<strong>de</strong>s sur le sujet, nous <strong>de</strong>vons également souligner que l’intervention <strong>de</strong>s<br />
sociétés <strong>de</strong> leasing crée un attrait supplémentaire pour ce mo<strong>de</strong> <strong>de</strong> …nancement. <strong>Le</strong>s sociétés<br />
<strong>de</strong> leasing ne sont pas seulement <strong>de</strong>s intermédiaires et leur expertise produit une valeur ajou-<br />
tée dans la démarche <strong>de</strong> leasing. Elles sélectionnent le matériel approprié en fonction <strong>de</strong> sa<br />
capacité à améliorer le ren<strong>de</strong>ment du locataire et prennent en compte divers facteurs tels que<br />
les caractéristiques du matériel, sa durée <strong>de</strong> vie économique, la …scalité, et la valeur résiduelle<br />
(voir infra). <strong>Le</strong>s sociétés <strong>de</strong> leasing ont aussi <strong>de</strong>s compétences en …nance, en risque <strong>de</strong> crédit,<br />
et en négociation pour l’acquisition d’équipement. D’une manière generale, elles facilitent les<br />
échanges entre les fournisseurs d’équipement et les utilisateurs 11 .<br />
Pour les sociétés <strong>de</strong> leasing, le risque <strong>de</strong> perte à la revente à la …n <strong>de</strong> la durée du contrat,<br />
ainsi que la tari…cation, sont fortement impactés par le prix <strong>de</strong> revente estimé <strong>de</strong> l’actif.<br />
Dans cette thèse, nous étudions un dé…crucial pour le bailleur : le risque <strong>de</strong> valeur résiduelle.<br />
<strong>Le</strong>s trois paramètres essentiels d’un contrat <strong>de</strong> leasing sont le prix <strong>de</strong> l’équipement original,<br />
la durée du contrat et la valeur résiduelle. Ils déterminent la compétitivité et, en même temps,<br />
l’exposition à un risque attaché à la valeur <strong>de</strong> l’actif. La valeur résiduelle est la valeur estimée <strong>de</strong><br />
l’actif à la …n du contrat car le bailleur doit estimer la valeur au prix du marché <strong>de</strong> l’équipement<br />
à la …n <strong>de</strong> la pério<strong>de</strong> contractuelle.<br />
Ces trois paramètres dé…nissent l’essentiel du niveau <strong>de</strong> dépréciation (qui peut être compris<br />
comme l’écart entre le prix <strong>de</strong> l’équipement d’origine et la valeur résiduelle) et du montant <strong>de</strong><br />
loyer payé par le locataire pour utiliser l’équipement. La part <strong>de</strong> la dépréciation dans le loyer<br />
(qui, généralement, en constitue la plus gran<strong>de</strong> partie) peut être calculée par le montant total <strong>de</strong><br />
dépréciation divisé par le nombre <strong>de</strong> paiements 12 . De plus, plusieurs éléments sont inclus dans<br />
11 Parmi les nombreuses étu<strong>de</strong>s relatives aux avantages du leasing, nous <strong>de</strong>vons aussi mentionner Kichler et<br />
Haiss (2009), qui expliquent la contribution du leasing à la croissance économique <strong>de</strong>s économies d’Europe<br />
centrale et orientale, ainsi que la thèse <strong>de</strong> Brage et Eckerstom (2009), qui comparent les di¤érents avantages du<br />
leasing en Suè<strong>de</strong> et au Japon.<br />
12 Par exemple, dans un contrat <strong>de</strong> leasing automobile avec un prix d’équipement d’origine <strong>de</strong> 12000 $, une<br />
valeur résiduelle <strong>de</strong> 7200 $ et une pério<strong>de</strong> <strong>de</strong> bail <strong>de</strong> 24 mois, le paiement mensuel <strong>de</strong> l’amortissement (à<br />
l’exclusion <strong>de</strong>s taux d’intérêt et impôts) est <strong>de</strong> 200 $ par mois (<br />
12000 7000<br />
24<br />
).
les paiements e¤ectués par le locataire tout au long du contrat : les intérêts sur l’investissement<br />
du bailleur, les frais <strong>de</strong> service (y compris les coûts d’exploitation, l’assurance, le conseil, les<br />
réparations) et les taxes. La …gure A illustre les mécanismes en jeu dans le calcul <strong>de</strong>s paiements<br />
d’un contrat <strong>de</strong> leasing 13 .<br />
Figure A : La dépréciation dans un contrat <strong>de</strong> leasing<br />
Loyer = (<br />
xvii<br />
Prix d’achat <strong>de</strong> l’equipement - <strong>Valeur</strong> residuelle<br />
) + Taux d’intérêt + Taxes + Frais <strong>de</strong> Services.<br />
nombre total <strong>de</strong> paiements<br />
Quand la valeur résiduelle augmente, l’écart avec le prix initial <strong>de</strong> l’équipement diminue et<br />
le montant du loyer diminue aussi. Une valeur résiduelle élevée permet au locataire <strong>de</strong> payer<br />
un montant plus bas pour utiliser l’équipement. <strong>Le</strong> contrat proposé par le bailleur <strong>de</strong>vient plus<br />
compétitif.<br />
Cependant, ce qui contribue au succès d’une société <strong>de</strong> leasing peut entraîner <strong>de</strong>s di¢ cultés<br />
lorsque les conditions du marché changent. <strong>Le</strong> bailleur prend le risque <strong>de</strong> ne pas être en mesure<br />
13 A <strong>de</strong>s …ns <strong>de</strong> simpli…cation, nous n’avons pas mentionné un quatrième élément : les options <strong>de</strong> …n <strong>de</strong> contrat.<br />
Di¤érentes options peuvent être disponibles pour le locataire : la pério<strong>de</strong> <strong>de</strong> location peut être prolongée, le<br />
contrat peut être renouvelé, les équipements peuvent être rachetés ou rétrocédés.
xviii INTRODUCTION GÉNÉRALE<br />
<strong>de</strong> récupérer su¢ samment <strong>de</strong> capital lors <strong>de</strong> la revente <strong>de</strong> l’actif. Il existe un risque <strong>de</strong> valeur<br />
résiduelle. Comme cela est illustré par la …gure B, la courbe <strong>de</strong> la valeur <strong>de</strong> marché révèle un<br />
gain ou une perte à la revente, en fonction du niveau <strong>de</strong> valeur résiduelle.<br />
Figure B : La valeur marché d’un actif<br />
<strong>Le</strong> bailleur fait ainsi face à un dilemme. Plus la valeur résiduelle est basse, plus le risque<br />
<strong>de</strong> perte à la revente est faible. Mais, en même temps, le loyer augmente et le bailleur perd<br />
sa compétitivité. Inversement, plus le risque <strong>de</strong> valeur résiduelle est élevé et plus le contrat <strong>de</strong><br />
leasing est compétitif.<br />
Nous apportons une perspective académique à la pratique <strong>de</strong> la gestion du risque <strong>de</strong> valeur<br />
résiduelle.<br />
Dans une société <strong>de</strong> leasing, le département <strong>de</strong> gestion d’actifs est en charge du risque<br />
<strong>de</strong> valeur résiduelle et estime les prix <strong>de</strong> revente <strong>de</strong>s équipements en leasing. Au cours <strong>de</strong>s<br />
sept <strong>de</strong>rnières années, j’ai travaillé sur l’analyse <strong>de</strong> la valeur résiduelle au sein <strong>de</strong> General<br />
Electric Capital, une <strong>de</strong>s plus gran<strong>de</strong>s entreprises <strong>de</strong> leasing dans le mon<strong>de</strong> 14 . Grâce à ma<br />
position européenne au sein du groupe, j’ai eu la possibilité <strong>de</strong> rencontrer <strong>de</strong>s analystes <strong>de</strong><br />
14 L’actif total <strong>de</strong> GE Capital Commercial Finance était <strong>de</strong> plus <strong>de</strong> 230 milliards <strong>de</strong> dollars en 2008.
gestion d’actifs à travers di¤érents pays. J’ai aussi eu un aperçu <strong>de</strong>s pratiques aux États-Unis,<br />
en Nouvelle-Zélan<strong>de</strong>, en Australie et au Japon. J’ai vécu une situation qui est partagée par<br />
les professionnels dans <strong>de</strong> nombreux domaines : les équipes <strong>de</strong> gestion d’actifs reproduisent<br />
<strong>de</strong>s métho<strong>de</strong>s et <strong>de</strong>s processus opérationnels, créés par leurs prédécesseurs, en les améliorant<br />
par tâtonnement 15 . Il y a une transmission du savoir-faire par l’application d’un minimum <strong>de</strong><br />
théorie. Plus spéci…quement, peu <strong>de</strong> travaux académiques 16 et très peu <strong>de</strong> modèles statistiques<br />
sont dédiés au risque <strong>de</strong> valeur résiduelle. Par exemple, bien que les volumes …nanciers soient<br />
du même ordre <strong>de</strong> gran<strong>de</strong>ur (Figure C) 17 , le …nancement structuré <strong>de</strong>s CDO (Collateralized<br />
Debt Obligation) a attiré bien plus <strong>de</strong> recherche académique que le leasing.<br />
Figure C : <strong>Le</strong> volume <strong>de</strong> leasing dans le mon<strong>de</strong><br />
Néanmoins, les analystes <strong>de</strong> gestion d’actifs n’ont pas attendu la théorie et les apports aca-<br />
démiques pour estimer la valeur d’un équipement en …n <strong>de</strong> pério<strong>de</strong> contractuelle. Ils doivent en<br />
e¤et proposer un prix pour établir un contrat. Notre objectif général est d’enrichir la littérature<br />
sur le sujet et ainsi d’apporter ‘un peu <strong>de</strong> la théorie à la pratique’ 18 . L’objet <strong>de</strong> toute théorie<br />
15 Par exemple, la situation est semblable dans l’industrie <strong>de</strong>s produits …nanciers dérivés. “Option hedging,<br />
pricing, and trading (. . . ) is a rich craft with tra<strong>de</strong>rs learning from tra<strong>de</strong>rs (or tra<strong>de</strong>rs copying other tra<strong>de</strong>rs)<br />
and tricks <strong>de</strong>veloping un<strong>de</strong>r evolution pressures, in a bottom-up manner.”Haug et Taleb (2009).<br />
16 <strong>Le</strong>s rares contributions sont mentionnées dans le <strong>de</strong>uxième chapitre.<br />
17 Sources : White Clark Global rapport <strong>de</strong> leasing, World <strong>Le</strong>asing Yearbook 2009, SIFMA.<br />
18 <strong>Le</strong> leasing se situe entre la …nance et l’ingénierie. Cela pourrait explique le peu <strong>de</strong> travaux académiques<br />
xix
xx INTRODUCTION GÉNÉRALE<br />
est <strong>de</strong> modéliser un phénomène a…n <strong>de</strong> mieux le comprendre et <strong>de</strong> faciliter son exploitation.<br />
Or le point <strong>de</strong> vue académique ajoute un contrôle théorique sur les outils et les hypothèses<br />
utilisées par les spécialistes. De plus, la position académique fournit une approche libérée <strong>de</strong><br />
tous préjugés créés par l’appartenance aux métiers du leasing.<br />
Une analyse <strong>de</strong> la valeur résiduelle comporte plusieurs éléments parmi lequels : les ca-<br />
ractéristiques techniques <strong>de</strong> l’actif, la composition du portefeuille d’équipement et la courbe<br />
<strong>de</strong> dépréciation. C’est pourquoi nous pouvons béné…cier <strong>de</strong> la littérature déjà en usage dans<br />
d’autres domaines, comme les modèles économétriques <strong>de</strong>s prix hédonique ou la litterature en<br />
macroéconomie.<br />
<strong>Le</strong>s sections empiriques <strong>de</strong> la thèse se concentrent sur les contrats <strong>de</strong> leasing automobile.<br />
L’automobile constitue un vaste marché et permet <strong>de</strong> collecter <strong>de</strong> nombreuses informations sur<br />
le comportement <strong>de</strong> dépréciation <strong>de</strong>s actifs. <strong>Le</strong> niveau élevé <strong>de</strong> la valeur résiduelle <strong>de</strong>s voitures<br />
à la …n du contrat, par comparaison avec d’autres types d’équipements, augmente le risque <strong>de</strong><br />
pertes et constitue un dé… majeur pour les sociétés <strong>de</strong> leasing.<br />
Deux types <strong>de</strong> contrats <strong>de</strong> location d’automobiles peuvent être dé…nis. <strong>Le</strong>s contrats <strong>de</strong><br />
location courte durée concernent les automobiles louées à <strong>de</strong>s clients privés ou professionnels<br />
pour une pério<strong>de</strong> <strong>de</strong> temps relativement courte, a…n <strong>de</strong> répondre à <strong>de</strong>s besoins occasionnels.<br />
En revanche, la location longue durée couvre les contrats pour les entreprises qui externalisent<br />
leurs besoins en ‡otte <strong>de</strong> véhicules à une société <strong>de</strong> leasing. En plus <strong>de</strong>s véhicules nécessaires, la<br />
société <strong>de</strong> leasing fournit généralement <strong>de</strong>s services connexes, comme la maintenance, la gestion<br />
du carburant et l’assurance. La thèse se concentre principalement sur la location longue durée.<br />
La thèse s’organise en trois chapitres. Dans le premier chapitre, nous étudions la valorisation<br />
et le comportement <strong>de</strong> dépréciation d’un actif : l’automobile. Dans le <strong>de</strong>uxieme chapitre, nous<br />
proposons une nouvelle façon <strong>de</strong> couvrir le risque <strong>de</strong> valeur résiduelle. Dans le troisième chapitre,<br />
nous étudions la relation entre les marchés du neuf et <strong>de</strong> l’occasion.<br />
Dans le premier chapitre, nous appliquons la métho<strong>de</strong> <strong>de</strong>s prix hédoniques à un por-<br />
tefeuille européen <strong>de</strong> leasing, a…n d’estimer la distribution <strong>de</strong>s prix <strong>de</strong> revente d’automobiles.<br />
sr le sujet. En e¤et, le …nancement d’équipements nécessite di¤érents domaines d’expertise : la …nance et une<br />
connaissance du secteur industriel où les agents opèrent.
L’approche hédonique estime le prix d’un bien par la valorisation <strong>de</strong> ses attributs. Suite à une<br />
discussion sur les prix hédoniques, nous proposons un modèle opérationnel pour le marché <strong>de</strong><br />
l’automobile d’occasion. <strong>Le</strong> modèle est appliqué à quatre pays européens (l’Allemagne, l’Es-<br />
pagne, la France et la Gran<strong>de</strong>-Bretagne), et les distributions sont calculées sur <strong>de</strong>ux modèles<br />
<strong>de</strong> véhicules (Audi A4 et Ford Focus) permettant la comparaison <strong>de</strong>s pro…ls <strong>de</strong> dépréciation et<br />
<strong>de</strong>s risques <strong>de</strong> valeur résiduelle.<br />
<strong>Le</strong> <strong>de</strong>uxième chapitre propose un modèle statistique pour couvrir le risque <strong>de</strong> valeur<br />
résiduelle en utilisant la technique <strong>de</strong>s copules gaussiens. A la suite d’une discussion sur la<br />
problématique du risque <strong>de</strong> valeur résiduelle et <strong>de</strong>s modèles <strong>de</strong> risque <strong>de</strong> crédit existant, un<br />
nouveau produit dérivé est proposé et analysé : le Collateralized Residual Values (CRV). <strong>Le</strong><br />
modèle est appliqué à un portefeuille européen <strong>de</strong> location longue durée d’automobiles. Nos<br />
résultats indiquent que ce produit …nancier est facile à adapter et à mettre en œuvre en fonction<br />
<strong>de</strong>s caractéristiques du contrat et du niveau <strong>de</strong> corrélation. <strong>Le</strong> <strong>de</strong>uxième chapitre s’adresse<br />
aux professionnels du leasing intéressés par un nouvel outil …nancier, ainsi qu’aux acteurs <strong>de</strong>s<br />
marchés …nanciers concernés par <strong>de</strong> nouvelles opportunités d’investissement autour du risque<br />
<strong>de</strong> valeur résiduelle.<br />
<strong>Le</strong>s équipes <strong>de</strong> gestion d’actifs doivent prendre en considération les facteurs macroécono-<br />
miques pouvant in‡uencer les prix <strong>de</strong> revente <strong>de</strong>s actifs. <strong>Le</strong> <strong>de</strong>rnier chapitre analyse un<br />
élément crucial <strong>de</strong> cette question. <strong>Le</strong>s voitures neuves d’aujourd’hui seront les voitures d’occa-<br />
sion <strong>de</strong> <strong>de</strong>main, et l’on suppose une forme <strong>de</strong> compétition entre le marché du neuf et le marché<br />
<strong>de</strong> l’occasion. C’est pourquoi il existe quelques idées préconçues et <strong>de</strong> nombreuses théories sur<br />
les interactions entre le premier marché et le second marché. Nous proposons <strong>de</strong> développer la<br />
ré‡exion par une analyse macro-économique <strong>de</strong>s marchés automobiles Français, Britanniques<br />
et Nord-Américains. <strong>Le</strong>s di¤érents concepts sont répertoriés et statistiquement contrôlés a…n<br />
<strong>de</strong> répondre à <strong>de</strong>ux questions : Quelles sont les interactions entre les automobiles neuves et<br />
d’occasion ? Pouvons-nous utiliser ces interactions a…n d’estimer le prix <strong>de</strong> revente <strong>de</strong>s véhi-<br />
cules ? Nos résultats indiquent que les relations entre les di¤érents marchés semblent limitées<br />
en France et au Royaume-Uni, alors que le marché Nord-Américain est confronté à un méca-<br />
nisme dit <strong>de</strong> ‘Scitovscky’. Dans tous les cas, les relations ne sont pas assez fortes pour expliquer<br />
complètement les comportements <strong>de</strong>s marchés.<br />
xxi
xxii INTRODUCTION GÉNÉRALE
General Introduction<br />
"(. . . ) the real principle of the irreplaceable empirical research creativity : doing,<br />
without knowing exactly what we are doing, gives the opportunity to discover, in<br />
what we do, something we did not know."<br />
P. Bourdieu, Homo Aca<strong>de</strong>micus, <strong>Le</strong>s Editions <strong>de</strong> Minuit, 1984, p17.<br />
The leasing industry appears as a little known area and a great business.<br />
The International Accounting Standard for <strong>Le</strong>ases, or IAS17 19 , <strong>de</strong>…nes a lease as "an agree-<br />
ment whereby the lessor conveys to the lessee, in return for a payment or series of payments,<br />
the right to use an asset for an agreed period of time". <strong>Le</strong>gislation may be di¤erent across<br />
countries, contracts can be adjusted to meet the needs of a customer, and any sort of good can,<br />
in theory, be leased ; therefore, the term ‘lease’inclu<strong>de</strong>s a large variety of contracts.<br />
On the whole, a lease is a …nancial instrument for the procurement of an equipment. In a<br />
leasing contract, a lessor provi<strong>de</strong>s equipment for usage on a <strong>de</strong>…ned period of time to a lessee<br />
for speci…ed payments. The asset leased could be any kind of equipment (i.e. printers, trucks,<br />
aircrafts. . . ) used by the lessee for business purposes. The lessor purchases the equipment and<br />
has the legal ownership of the asset. To use the equipment the lessee makes periodic payments<br />
throughout the contract to the lessor.<br />
The entire Global leasing market 20 was estimated to be more than $ 633 billion in 2006.<br />
Europe and North America accounted for 41% and 38% of the world market. The ‘World<br />
19 All listed companies in the European Union are obliged to adopt the International Standards. The equivalent<br />
standard in the USA is FAS 13.<br />
20 White Clarke Global <strong>Le</strong>asing report (2008).<br />
xxiii
xxiv GENERAL INTRODUCTION<br />
<strong>Le</strong>asing Yearbook 2009’reported a total global amount of equipment leased to be more than<br />
$ 760 billion for 2007. The European leasing associations reported a new leasing volume above<br />
e 330 billion and a contribution to …nancing, on average, of 18% of total European investment<br />
for 2008. Furthermore, leasing involved more than 16 million cars in Europe 21 .<br />
Broadly speaking, almost all aca<strong>de</strong>mic contributions on the leasing subject are related to<br />
the comparison of leasing over lending and purchasing. Researches can be divi<strong>de</strong>d into three<br />
groups.<br />
Firstly, some papers analyze tax advantages regarding the choice between leasing and regular<br />
<strong>de</strong>bt 22 . The second group of aca<strong>de</strong>mic articles discusses the ‘<strong>Le</strong>asing Puzzle’. Theories in Finance<br />
and Economics suggest that leases and <strong>de</strong>bt are substitutes ; an increase of leasing should lead to<br />
a <strong>de</strong>crease of <strong>de</strong>bt ; moreover, standard …nance theories manage cash ‡ows from lease obligations<br />
as an equivalent to cash <strong>de</strong>bt ‡ows. Ang and Peterson (1984) found empirically that lease and<br />
<strong>de</strong>bt appear as complements for companies. They argued that greater leasing is associated<br />
with greater <strong>de</strong>bt. They could not …nd a conclusive explanation and they called their …nding<br />
the unsolved puzzle in Finance or the “<strong>Le</strong>asing Puzzle”. Following their seminal article, the<br />
aca<strong>de</strong>mic contributions have been numerous to reinvestigate the results 23 .<br />
The ‘Puzzle’leads to the third area of research covering every article related to the incen-<br />
tives and advantages of leasing. Lasfer and <strong>Le</strong>vis (1998), for instance, rephrased the problem.<br />
In theory, leasing provi<strong>de</strong>s no ad<strong>de</strong>d value to the purchase of equipment when a lessee or a<br />
purchasing …rm, lend or borrow at the same rate of interest, have a similar tax status and<br />
expect the same resale price of the asset at the end of the contract. In practice, however, these<br />
conditions are not satis…ed and there are several motives for leasing 24 . For large …rms, their<br />
study reveals that …nancial managers use leasing as an instrument to minimize the after tax<br />
21 <strong>Le</strong>aseurope Association Website.<br />
22 See Smith and Wakeman (1985), Brick, Fung and Subrahmanyam (1987), Mackie-Mason (1990), Goodacre<br />
(2002).<br />
23 See Marston and Harris (1988), <strong>Le</strong>wis and Schallheim (1992), Krishnan and Moyer (1994), Branson (1995),<br />
Beattie, Goodacre and Thomson (1999), Yan (2006).<br />
24 They listed three main motives for leasing : First, leasing can reduce …nancial taxes. Second, it could be<br />
advantageous …nancially for distressed companies to get an agreement and access to the equipment because<br />
lessors have …rst claims over the asset. Finally, leasing can reduce the agency cost because it does not constitute<br />
an investment for the lessee.
cost of capital. For small companies, leasing appears as an opportunity for growth or survival.<br />
They have di¢ culties to access the <strong>de</strong>bt market and leasing facilitates the …nancing of …xed<br />
capital formation. In other words, small companies with potential important growth rates or<br />
low pro…ts are more likely to lease. As a consequence, without leasing many projects would not<br />
have been un<strong>de</strong>rtaken.<br />
Drakos and Goulas (2008) mention the uncertainty in entrepreneurship exacerbated by the<br />
irreversibility of capital. By allowing the separation of usage to the commitment of equipment<br />
ownership 25 , leasing facilitates a possible disengagement in unsuccessful projects. Schmitt and<br />
Stuyck (2002) 26 , Schmitt (2003) 27 and Schmitt (2004) <strong>de</strong>monstrate that leasing is a relatively<br />
low risk activity and that Basel 2 requirement should be reduced for leasing contracts. All in<br />
all, leasing appears as a safe …nancial instrument ; furthermore, leasing can reduce environ-<br />
mental problems 28 . The practice of leasing products, rather than selling them, prevents waste<br />
generation and creates a pattern of closed loop material use. For speci…c equipment and leasing<br />
contracts, manufacturers become more aware of operating problems and cost management for<br />
products at life end. Consequently, they may re<strong>de</strong>sign their products accordingly. Staying in<br />
a commercial channel, the equipment is less likely to be stored or discar<strong>de</strong>d when it becomes<br />
obsolete.<br />
Besi<strong>de</strong>s the lack of elements on the subject, we should also highlight that leasing companies’<br />
interventions create additional attractiveness. <strong>Le</strong>asing companies are not only intermediaries ;<br />
their expertise produces a real ad<strong>de</strong>d value in the leasing process. They select the appropriate<br />
equipment based on its ability to improve the leasing cash ‡ow through various parameters<br />
like equipment characteristics, economic life of the asset, taxes or residual value risk. <strong>Le</strong>asing<br />
companies have also skills in …nance, credit, equipment acquisition and <strong>de</strong>aling. All things<br />
consi<strong>de</strong>red, they facilitate the transactions between equipment suppliers and equipment users 29 .<br />
25 Capital heterogeneity would explain di¤erent choices of leasing by di¤erent <strong>de</strong>grees of irreversibility.<br />
26 Schmitt and Stuyck (2002) analyzed <strong>de</strong>faulting leasing contracts issued from 1976 to 2000 in 6 countries and<br />
originated from 12 major European companies and found that the recovery rate of <strong>de</strong>faulting leasing contracts<br />
are comparable to senior secured bonds.<br />
27 The estimation of the probability <strong>de</strong>nsity function of losses and the standard portfolio credit value at risk<br />
(VAR) measures in the leasing industry reveals a relatively low risk activity. See also Pirotte and Vaessen (2008).<br />
28 See Fishbein, McGarry and Dillon (2000).<br />
29 Among the numerous contributions related to the advantages of leasing, we could also mention Kichler and<br />
Haiss (2009), showing the support of leasing in economic growth of central and Eastern Europe, as well as the<br />
xxv
xxvi GENERAL INTRODUCTION<br />
For <strong>Le</strong>asing companies, the risk of loss on sales at the end of the contract term, as well as<br />
the pricing, are critically impacted by the forecasted resale price of the asset.<br />
In the thesis, we study a crucial challenge for the lessor : the residual value risk.<br />
The three key parameters of a leasing contract are the original equipment price, the lease<br />
period and the residual value. They drive the competitiveness and, at the same time, a risk<br />
on the asset. The lessor has to set the end of contract market value of the equipment and the<br />
residual value is a forecasted value of the asset. The three parameters mainly <strong>de</strong>…ne the level of<br />
<strong>de</strong>preciation (which can be seen as the variance between the original equipment price and the<br />
residual value all along the lease period) and the rental amount paid by the lessee to use the<br />
equipment. The <strong>de</strong>preciation part of the lease payment (usually the larger component) can be<br />
calculated by the total amount of <strong>de</strong>preciation divi<strong>de</strong>d by the number of periods 30 . Additionally,<br />
several features are inclu<strong>de</strong>d in the payments ma<strong>de</strong> by the lessee during the contract ; <strong>de</strong>pre-<br />
ciation of the asset interests on the lessor investment, servicing charges (including operational<br />
costs, insurance, counseling, repairs) and taxes. Figure A illustrates the mechanism involved in<br />
the calculation of the lease payments 31 .<br />
thesis of Brage and Eckerstom (2009), comparing the incentives to lease in Swe<strong>de</strong>n and Japan.<br />
30 For instance, in an automotive lease contract with an original equipment price of $ 12000, a residual value<br />
of $ 7200 and a lease period equal to 24 months, the monthly payment of the <strong>de</strong>preciation (excluding interest<br />
12000 7000<br />
rate and taxes) should be $ 200 per month ( 24 ).<br />
31For simpli…cation purpose, we did not mention another key element : the end of term options. At the end<br />
of the contract, there are options allowed to the lessee. <strong>Le</strong>ase period can be exten<strong>de</strong>d ; lease can be renewed ;<br />
the equipment can be bought or returned.
Figure A : Depreciation in a leasing contract<br />
<strong>Le</strong>aseRental = (<br />
xxvii<br />
Original Equipment Price - Residual Value<br />
) + interestrates + taxes + servicing charges.<br />
<strong>Le</strong>ase Period<br />
As a result, when the residual value increases, the variance with the original equipment<br />
cost <strong>de</strong>creases, as well as the rental amount. A high residual value creates, for the lessee, an<br />
opportunity to pay a lower amount for the usage of the equipment and therefore, for the lessor,<br />
better competitiveness.<br />
What makes the success of a leasing company can lead to di¢ culties when market conditions<br />
change. The lessor faces the risk to not being able to recover su¢ cient capital value from the<br />
resale of the asset, the residual value risk. As illustrated by Figure B, the fair market value<br />
curve implies a gain on sale, or a loss on sale, <strong>de</strong>pending on the level of residual value.
xxviii GENERAL INTRODUCTION<br />
Figure B : Fair Market Value of an Asset<br />
So the lessor faces a dilemma ; the lower the residual value, the lesser the risk of loss on<br />
sale, but the lower the residual value, the higher the rental payment and the worse the compe-<br />
titiveness. Conversely the higher the residual value risk, the better the competitiveness.<br />
We bring an aca<strong>de</strong>mic perspective to the practice of residual value risk management.<br />
In a leasing company, the Asset Management <strong>de</strong>partment is in charge of the residual value<br />
risk and forecasts how much the equipment will be worth at the end of the contract. For the last<br />
seven years, I have been working in General Electric Capital Finance, one of the biggest leasing<br />
companies in the world 32 , on residual value analysis. Thanks to my European position, I meet<br />
asset analysts across various countries and I have had some insight from the US, New Zealand,<br />
Australia and Japan. I experienced a common situation for professionals in various areas : asset<br />
teams reproduce operational processes, created by pre<strong>de</strong>cessors, and improved through trial<br />
and error 33 . There is a transmission of know-how, by applying minimum theory. As a matter of<br />
32 Commercial Finance’s assets total was over $230 billion in 2008.<br />
33 For instance the situation is similar in the …nancial <strong>de</strong>rivatives industry. “Option hedging, pricing, and<br />
trading (. . . ) is a rich craft with tra<strong>de</strong>rs learning from tra<strong>de</strong>rs (or tra<strong>de</strong>rs copying other tra<strong>de</strong>rs) and tricks<br />
<strong>de</strong>veloping un<strong>de</strong>r evolution pressures, in a bottom-up manner.”Haug and Taleb (2009).
fact, few aca<strong>de</strong>mic literature 34 and few <strong>de</strong>veloped mo<strong>de</strong>ls are <strong>de</strong>dicated to residual value risk.<br />
For instance, although the volumes involved are similar (Figure C) 35 , structured …nance and<br />
its vast growth attracted much more aca<strong>de</strong>mic research than leasing.<br />
Figure C : Volume of equipment leased in the world<br />
xxix<br />
Nevertheless, asset analysts did not wait for theory and aca<strong>de</strong>mics to estimate residual<br />
values. They have to propose a price in or<strong>de</strong>r to set a contract. Analysts are in a position of<br />
practice with limited theory 36 . As a general purpose, we aim to contribute to the rare literature<br />
in the area, and accordingly to bring theory to the practice. The aim of any theory is to mo<strong>de</strong>l<br />
phenomena so that we can better un<strong>de</strong>rstand and exploit them. The aca<strong>de</strong>mic view adds a<br />
theoretical control on tools and assumptions used by the specialists. Furthermore, it provi<strong>de</strong>s<br />
an overview free of bias created by the inner position of the asset analyst.<br />
A residual value analysis involves several elements including the characteristics of the equip-<br />
ment, the mix of the portfolio, and the <strong>de</strong>preciation curve. Consequently, we can bene…t from<br />
diverse kinds of literature already in use in others area, like hedonic or macroeconomic mo<strong>de</strong>ls.<br />
34 The rare contributions are listed in the second chapter.<br />
35 Sources : White Clark Global rapport <strong>de</strong> leasing, World <strong>Le</strong>asing Yearbook 2009, SIFMA.<br />
36 An explanation of the few aca<strong>de</strong>mic studies could be that the leasing business is in the middle of …nance<br />
and engineering. Equipment …nancing involves di¤erent areas of expertise : …nance and the industrial sectors<br />
where it operates.
xxx GENERAL INTRODUCTION<br />
The empirical parts of the thesis focus on automotive leasing contracts. By and large, auto-<br />
motive constitutes a huge market providing numerous information. The high level of residual<br />
value of cars at the end of the contract, by comparison with other types of equipment, increases<br />
the probability of losses and represents a critical challenge for leasing companies.<br />
Two kinds of auto lease contracts can be <strong>de</strong>…ned : short-term auto lease contracts inclu<strong>de</strong><br />
cars (or trucks) rented to private or professional clients for a relatively short period of time<br />
in or<strong>de</strong>r to meet their occasional transport needs ; in contrast, long-term auto lease covers<br />
contracts for businesses outsourcing their vehicle ‡eet needs to a leasing company. In addition<br />
to the necessary cars (or trucks) the leasing company usually provi<strong>de</strong>s various related services,<br />
like maintenance, fuel management, and insurance. The thesis primarily focuses on long-term<br />
auto leasing.<br />
The thesis is divi<strong>de</strong>d into three chapters. In the …rst chapter, we discuss the valuation and<br />
the <strong>de</strong>preciation of an asset : a car. In the second chapter, we propose a new way to hedge<br />
residual value risk. In the third chapter, we study the relation between the new and the used<br />
markets.<br />
In the …rst chapter, we apply the Hedonic methodology to European auto lease portfolios,<br />
in or<strong>de</strong>r to estimate the resale price distribution. The Hedonic approach estimates the price<br />
of a good through the valuation of its attributes. Following a discussion on Hedonic prices,<br />
we propose an operational mo<strong>de</strong>l for the automobile resale market. The mo<strong>de</strong>l is applied to<br />
four European countries (France, Germany, Spain and Great Britain), and distributions are<br />
calculated on two vehicle versions (Audi A4 and Ford Focus) allowing a comparison of market<br />
<strong>de</strong>preciation patterns and residual value risks.<br />
The second chapter proposes a mo<strong>de</strong>l to hedge residual value risk using the Gaussian<br />
copula methodology. After discussing residual value risk and credit risk mo<strong>de</strong>ls, a new <strong>de</strong>rivative<br />
product is introduced and analyzed ; the Collateralized Residual Value (CRV). The mo<strong>de</strong>l<br />
is applied to a European auto lease portfolio of Operating <strong>Le</strong>ase contracts pertaining to a<br />
major company. Our results indicate that the …nancial product is easy to customize, and to<br />
implement through the contract characteristics and the level of correlation between the assets<br />
of the portfolio. The second chapter is inten<strong>de</strong>d for people within the leasing industry interested<br />
by an innovative …nancial product, as well as people from the …nancial market concerned by
leasing risk opportunities.<br />
xxxi<br />
Asset Management teams have to take into consi<strong>de</strong>ration macroeconomic factors impacting<br />
the asset resale prices in the used market. The last chapter analyzes a crucial element of<br />
the problem. The new cars of today are used cars of tomorrow and a competition is assumed<br />
between new and used markets. There are numerous, pre-conceived i<strong>de</strong>as and aca<strong>de</strong>mic theories<br />
regarding the interactions between primary and secondary markets. We propose to go further<br />
through a macroeconomic analysis of the French, the British and the US car markets. The<br />
di¤erent concepts are listed and statistically evaluated. What are the interactions between the<br />
new and the second-hand car markets ? Can we use the interactions to estimate the car prices<br />
of tomorrow ? Our results indicate that the relations appear limited for France and the UK,<br />
whereas the US market faces a Scitovscky mechanism. Furthermore, they illustrate that the<br />
interrelations are not strong enough to fully explain and forecast market patterns.
xxxii GENERAL INTRODUCTION
Chapitre 1<br />
The European used-car market at a<br />
glance<br />
Hedonic resale price valuation in automotive leasing industry 1<br />
1 This chapter has been published in Economics Bulletin : Prado Sylvain M. (2009) The European used-car<br />
market at a glance : Hedonic resale price valuation in automotive leasing industry. Economics Bulletin, Vol. 29<br />
No.3 pp. 2086-2099.<br />
1
2 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
1.1 Introduction<br />
In the auto lease industry, a large part of the rent paid by the customer during a life contract<br />
is the di¤erence between the list price and the residual value. The leasing company makes or<br />
losses money <strong>de</strong>pending on whether it accurately predicts the value of the asset at the end of<br />
the contract (fair market value). If residual values are forecasted to be higher than what the<br />
asset is actually worth at lease-end, then there will be a loss. At the opposite, if residual values<br />
are forecasted to be lower, then there will be a gain on resale. The estimated resale price of<br />
the car at the end of the contract term appears as a key component for the pricing, the risk of<br />
losses and the reserve calculation 2 .<br />
Akerlof (1970) explained why used car valuation is so much lower than new car valuation.<br />
The automotive resale market is a¤ected by something called the ’lemon e¤ect’. A used car has<br />
the probability to be of a good quality or a bad one (i.e. lemon), and the uncertainty about<br />
quality implies a price adjustment 3 . The Akerlof theory helps to un<strong>de</strong>rstand the large variance<br />
of prices between new and used markets, but it does not propose a methodology to calculate<br />
car <strong>de</strong>preciation.<br />
Another way of looking at it is the Hedonic approach. The Hedonic theory provi<strong>de</strong>s solu-<br />
tions and estimates price-quality relation through a <strong>de</strong>tailed calculation. A Hedonic mo<strong>de</strong>l has<br />
been originally proposed by Waugh (1928) on vegetable products and by Court (1939) in the<br />
automobile industry. Hedonic mo<strong>de</strong>ls have been applied to a lot of commodities (mainly real<br />
estate and automobile but also fruits or vine 4 ). The automobile market itself has had di¤erent<br />
applications (quality corrected price in<strong>de</strong>x 5 , <strong>de</strong>mand for fuel e¢ ciency, valuation of environmen-<br />
2 This article is part of a general study on resale market hedging (Prado, 2008). We aim to estimate the<br />
distribution of the resale price in or<strong>de</strong>r to inclu<strong>de</strong> the <strong>de</strong>preciation behavior in a <strong>de</strong>rivative product.<br />
3 In the resale market, there is an asymetry of information ; the car owner has a better knowleg<strong>de</strong> of the<br />
probability of bad lemons. If Second hand vehicles were valued like as new vehicles, then it would attract lemons<br />
(lemons’sellers would have the opportunity to sale their vehicles and buy a new one on the new vehicle market)<br />
and it would create an arbitraging opportunity. Akerlof used the automotive market as a best illustration and<br />
exten<strong>de</strong>d his i<strong>de</strong>a to other markets (the cost of <strong>de</strong>shonesty...).<br />
4 Combris, <strong>Le</strong>coq and Visser (1997).<br />
5 Cowling and Cubbin (1972) and Van Dalen and Bo<strong>de</strong> (2004).
1.1. INTRODUCTION 3<br />
tal and safety <strong>de</strong>mand 6 , test of the Akerlof e¤ect 7 , behavior of the automobile market through<br />
price quality and competition 8 ...). The main point un<strong>de</strong>rlying this paper is to apply the Hedo-<br />
nic methodology to estimate the resale price distribution of cars in a leasing perspective. The<br />
…rst chapter is inten<strong>de</strong>d for people within the leasing industry intersted by residual value risk<br />
management, as well as aca<strong>de</strong>mics concerned by a comparison of European markets.<br />
We propose a methodology for operational applications to estimate the distribution of resale<br />
price. To this end, we apply a Hedonic mo<strong>de</strong>l (a method of estimating value through constituent<br />
characteristics of the asset) on historical information from a major leasing company 9 . Further<br />
to this, we estimate a value according to vehicle characteristics and country singularities. Resale<br />
price distributions of two vehicles (Ford focus C-max, Audi A4) are calculated in various Euro-<br />
pean markets (France, Germany, Spain and Great Britain). The chapter is organized as follows.<br />
Section 2 discusses the Hedonic theory un<strong>de</strong>rlying our mo<strong>de</strong>l. In section 3 some meaningful<br />
characteristics of the mo<strong>de</strong>l are exposed. Section 4 presents our approach. Section 5 estimates<br />
the distributions and analyzes the results, …nally. Section 6 conclu<strong>de</strong>s.<br />
6 Atkinson and Halvorsen (1990).<br />
7 Couton, Gar<strong>de</strong>s, and Thepaut (1995).<br />
8 Cowling and Cubbin (1971) and Cubbin (1975).<br />
9 In Europe, statistics on resale prices are not as abundant as in …nancial markets and leasing companies<br />
often have to use internal data to forecast the market value. External information is usually not available on<br />
line, costly and time consuming to collect. Morevover, there is a non homogeneous information and format by<br />
country. Therefore we use the internal resale information (GE resale data warehouse).
4 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
1.2 The Hedonic theory un<strong>de</strong>rlies our mo<strong>de</strong>l<br />
The section discusses the Hedonic mo<strong>de</strong>l approach, i<strong>de</strong>nti…cation issues and automotive<br />
assets speci…cities.<br />
1.2.1 Goods attributes constitute the Hedonic theory.<br />
To explain consumer behavior, Lancaster (1966) assumes that consumers get utility from<br />
goods attributes 10 . Assuming that a car is the only good involved in the activity consumption<br />
of driving, it produces a …xed vector of attributes and the level of activity is a scalar associated<br />
with the vector (the relationship could be linear). The driver chooses a combination to maximize<br />
his utility function according to the characteristics of the goods un<strong>de</strong>r a constraint budget.<br />
Inspired by Lancaster (1966), Pickering et al(1973) ad<strong>de</strong>d an empirical perspective to the<br />
approach by conducting a survey in the UK. Following their results, they <strong>de</strong>…ned …ve groups of<br />
commodities (utilities, luxuries, leisure goods, central heating and automotive) and i<strong>de</strong>nti…ed<br />
eleven characteristics as signi…cant discriminators between groups. The principal attributes<br />
<strong>de</strong>sired by car buyers were comfort, durability, economical, manoeuvrability, performance safety<br />
and style. They acknowledged that products and attributes may change groups through time<br />
because of product life cycle, di¤erent tastes between consumers, the growth of the market<br />
penetration (i.e. luxuries becoming utilities), complementarity or substitutability of goods 11 .<br />
They also …gured out that it could be relevant sometime to disaggregate a group (i.e. cars by<br />
makes).<br />
The Hedonic mo<strong>de</strong>l assumes that goods are valued for their utility-bearing attributes or<br />
characteristics. In 1974, Rosen 12 <strong>de</strong>veloped the framework of Hedonic mo<strong>de</strong>ls. The theory <strong>de</strong>s-<br />
cribes cars by n measurable characteristics (oil consumption, car size, power, technology...) and<br />
a vector Z(= z1; z2; :::; zn) with zi measuring the amount of the i th characteristics. The exis-<br />
10 Similar attributes or characteristics could be shared by di¤erent goods. Usually goods have several charac-<br />
teristics, and a combination of goods may have attributes di¤erent to goods used separately.<br />
11 We could also add the technology obsolescence to the list.<br />
12 See Appendix A1.
1.2. THE HEDONIC THEORY UNDERLIES OUR MODEL 5<br />
tence of product di¤erentiation implies that a wi<strong>de</strong> variety of alternative packages, completely<br />
<strong>de</strong>scribed by numerical value of z, are available. Buyers and sellers locate in a spatial equili-<br />
brium. On one si<strong>de</strong>, the consumption <strong>de</strong>cision is ma<strong>de</strong> by a maximization of utility. On the<br />
other si<strong>de</strong>, the production <strong>de</strong>cision is ma<strong>de</strong> by minimizing factor costs subject to a joint pro-<br />
duction function constraint relating to the number of units and factors of production. A price<br />
p(z) = p(z1; z2; :::; zn) is <strong>de</strong>…ned at each point on the plane. Both consumers and producers<br />
are gui<strong>de</strong>d by prices through packages of characteristics bought and sold. Observations of p(z)<br />
represent a joint envelope of a family of value functions and another family of o¤er functions.<br />
At equilibrium, buyer and seller are perfectly matched when their <strong>de</strong>mand and o¤er functions<br />
meet at eye level.<br />
The approach consists in estimating the following mo<strong>de</strong>l :<br />
P i(z) = F i(zi; :::; zn; y 1) (<strong>de</strong>mand)<br />
P i(z) = Gi(zi; :::; zn; y 2) (supply)<br />
P i(z) is the implicit market price for attribute zi, y1 and y2 are vector of exogenous <strong>de</strong>mand<br />
shift variables and a vector of exogenous supply shift variables, respectively. At equilibrium,<br />
market quantity <strong>de</strong>man<strong>de</strong>d for products with characteristics z, (Q d (zi)) is equal to market<br />
quantity supplied with those attributes (Q s (zi)). A P (z) function has to be found to make this<br />
equality possible. Unfortunately, di¤erential equations for setting (Q d (zi)) = (Q s (zi)) are not<br />
linear in most cases and closed solution are not always possible.<br />
1.2.2 An i<strong>de</strong>nti…cation problem appears in Hedonic mo<strong>de</strong>ls.<br />
There are i<strong>de</strong>nti…cation problems in the Rosen mo<strong>de</strong>l : if p(z) is non linear, it may not be<br />
possible to …nd closed solutions. A lot of conditions must be imposed and partial di¤erential<br />
equations must be solved when there is more than one characteristic. Rosen believed that the<br />
form of the Hedonic function is an empirical matter and <strong>de</strong>veloped an empirical methodology to<br />
estimate <strong>de</strong>mand and supply parameters (if no explicit solution for the Hedonic price function<br />
is available). Rosen solved the "gar<strong>de</strong>n variety i<strong>de</strong>nti…cation problem" by simultaneous i<strong>de</strong>nti-
6 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
…cation methods like 2SLS : p(z) is estimated by regressing all observed di¤erentiated product<br />
prices p on all their characteristics, z, using the best adaptable function. The estimated prices<br />
are then inclu<strong>de</strong>d in the complete formula as endogenous variables. Later, Brown and Rosen<br />
(1982) showed that this technique is not always possible (it still requires prior restriction on<br />
functional form) 13 .<br />
But Bartik (1987) argued that the econometric problem of estimating Hedonic <strong>de</strong>mand<br />
parameters is not a standard i<strong>de</strong>nti…cation problem caused by <strong>de</strong>mand-supply interactions :<br />
because a consumer <strong>de</strong>cision cannot a¤ect an Hedonic function, it does not a¤ect the supplier.<br />
He pointed out another i<strong>de</strong>nti…cation problem : the Hedonic price function is not linear and the<br />
consumer can endogenously choose both quantities and marginal prices. Formulated through a<br />
characteristic bid equation 14 it highlights the impact of consumer traits.<br />
<strong>Le</strong>t @p<br />
@zj (Zi) be the estimated Hedonic marginal price of characteristics zj = Wij, where Zi<br />
<strong>de</strong>notes a vector of observed characteristics of the product and Wij a consumer marginal bid<br />
for zj :<br />
@p<br />
@zj (Zi) = b0 + b1Zi +b2Xi +bD0i +eij.<br />
Xi is consumer expenditure on commodities others than Z. D 0i is a vector of observed<br />
<strong>de</strong>man<strong>de</strong>r traits a¤ecting the marginal bid. eij is a disturbance term.<br />
It becomes @p<br />
@zj (Zi) = b0 + b1Zi +b2Xi +bD0i + Dui +rij.<br />
Dui is an unobserved taste component form. rij is a random component and rij + Dui = eij.<br />
Therefore Zi and Xi are correlated with unobserved tastes in the residual, leading to biased<br />
results (equivalent to di¤erent population of consumers).<br />
In Bartik’s article, the i<strong>de</strong>nti…cation problem is caused by the endogeneity of both prices<br />
and quantities when households face a nonlinear budget constraint (the distribution of income<br />
13 Ekeland, Heckman and Nesheim (2004) reconsi<strong>de</strong>red the i<strong>de</strong>nti…cation and estimation of the hedonic<br />
mo<strong>de</strong>l. They show that most of empirical studies are based on arbitrary linearisation. Two<br />
new estimations procedures are proposed : a non parametric transformation method and instrumental<br />
variables in a general nonlinear setting.<br />
14 See Appendix A1.
1.2. THE HEDONIC THEORY UNDERLIES OUR MODEL 7<br />
follows no simple law through its range making it di¢ cult to specify the problem entirely). An<br />
instrumental variable solution is suggested and applied (household example with addition of<br />
budget constraint). The implicit market price is estimated by regressing all observed di¤eren-<br />
tiated product prices p on all their characteristics by group of modality of Dui 15 . We follow on<br />
the Bartik critic in our analysis and propose a solution to manage the unobserved taste issue<br />
in Section 3.<br />
1.2.3 Used cars are durable commodities.<br />
Berndt (1983) provi<strong>de</strong>d general frameworks on Hedonic prices for durable goods. Assuming<br />
that the asset price of the n th capital good of vintage at time t is equal to the present value<br />
of its future services, we have :<br />
qn;t; = s=TnP<br />
s=0<br />
1<br />
1+r<br />
s Vn;t+s; +s<br />
where Tn is the life time of the asset, r the interest rate, Vn;t; the value of the asset at<br />
time of the ‡ow of services of the n th capital good of vintage . Berndt <strong>de</strong>monstrated that the<br />
Hedonic price equation can be expressed in terms of service prices in a single equation 16 .<br />
This concept has been used originally in the second-hand automobile market analysis by<br />
Akerman (1973), who produced one of the …rst study on the rapid used car falling prices. The<br />
price of an automobile is evaluated as the discounted present value of its remaining services. The<br />
Akerman mo<strong>de</strong>l inclu<strong>de</strong>d a Hedonic price, a repair cost, a service function and an expected gain<br />
on resale estimation. Akerman used a single equation and a regression to estimate the Hedonic<br />
price 17 . Ho¤er and Pratt (1990), inspired by Akerman approach (the price of a resold vehicle<br />
as an implicit rental cost of holding a s year old automobile, including also automotive price<br />
less market price of interest) proposed a simpler mo<strong>de</strong>l. A single equation, where <strong>de</strong>preciation<br />
<strong>de</strong>clines with age at constant exponential rate, inclu<strong>de</strong>s technological obsolescence, di¤erential<br />
repair record and fuel e¢ ciency as shift variables. The <strong>de</strong>preciated value (s; t) of an s-year old<br />
machine in year t is<br />
15 Bartick ma<strong>de</strong> an adjustment by group of cities.<br />
16 See Appendix A2.<br />
17 See Appendix A3.
8 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
ln( (s; t)) = A b1 s + b2 tech + b3 maint + b4 EP A:<br />
tech = 0 if the vehicle is not discontinued. maint = 1 if the maintenance expenses are<br />
greater than average and EP A is a fuel e¢ ciency indicator.<br />
All along the referenced studies, methodology moved from a remaining service approach to<br />
a Hedonic mo<strong>de</strong>l including essentially the vehicle characteristics (physical or not). We acknow-<br />
ledge the "remaining service approach", however we believe that vehicle characteristics contain<br />
most of the information. As a consequence, we adjust the resale price from in‡ation and we set<br />
a statistical mo<strong>de</strong>l mainly through variables related to the vehicle characteristics.<br />
1.3 Some characteristics of the mo<strong>de</strong>l are discussed.<br />
The mo<strong>de</strong>l construction brings comments and discussions : The used market is (i)<strong>de</strong>mand<br />
oriented and (ii)correlated with fuel price ; (iii)Multicollinearity is a critical issue in Hedonic<br />
calculation ; (iv)We have to choose a functional form, and (v)Heteroscedasticity impacts the<br />
mo<strong>de</strong>l speci…cation.<br />
1.3.1 Coe¢ cients interpretation <strong>de</strong>pends on used market substitu-<br />
tion to new market.<br />
Berndt (1983) pointed out an argument against the Rosen i<strong>de</strong>nti…cation problem for the used<br />
market : un<strong>de</strong>r speci…c conditions, equation parameters can be directly interpreted as re‡ecting<br />
<strong>de</strong>mand (rather than cost or supply) and there is no i<strong>de</strong>nti…cation problem. If the supply curves<br />
of products are perfectly inelastic, then the market <strong>de</strong>mand and supply curves would intersect<br />
at di¤erent levels of each combination of characteristics. The structure combination would be<br />
<strong>de</strong>termined by the <strong>de</strong>mand. The di¤erence of price level among products could be interpreted<br />
unambiguously as providing implicit measures of consumers’ evaluation of the characteristic<br />
combinations. So coe¢ cients of the equation are well i<strong>de</strong>nti…ed, as well as estimates of the<br />
<strong>de</strong>mand function parameters. Because the total quantities are …xed (assuming that there is
1.3. SOME CHARACTERISTICS OF THE MODEL ARE DISCUSSED. 9<br />
a non signi…cant link with new market), the equation only re‡ects <strong>de</strong>mand in the used car<br />
market.<br />
Hartman (1987) results validate that an application to the resale market avoids the i<strong>de</strong>n-<br />
ti…cation problem. If the supply of the attributes embodied into used cars is almost perfectly<br />
inelastic, he states that simultaneity should not pose a problem in recovering Hedonic <strong>de</strong>mand<br />
and supply parameters in new product market. If the simultaneity is important, di¤erent as-<br />
sumptions about quantity of each make and mo<strong>de</strong>l sold should generate di¤erent parameter<br />
estimates. Therefore the only question is : are the parameters statistically and economically<br />
signi…cant ? In his analysis, the resale value calculation was very robust to alternative sales as-<br />
sumptions. Hartman applied a single equation mo<strong>de</strong>l 18 to estimate the e¤ect of product recalls<br />
on resale prices and …rm valuation.<br />
Two main conclusions can be stated : All referenced automotive studies use single equation<br />
techniques, and remarketing professionals usually believe in a substitution relation for young<br />
resale automotive market only which is a situation where <strong>de</strong>mand and supply characteristics<br />
are quite similar. Therefore we apply a single equation and we exclu<strong>de</strong> short term duration (less<br />
than 12 months age) vehicles.<br />
1.3.2 Others products interact with price.<br />
De…ning a framework on the <strong>de</strong>mand analysis, Berndt (1983) discussed the input price-<br />
<strong>de</strong>pen<strong>de</strong>nt quality adjustment case : the quality of a good (i.e. fuel e¢ ciency) is <strong>de</strong>pen<strong>de</strong>nt on<br />
the quantity (or price) of another good (i.e fuel price). Berndt states that we could test the<br />
<strong>de</strong>pen<strong>de</strong>nt 19 (or in<strong>de</strong>pen<strong>de</strong>nt) price hypothesis using classical testing procedures (i.e. economical<br />
and statistical signi…cance of fuel price on auto price). Fuel price has a signi…cant part in the<br />
total cost of automobile usage, and then monthly fuel price constitutes our mo<strong>de</strong>l.<br />
18 See Appendix A4.<br />
19 See Appendix A5.
10 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
1.3.3 Multicollinearity is a main issue in Hedonic mo<strong>de</strong>ls.<br />
The econometrician walks between the two following risks while he selects the relevant va-<br />
riables for an Hedonic estimation : correlated explanatory variables and trickle down hypothesis.<br />
In the automotive area, physical characteristics are often correlated (i.e. four wheels correla-<br />
ted to fuel capacities). According to the Gauss Markov theorem, OLS has the smallest variance.<br />
However, if explanatory variables are correlated, then small change in the data produces wrong<br />
sign, implausible magnitu<strong>de</strong> and wi<strong>de</strong> swings in parameter estimates 20 . As a consequence, pa-<br />
rameter correlations present a major issue for forecast applications. The simplest solution is<br />
to exclu<strong>de</strong> variables at risk (i.e all variables related to the engine power, number of cylin<strong>de</strong>rs,<br />
kilowatt, fuel consumption, fuel capacity...) in the case of non economical signi…cance 21 .<br />
Triplett (1969) highlights another problem. Because a small amount of variables is able<br />
to explain most of the variance (i.e. the weight of the vehicle correlated with engine power<br />
and price), there are some risk of biases in the Hedonic mo<strong>de</strong>l and a substantial number of<br />
innovations are missed throughout this ’trickle down’hypothesis.<br />
Therefore, the selected parameters of our mo<strong>de</strong>l cover four axes of <strong>de</strong>preciation e¤ects :<br />
the level of usage, the original equipment cost, the market interactions and the pure physical<br />
characteristics of the vehicle.<br />
1.3.4 Which functional form ?<br />
Rosen (1974) states that the functional form is an empirical matter. In the same logic,<br />
Grilitch and Otha (1976) choose a semilogarithmic form for their regression because ’it provi<strong>de</strong>d<br />
a good …t of the data’. Most of the literature suggests the log form, others studies apply the<br />
20 But it also produces instability of coe¢ cient and higher standard errors, R 2 quite high, coe¢ cient with high<br />
standard error and low signi…cance levels (even if signi…cant). See Greene (2003) chapter 4 p57.<br />
21 An advanced solution is the ridge regression estimator or principal component methodology. The problem<br />
is that we lost visibility on coe¢ cients meaning.
1.3. SOME CHARACTERISTICS OF THE MODEL ARE DISCUSSED. 11<br />
log-log form 22 , and the Box Cox test 23 has also been used to compare several functional forms.<br />
The Hedonic functional form problem constitutes a great discussion but it is not the main<br />
purpose of the chapter.<br />
We followed the Grilitch and Otha position (1976) (’a good …t of the data’) and empirical<br />
results lead us to the linear form of Cowling and Cubbin (1972). Their linear mo<strong>de</strong>l inclu<strong>de</strong>s<br />
multiple physical variables like horse power and length and to allow approximation to a non<br />
linear form, square transformation, cubic transformation and log transformation were applied<br />
to exogenous variables. Interactions terms were also inclu<strong>de</strong>d.<br />
1.3.5 Unobserved tastes create heteroscedasticity.<br />
As previously mentioned in Bartik’s critics 24 , because the choice for the studied commodities<br />
quality and other commodities is correlated with unobserved tastes in the residuals, then an<br />
heteroscedasticity issue appears. If residuals from the economic relation do not have constant<br />
variance, the mo<strong>de</strong>l is not biased but the variance increases. Bartik states that any variable<br />
that exogenously shifts the budget constraint of the buyer will be an appropriate instrument :<br />
the budget constraint shift is correlated with the buyer choice of car attributes and the choice<br />
of other products yet uncorrelated with unobserved tastes.<br />
We follow Bartik’s approach including the in<strong>de</strong>x of industrial production 25 as a proxy of<br />
the economic situation of the buyer (we propose a temporal budget constraint shifter). Because<br />
most of buyers are professionals impacted by a market seasonality, we inclu<strong>de</strong> a seasonality<br />
variable on a quarterly basis. Finally, in or<strong>de</strong>r to manage unobserved characteristics (i.e. brand<br />
name perception and reputation...), we also insert a manufacturer e¤ect 26 .<br />
22See Hogarty (1975).<br />
23See Atkinson and Halvorsen (1990), Van Dalen and Bo<strong>de</strong> (2004).<br />
24See Section 1.2.2.<br />
25Excluding energy and construction.<br />
26We do not work with a mo<strong>de</strong>l car type level, because our goal is to apply a methodology ‡exible enough<br />
to inclu<strong>de</strong> new cars and non exhaustive data. Moreover, our mo<strong>de</strong>l does not inclu<strong>de</strong> the life cycle of vehicles<br />
(’honey moon’e¤ect for new mo<strong>de</strong>ls...) because of the di¢ culty to collect and to standardize the information. In<br />
the list of unobserved characteristics, there is also the remarketing performance. The value could be impacted<br />
by the remarketing team in charge of the resale process. Finally, we do not inclu<strong>de</strong> macroeconomic impacts
12 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
1.4 We use the Hedonic mo<strong>de</strong>l to estimate the distribu-<br />
tion of resale price.<br />
We apply the straightforward regression approach of Otha and Grilitch (1976). Removing the<br />
impact of uncertain variables and using the classical OLS properties, resale price distributions<br />
are calculated.<br />
1.4.1 Ohta and Griliches have an empirical approach.<br />
Regarding theoretical issues (including the one discussed in Sections 2 and 3), Ohta and<br />
Griliches state that Hedonic mo<strong>de</strong>l usage ’has an air of "measurement without theory", but<br />
one should remember the limited aspirations of the Hedonic approach and not confuse it with<br />
attempts to provi<strong>de</strong> a complete structural explanation of the events in a particular market’ 27 .<br />
They exposed a strong empirical criterion for hypothesis testing 28 . They inclu<strong>de</strong>d a make e¤ect<br />
as a proxy of unmeasured characteristics. A real e¤ect linked to unmeasured physical cha-<br />
racteristics and a putative one (linked to prestige, service availability...) constitute the make<br />
e¤ect.<br />
In their mo<strong>de</strong>l, the price of mo<strong>de</strong>l k of make i and age s at time t is<br />
Pk;i;t;s = fct(Mi; Pt; Ds; e P aijxkivj)<br />
with Mi the e¤ect of the i th make, Pt the pure Hedonic price in<strong>de</strong>x at time t, Ds the e¤ect of<br />
age s (<strong>de</strong>preciation). aij are parameters re‡ecting the imputed price of physical characteristic<br />
(which need a proper analysis). Therefore unobserved e¤ects mentioned above constitute the random variable<br />
of the statistical mo<strong>de</strong>l.<br />
27 Ohta and Griliches (1976) p326.<br />
28 "The rejection or acceptance of an hypothesis should <strong>de</strong>pend on the researcher’s interests and his loss<br />
function"(p 339). Grilitch and Otha put in perspective the statistical and economic signi…cance. Instead of<br />
following a formal Fisher test, they use the di¤erence in the standard errors of the unconstrained and constrained<br />
regressions as a relevant measure of the price-explanatory power of a particular mo<strong>de</strong>l. They do not reject null<br />
hypothesis if di¤erences between the standard errors of the unconstrained and constrained regressions are less<br />
than or equal to 0:01.
1.4. WE USE THE HEDONIC MODEL TO ESTIMATE THE DISTRIBUTION OF RESALE PRICE.13<br />
j at time t. xkivj is the level of the physical characteristic j embodied in mo<strong>de</strong>l k of make i and<br />
vintage v (v = t s).<br />
They applied their mo<strong>de</strong>ls on new and used cars and tested di¤erent hypotheses 29 (i.e<br />
geometric <strong>de</strong>preciation held separately from makers). Otha and Grilitch approach is now a<br />
standard. As a consequence, Yerger (1995) used this method to discuss an article written by<br />
Ho¤er and Pratt (1990) which was inspired by Akerman approach 30 .<br />
Following these authors, our approach is mainly empirical. We select the mo<strong>de</strong>l structure<br />
that best …ts to reality and choose exogenous variables with a statistical and economic signi…-<br />
cance.<br />
1.4.2 Statistical mo<strong>de</strong>ls are slightly di¤erent by country.<br />
Our analysis inclu<strong>de</strong>s four countries (France, Germany, Spain, Great Britain) and we <strong>de</strong>…ne<br />
a mo<strong>de</strong>l for each of them 31 . The real resale price is explained by a …rst group of variables<br />
indicating the level of usage : age and mileage are in logarithm due to the well known non<br />
linearity property of car <strong>de</strong>preciation. An indicator of usage intensity, the mileage per month,<br />
is also inclu<strong>de</strong>d and signi…cant. The second group of variables is related to the list price. A<br />
cubicle variable of list price is ad<strong>de</strong>d (high initial price increase <strong>de</strong>valuation). The make e¤ect<br />
is introduced through a dummy variable of manufacturer multiplied by the list price. Variables<br />
bringing market information contitute the third group : the diesel pump price, the industrial<br />
production in<strong>de</strong>x and the quarter sale date. The last group inclu<strong>de</strong>s pure physical characteristics<br />
that are slightly di¤erent from a country to another (average fuel consumption, body type,<br />
number of seats, engine power, number of cylin<strong>de</strong>rs, automatic transmission, number of doors).<br />
29 Their results on the US market are worth to mention : no gains to move to performance variables (so we can<br />
only use the vehicle characteristics) ; geometric <strong>de</strong>preciation is an a<strong>de</strong>quate approximation but it is not constant<br />
accross time and manufacturers ; New and used car market can be analysed jointly. Unfortunately, because of<br />
the rise of fuel cost (1973) they aknowledged that their analysis was already obsolete.<br />
30 See Appendix A6.<br />
31 See mo<strong>de</strong>ls <strong>de</strong>tails in Appendix B.
14 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
1.4.3 We estimate the distribution of resale price.<br />
We wish to calculate the distribution of y0 (the resale price) for a regressor vector x0 (group<br />
of variables explaining the resale price). The usual regression formula is y0 = a0 b0x0. X and<br />
y0 <strong>de</strong>note the full data matrices. b0 is the coe¢ cient vector.<br />
We assume 32 that y0 follows a normal distribution 33 equal to<br />
N(x T 0 b0 + e; s 2 [1 + x T 0 (X T X) 1 x0]).<br />
The con…<strong>de</strong>nce interval is calculated with<br />
xT p<br />
T<br />
0 b0 t=2(n p 1) MSE[1 + x0 (XT X) 1x0] 1=2 :<br />
1.4.4 An adjustment removes uncertain variables e¤ects.<br />
All the exogenous variable values are known with certainty 34 , except the fuel pump price<br />
and the production distribution in<strong>de</strong>x. We aim to remove the product interaction e¤ect (Dp)<br />
and the temporal budget constraint (Ip) in or<strong>de</strong>r to focus on the vehicle valuation. Assuming<br />
that the diesel price and the production price follow a normal distribution, we calculate the<br />
mean and the variance from 2004 to 2008 and we estimate a risk neutral distribution of the<br />
resale price.<br />
The unconditional resale price distribution of x T 0 be0 can be solved as<br />
1R<br />
N[<br />
1<br />
1R<br />
1<br />
m(x0=Dp; Ip) g(Dp) j(Ip) dDp dIp;<br />
1R<br />
1<br />
1R<br />
1<br />
n(x0=Dp; Ip) g(Dp) j(Ip) dDp dIp]<br />
32 Data are composed of subgroups by mo<strong>de</strong>ls, age, mileage and physical vehicle characteristics. Normality<br />
hypothesis test are possible on subgroups with a signi…cant amount of data. For mo<strong>de</strong>ls with same age and<br />
mileage, H0 is not rejected. The test of normality on the two analyzed vehicles (Ford focus and the Audi A4)<br />
is not rejected.<br />
33 See Appendix A7.<br />
34 We limit our analysis to …xed contract with no purchase option and no rewrite, therefore age, mileage and<br />
sale dates are known with certainty.
1.5. WE APPLY THE METHODOLOGY TO FOUR EUROPEAN COUNTRIES. 15<br />
in<strong>de</strong>x.<br />
Where m() = x T 0 b0 + e<br />
and n() = s 2 [1 + x T 0 (X T X) 1 x0].<br />
g() and j() are the probability <strong>de</strong>nsity of the fuel pump price and the production distribution<br />
The integrals are calculated with numerical integration.<br />
1.5 We apply the methodology to four European coun-<br />
tries.<br />
Mo<strong>de</strong>ls by country, regression results and graphical illustrations, through two vehicle ver-<br />
sions, provi<strong>de</strong> an insight of European markets.<br />
1.5.1 Mo<strong>de</strong>ls are created according to the information usually avai-<br />
lable in the leasing industry.<br />
In or<strong>de</strong>r to quantify the Hedonic price, we apply the mo<strong>de</strong>l to four European markets<br />
(France, Germany, Spain, and Great Britain 35 ) using internal sales data from January 1st 2004<br />
to December 31st 2008 of a major leasing company. Statistics are based on random samples of<br />
cars sold in various channels (auction, <strong>de</strong>alers, private sellers, etc). Vehicle age samples range<br />
from 1 to 10 years, and have mileage ranging from 1,000 to 400,000 km. As expected for leasing<br />
companies resale statistics, a concentration of vehicles with high mileage and short age spans<br />
(concentration on 24, 36 and 48 months of age with a mileage between 80000 km and 120000<br />
km) constitutes a large part of our sample. All monetary values (sales prices, diesel prices) are<br />
adjusted according to the in‡ation. We aim to create a tool allowing a leasing company to catch<br />
35 Great Britain has a sterling pound currency and very limited cross bor<strong>de</strong>ring sales with others european<br />
countries because of the right hand si<strong>de</strong> weel of the car. Therefore, GB statistics add an original perspective of<br />
european markets analysis.
16 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
all the available Hedonic information of the car activity from it’s historical sales. According to<br />
the company position in markets, the amount of data is signi…cantly di¤erent by country but<br />
su¢ cient for calculation (Fr : 112,875 units, Ger : 7,398 units, Sp : 14,674 units ; Gb : 33,506<br />
units). Contrary to some referenced studies applying the Hedonic mo<strong>de</strong>l to the car market,<br />
we do not limit our analysis to a segment or version of cars. As a consequence, the explained<br />
variance (R 2 ) is slightly lower (and even more to applied studies on the much more stable new<br />
car market). To estimate the manufacturer e¤ect, statistics inclu<strong>de</strong> several manufacturer names<br />
(Fr : 9, Ger : 4, Sp : 6, Gb : 8) by country.<br />
1.5.2 The regression provi<strong>de</strong>s a Hedonic price assessment of the<br />
European markets.<br />
All variables have a signi…cant economic value 36 . The explained variances of the OLS re-<br />
gressions are between 0.75 and 0.8. Characteristics adding quality to the car (engine power,<br />
number of seats, etc) as well as the industrial production in<strong>de</strong>x (as a proxy of budget variation)<br />
have a positive sign. According to the Hedonic theory, the price of fuel is an additional cost<br />
of the driving activity and has therefore a negative e¤ect. The variables of age, mileage and<br />
usage intensity (mileage per month) reduce the resale price, there are parameters correlated to<br />
obsolescence and wear. A slight seasonal e¤ect exists in all markets. The well known and better<br />
valuations of German manufactured cars (positive make e¤ect) are veri…ed in all countries.<br />
1.5.3 The analysis on Ford focus and Audi A4 give additional infor-<br />
mations.<br />
France, Germany and Spain share the same currency (Euro) and results estimate the resale<br />
price distribution of a vehicle, according to the amount of information available from historical<br />
sales. The samples of the four countries have two manufacturers in common : Audi and Ford.<br />
We choose the characteristics of the Ford Focus (C-max 1800 TDCI 115 Ghia 5P) and Audi<br />
36 See mo<strong>de</strong>ls results in Appendix C. An indicator of automatic transmission was tested and statistically<br />
signi…cant for France. Because the coe¢ cient sign was negative, we removed it.
1.5. WE APPLY THE METHODOLOGY TO FOUR EUROPEAN COUNTRIES. 17<br />
A4 (1.9 Tdi 130 Pack 4P) as a basis to compare the four markets. The information provi<strong>de</strong>d<br />
by the mo<strong>de</strong>l could be summarized by two elements. On one hand, a higher valuation of car at<br />
the end of the contract reveals better opportunities for leasing business. On the other hand, a<br />
higher volatility implies uncertainty on the resale price, and therefore a higher risk of loss on<br />
sale.<br />
Bucket results : A …rst analysis approach 37 on the bucket of a 36 month age group, and<br />
90000 kilometers emphasizes three points. First, the Audi A4 has a better valuation than the<br />
Ford Focus in every country. As mentioned previously, German cars bene…t from a ’positive<br />
make e¤ect’; they are objects of prestige and share a reputation of good quality cars. Secondly,<br />
the high level of standard <strong>de</strong>viation in all markets reveals a huge volatility. Acknowledging that<br />
the second hand market is not as liquid as a …nancial market, it illustrates that a car, as an<br />
asset in a balance sheet of a company, constitutes a signi…cant risk. Thirdly, in Germany, cars<br />
get a better valuation. A high resale price constitutes a good element for a leasing business ;<br />
however the German market also has a higher standard <strong>de</strong>viation, and therefore a higher risk<br />
of loss on sales.<br />
Graphical results : The graphics of distribution through age and mileage give an additio-<br />
nal perspective of the <strong>de</strong>preciation 38 . The variance is not economically di¤erent when we modify<br />
age and mileage parameters (whatever the currency, the age and the mileage, the standard <strong>de</strong>-<br />
viation does not exceed two Euros). Age and Mileage do not increase the volatility. Regarding<br />
average <strong>de</strong>preciation, German vehicles are highly correlated with mileage, but Spanish cars are<br />
not. Surprisingly, the graphical analysis of age impact on vehicles, reveals that British cars<br />
are heavily impacted by the level of usage (kilometer per month variable coe¢ cient) and as a<br />
consequence, 12 month age vehicles have a resale price equivalent to 24 age month vehicles.<br />
The last two points indicate that Hedonic valuations are signi…cantly di¤erent by country. Eu-<br />
ropean markets are not homogeneous, and residual value distributions are always singular. On<br />
a business perspective, leasing contracts would be impacted by country speci…cities.<br />
37 See Appendix D.<br />
38 See Appendix E.
18 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
1.6 Conclusion and extensions<br />
The Hedonic theory has been wi<strong>de</strong>ly used for the automotive market analysis. We discuss<br />
and propose an application to second-hand vehicles in the leasing industry, where the residual<br />
value is a critical parameter (residual value risk). The mo<strong>de</strong>l is based on attributes in or<strong>de</strong>r to<br />
estimate the resale price distribution. A product interaction e¤ect (fuel price), and a temporal<br />
budget shifter (industrial production in<strong>de</strong>x) are also inclu<strong>de</strong>d. The methodology applied to four<br />
European countries provi<strong>de</strong>s a perspective of the automotive resale markets. Focusing on the<br />
pattern of <strong>de</strong>preciation of two vehicles (Ford Focus and Audi A4), the approach illustrates the<br />
di¤erent levels of probability of losses according to the resale information available by a leasing<br />
company. The approach also allows the comparison of market opportunities, through pricing<br />
analysis and risk. Our study can be exten<strong>de</strong>d in several ways. The leasing industry inclu<strong>de</strong>s all<br />
types of equipment and the application of the Hedonic valuation would be ‡exible enough to<br />
be exten<strong>de</strong>d to assets other than automotive. Moreover, our analysis could also be exten<strong>de</strong>d<br />
to contracts with a purchase option or a rewrite option on age and mileage (i.e. customers can<br />
choose to extend or interrupt their contract(s)). Two other elements in the area of residual<br />
value risk should be inclu<strong>de</strong>d to complete the analysis : the vehicle life cycle impact and the<br />
macroeconomic impact (the general market <strong>de</strong>preciation). The macroeconomic element would<br />
need a more thorough study.
1.7. APPENDIX 19<br />
1.7 Appendix<br />
1.7.1 Appendix A : Methodological aspects.<br />
A 1 : In Rosen Hedonic framework, we can <strong>de</strong>…ne the marginal price on a characteristic<br />
level. For any vector of observed characteristics Z (of the car), the Hedonic marginal price<br />
for a characteristic z (i.e. fuel consumption) is an estimate of both the marginal bid for z<br />
of the household purchasing Z and the marginal o¤er for z of the …rm producing z. Linear<br />
version of these marginal bid and marginal o¤er function are <strong>de</strong>…ned through two equations :<br />
Estimated Hedonic marginal price of characteristics<br />
p<br />
zj (Zi) = Wij consumer marginal bid for<br />
zj = B0 + B1Zi(vector of observed characteristics of the product) +B2Xt (consumer expendi-<br />
ture on commodities others than Z) +B2D0i(vector of observed <strong>de</strong>man<strong>de</strong>r traits a¤ecting the<br />
marginal bid) +eij.<br />
p<br />
zj (Zi) = Gij …rm marginal o¤er price for zj = Ao + A1Zt + A2S0i(vector<br />
of observed supplier traits a¤ecting the marginal o¤er) +uij:uij and eij are disturbance terms.<br />
A 2 : Berndt <strong>de</strong>…nes general framework on durables commodities in term of service price.<br />
He <strong>de</strong>monstrates that in the case of the input price-<strong>de</strong>pendant quality adjustment ("variable<br />
repackaging hypothesis") the Hedonic price equation can be expressed in term of service price<br />
as :<br />
ln un;t; = lnp n;t + ln h 0 n(zn1; zn2; :::; Znk; pn 1) + lnDn; :<br />
With un;t; the resulting asset price, lnp n;tis the quality adjusted "base" price in<strong>de</strong>x of the<br />
n th capital good at time t, Dn; is a <strong>de</strong>preciation in<strong>de</strong>x varying only with the age of the asset.<br />
hn is the quality aggregation function that link the quality bn to the physical characteristics zn.<br />
b 0 n = hn0(zn1; zn2; :::; znk) TnP<br />
s=0<br />
( 1<br />
intercept is the quality adjusted service price.<br />
1+r )s dn;s: dn;s is the <strong>de</strong>terioration of the service over time. The<br />
A 3 : Akerman mo<strong>de</strong>l estimates used car value.The price of an Automobile of a gi-<br />
ven age, K, can be expressed as the discounted present value of its remaining services :
20 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
P (K) = R D<br />
K S(X)e r(X K) dX with K present age of car, D age of scrappage, X age, r discount<br />
rate(assumed constant), S(X) value of services provi<strong>de</strong>d by a car of age X, P (K) price of a<br />
car of age K.<br />
An Hedonic price, repair cost, service function and expected gain on resale estimation are<br />
components of the mo<strong>de</strong>l. Akerman use a single equation and a regression to estimate the<br />
Hedonic price :<br />
logA(v; m) = C + E(v; m) + C(v; M) + W (v; M) + L(v; M) + H(v; M)<br />
With A(v; m)=new car list price including fe<strong>de</strong>ral tax and handling and transportation<br />
charges. E(v; m)=1 if car has height cylin<strong>de</strong>rs. C(v; M)=1 if compact. W (v; M), L(v; M) and<br />
H(v; M) are weight, length and horse power. v is mo<strong>de</strong>l year and m is the mo<strong>de</strong>l.<br />
A 4 : Hartman Equation inspired by Grilitch and Otha equation :<br />
LogP kit = Bo + B1MKi + B2MDk + B3AGEs + B4jAkij + B5jRjk<br />
P kit is the resale price in period t for a car of make i and mo<strong>de</strong>l k.<br />
MKiand MDkare dummy variables indication Make and mo<strong>de</strong>l. Age is the age of the car<br />
in t. Akij is the level of attribute j embodied in mo<strong>de</strong>l k and make i. Rjk summarize the car<br />
recalls history indicating cumulative recalls of type j for mo<strong>de</strong>l k.<br />
A 5 : Berndt <strong>de</strong>…nes a general framework on commodities.<br />
X(= x1; x2; :::xn) a vector of commodity, B(= b1; b2; :::; bn)a vector of qualities for each<br />
commodity, Z(= z1; z2; :::; zi; zn) a vector of physical characteristics for each commodity and<br />
P (= p1; p2; :::; pn) a vector of price for each commodity. Moreover we have an utility function<br />
u = F (x; b) and Bn = Hn(Z).<br />
As a result, we have xn = f(u; x1; x2; :::; xn 1; bn)<br />
For a new quality level from bn0 to bn1 un<strong>de</strong>r the assumption of a log-log form ;
1.7. APPENDIX 21<br />
In the case called the "simple packaging hypothesis" (or input price-in<strong>de</strong>pendant quality<br />
adjustment), bn is only <strong>de</strong>pendant of zi, we have a quality function bi = hi(zi) ;<br />
xn must be equalized at the margin : pn0<br />
pn0<br />
= pn1<br />
pn1 = p n<br />
where p n is a base price constant re‡ecting the price of the standardized unit.<br />
Through a log transformation of 1), then lnpn1 = lnpn0 + lnhn1(zn1) and an assumption of<br />
log-log form of the quality conversion function lnhn1(zn) = kP<br />
bnk ln zn1;k :<br />
lnpn1 = lnpn + kP<br />
bnk ln zn1;k where bnk are the coe¢ cient on the kth characteristics of the<br />
n th commodity.<br />
k=1<br />
Using this framework we are now able to calculate a price according to the physical charac-<br />
teristics of a commodity.<br />
In the case called the "variable packaging hypothesis" (or input price-<strong>de</strong>pendant quality<br />
adjustment), for instance if bn is <strong>de</strong>pendant of xn 1as well ; bn = hn(xn 1;zn) :<br />
lnpn(bn) = lnp 0 n + lnhn(pn 1; zn)<br />
Using this formula, in an empirical analysis, we could test the simple versus the variable<br />
repackaging hypothesis using classical hypothesis testing procedures. (i.e. fuel price on auto<br />
price).<br />
A 6 : Yerger(1995) applied Grilitch and Otha method to discuss an article written by Ho¤er<br />
and Pratt which was inspired by Akerman approach.<br />
For a mo<strong>de</strong>l i and at trend variable, time t ((t = 1; :::; 12), the price P it is<br />
LogP it = 0 + 1 t + j 2jCAT j + k 3kAik + 4T ECH + 5RECOM + 6AV OID<br />
with CAT j as a variable of the category of vehicle (subcompact, midsize....) and Aik as a<br />
k=1
22 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
vector summarizing the level of attribute k in mo<strong>de</strong>l i. If the vehicle is not discontinued then<br />
tech = 0. If the vehicle have been recommen<strong>de</strong>d to buy then RECOM = 1. If recommend<br />
to avoid to buy by ’consumer reports’magazine evaluation then AV OID = 1. By his mo<strong>de</strong>l,<br />
Yerger tested and approved the market e¢ ciency in Automotive market.<br />
A 7 : Ordinary <strong>Le</strong>ast Square allows prediction interval calculation 39 .<br />
The Ordinary <strong>Le</strong>ast Square Method estimate a and b by minimizing the sum of squared<br />
error SSE n<br />
= P<br />
(y yei) i<br />
2 = nP<br />
(y a bx ) i i 2 = e2 i=1<br />
i=1<br />
An unbiased estimate s 2 of e 2 is given by mean squared error :<br />
s 2 = SSE<br />
n p =<br />
n<br />
1<br />
n p<br />
i=1<br />
P<br />
(y i ae beX i ) 2 = MSE. ae and be <strong>de</strong>note the linear least squares<br />
estimators for a and b. n is the size of the sample and p the number of parameters.<br />
Distribution and interval calculation :<br />
<strong>Le</strong>t x0 = (1; x1; x2; x3; :::; xp) ; b0 = (a; b1; b2; b3; :::; bp) and be0 = (ae; be1; be2; :::; bep)<br />
Y j(X = x0) = x T 0 b0 + e0:e0 is the random error corresponding to the new estimation Y and<br />
e0~N(0; 2 ):<br />
We use x T 0 be0 to estimate x T 0 b0 + e0:<br />
The distribution of x T 0 be0 is N(x T 0 b0 + e; s 2 [1 + x T 0 (X T X) 1 x0]) and the interval is x T 0 be0<br />
t=2(n p 1)<br />
p MSE[1 + x T 0 (X T X) 1 x0] 1=2<br />
1.7.2 Appendix B : Regression equations and notations<br />
Resaleprice = fct1(age; mileage; mileagepermonth) + fct2(make listprice; listprice) +<br />
fct3(pump_price; industrial_production_in<strong>de</strong>x; sale_date)+fct4(car_physical_attributes):<br />
39 Green (1992) Econometric analysis. 5 th edition. p 111.
1.7. APPENDIX 23<br />
France :<br />
P = 0 + 1 logAge+ 2 logDis+ 3 Kpm+ 4j MKj Lp+ 5 Lp 2 + 6 Indx_pdrt+<br />
7 QT Rl + 8 Diesl_p+ 9 AvgF uel1+ 10 Seat+ 11k Bodyk + 12 Kwt+ 13 EngnCap<br />
Germany :<br />
P = 0 + 1 logAge+ 2 logDis+ 3 Kpm+ 4j MKj Lp+ 5 Lp 2 + 6 Indx_pdrt+<br />
7 QT Rl + 8 Diesl_p+ 9 AvgF uel1+ 10 Seat+ 11k Bodyk + 12 Kwt+ 14 F uelCap<br />
Spain :<br />
P = 0+ 1 logAge+ 2 logDis+ 3 Kpm+ 4j MKj Lp+ 5 Lp 2 + 6 Indx_pdrt+ 7<br />
QT Rl + 8 Diesl_p+ 9 AvgF uel1+ 11k Bodyk + 12 Kwt+ 13 EngnCap+ 15 Door_5<br />
Great Britain :<br />
P = 0 + 1 logAge+ 2 logDis+ 3 Kpm+ 4j MKj Lp+ 5 Lp 2 + 6 Indx_pdrt+<br />
7 QT Rl + 8 Diesl_p + 9 AvgF uel1 + 11k Bodyk + 13 EngnCap + 16 AutoT<br />
P is the real resale price.<br />
Age is number of month between the registration and the sale date.<br />
Dis is the distance travelled, including any distance done on an odometer that has been<br />
changed.<br />
Kpm is the distance travelled per month.<br />
Lp 2 is the cubic of the real least price (including option price).<br />
MKj are dummy variables indicating make multiplied by Lp. ( France : Audi,Bmw, Citroen,<br />
Ford, Merce<strong>de</strong>s, Opel, Peugeot, Renault, Volkswagen. Germany : Audi,Bmw, Ford, Volkswa-<br />
gen.Spain : Audi, Ford, Opel,
24 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
Peugeot, Renault.Seat. UK : Audi, Bmw, Ford, Toyota,Vauxhall, Volkswagen.)<br />
AvgF uel1 contains average fuel consumption …gures as given by the manufacturer (urban<br />
and road). It is a company <strong>de</strong>cision as to which statistical …gure goes into this attribute.<br />
Seat is the number of seat.<br />
Bodyk are dummy variable indicating the body type (France :berline, monospace. Germany :<br />
Kompact, Spain :estate, berline UK : estate car, or saloon (sedan))<br />
Kwt is the power of the engine expressed in kilowatt given by the manufacturer.<br />
Indx_pdrt is the Industrial production by monthly in<strong>de</strong>x (adjusted by working days).<br />
QT Rl are dummy variables indicating the quarter.<br />
Diesl_p is the diesel pump price, euro per liter all taxes inclu<strong>de</strong>d.<br />
EngnCap is the actual number of ccs the engine has.<br />
F uelCap is the capacity of the fuel tank or tanks, in litres as …tted as standard on the<br />
vehicle type.<br />
or not.<br />
AutoT is equal to 1 if the vehicle has a form of automatic transmission …tted as standard<br />
Door_5 is equal to 1 if the vehicle has 5 doors.
1.7. APPENDIX 25<br />
1.7.3 Appendix C : Regression results<br />
France Results<br />
Germany Results
26 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
Spain Results<br />
Great Britain Results
1.7. APPENDIX 27<br />
1.7.4 Appendix D : Pivot Point results<br />
Bucket 30 months and 90,000 kilometers
28 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
1.7.5 Appendix E : Graphical analysis :<br />
Ford Focus age impact :<br />
France<br />
Germany
1.7. APPENDIX 29<br />
Spain<br />
Great Britain
30 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
Ford Focus mileage impact :<br />
France<br />
Germany
1.7. APPENDIX 31<br />
Spain<br />
Great Britain
32 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
Audi A4 age impact :<br />
France<br />
Germany
1.7. APPENDIX 33<br />
Spain<br />
Great Britain
34 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE<br />
Audi A4 mileage impact :<br />
France<br />
Germany
1.7. APPENDIX 35<br />
Spain<br />
Great Britain
36 CHAPITRE 1. THE EUROPEAN USED-CAR MARKET AT A GLANCE
Chapitre 2<br />
Hedging residual value risk using<br />
<strong>de</strong>rivatives<br />
37
38 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
2.1 Introduction<br />
A lease is a contract in which one party transfers the use of an asset to another party for a<br />
speci…c period of time. <strong>Le</strong>asing equipment is an important means of …nancing, and consequently<br />
represents a signi…cant part in many …nancial institutional portfolios. In 2006, leasing represen-<br />
ted more than one-sixth of the world’s annual equipment …nancing requirement 1 . The value of<br />
the entire Global leasing market was estimated to be more than $633 billion 2 . Aca<strong>de</strong>mic results<br />
suggest that "leasing allows small …rms to …nance their growth, and/or survival while for large<br />
…rms, leasing appears to be a …nancial instrument used by sophisticated …nancial managers to<br />
minimize the after-tax cost of their capital 3 ".<br />
In the leasing industry, residual values are the forecasted prices of equipment in the second<br />
hand market. A large part of the rent paid by the customer during a life contract is the di¤erence<br />
between the list price and the residual value. The leasing company makes money or losses money<br />
<strong>de</strong>pending on whether it accurately predicts the value of the asset at the end of the contract<br />
(fair market value). If residual values are forecasted to be higher than what the asset is actually<br />
worth at lease-end, then there will be a loss. At the opposite, if residual values are forecasted<br />
to be lower, then there will be a gain on resale.<br />
In the European auto lease market, most leases are closed-end leases : leasing companies<br />
assume the residual value risk. In 2001, car resale’s price fell dramatically. As a result, US<br />
leasing companies su¤ered large losses, and some even dropped out of the business 4 . Although,<br />
residual value risk is a key element in the leasing industry, there is very few literature on the<br />
subject. The few studies were <strong>de</strong>veloped in three main areas : operational purpose 5 aiming<br />
1 Percentage market penetrations are highly signi…cant in United states (27.7%), Germany (23.6%), and Spain<br />
(29.1%).<br />
2 According to the White Clarke Global <strong>Le</strong>asing report (2008), "Globally, the industry continued to growth<br />
robustly, with the top 50 countries increasing volume by 8.8%" between 2005-2006. The Percentage of the world<br />
market volume was respectively 41.1% and 38% for Europe and North America.<br />
3 See Lasfer and <strong>Le</strong>vis (1998).<br />
4 See Gordon (2001) for a <strong>de</strong>scription of the 2001 <strong>Le</strong>asing industry crisis.<br />
5 Jost and Franke (2005) illustrate the use of a speci…c tool of statistical mo<strong>de</strong>lling to calculate residual value<br />
through a wi<strong>de</strong> range of parameters. In Lucko (2003) and Lucko, An<strong>de</strong>rson-cook, and Vorster (2006), residual<br />
values are set using regression methodology. Ro<strong>de</strong>, Paul, and Dean (2002) outline a framework for analysing<br />
the uncertainty of residual value for assets, such as power generation facilities, for which few data points exists.
2.1. INTRODUCTION 39<br />
to set the most accurate residual value ; Basel 2 requirements 6 calculation of reserves. Studies<br />
evaluate Basel 2 accuracy, and reserve calculation in relation to speci…c credit risk in the leasing<br />
industry, and <strong>Le</strong>asing Contract Valuation 7 ; in the valuation analysis, the residual value risk<br />
is inclu<strong>de</strong>d through an American option. It allows a comparison of leasing (…nancial lease and<br />
operating lease) v.s. purchase <strong>de</strong>cision. Unfortunately, it does not aim to hedge the speci…c<br />
Residual value risk, let-alone the correlation issue in a portfolio of equipment.<br />
A lack of <strong>de</strong>velopment on …nancial products hedging residual value risk lead my research<br />
to credit risk. The recent important contributions in …nance mo<strong>de</strong>lling and in new …nancial<br />
products were in credit <strong>de</strong>rivatives. This implies a change in credit management involving<br />
banks and other …nancial institutions. A credit <strong>de</strong>rivative is a contract between two parties<br />
that allows the use of a <strong>de</strong>rivative instrument to transfer credit risk from one party to another.<br />
The risk seller has to pay a fee to the risk buyer who will take the risk. Over the last ten years,<br />
the credit <strong>de</strong>rivative market has faced a substantial increase. A lot of credit risk mo<strong>de</strong>ls have<br />
been <strong>de</strong>veloped, therefore increasing investor interest 8 .<br />
In 2000, Li‘s Gaussian copula mo<strong>de</strong>l 9 facilitated a dramatic success of this <strong>de</strong>rivative sector.<br />
He proposed a fairly easy, and intuitive mo<strong>de</strong>l <strong>de</strong>picting the payment <strong>de</strong>fault of a company like<br />
the survival probability of a human life 10 . It was also a new tool to evaluate the ongoing<br />
issue of credit risk ; i.e. correlation. For instance, in a basket of loans there is an individual<br />
risk component. Each loan has a risk to <strong>de</strong>fault its payment. The systemic risk is the other<br />
component. An economic downturn could also impact the whole portfolio, and the systemic<br />
risk implies correlation.<br />
6 Schmit produced several articles on Credit risk in leasing industry to analyse Basel 2 requirements accuracy.<br />
See Schmit (2003), Schmit (2004), Irotte, Schmit, and Vaessen (2004), Laurent and Schmit (2007).<br />
7 T. Copeland and J. Weston (1982) apply an American put with a <strong>de</strong>creasing exercise price and S.E Miller<br />
(1995) inclu<strong>de</strong>s an American Call Option in a net present value formula to estimate the internal rate of return<br />
of the <strong>de</strong>al. S.R Grenadier (1995), focusing on the real estate arena, adds a residual value insurance that is<br />
equivalent to a put option on the un<strong>de</strong>rlying asset in the pricing of a variety of leasing contracts.<br />
8 “At the risky end of …nance”The economist (April 21st 2007) gives an up to date on the credit <strong>de</strong>rivatives<br />
market : “According to the Bank for International Settlements, the nominal amount of credit-<strong>de</strong>fault swaps had<br />
reached $20 trillion by June last year. With volumes almost doubling every year since 2000, some reckon the<br />
CDS market will soon be worth more than $30 trillion”.<br />
9 See Li (2000).<br />
10 In “Gaussian copula and credit <strong>de</strong>rivatives”the Wall Street Journal (September 12, 2005) tells the story of<br />
David Li discovery and his impact on …nancial markets.
40 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
Collateralized Debt Obligation (CDO) turns the correlation problem into a solution. It is<br />
a credit <strong>de</strong>rivative created from a portfolio of <strong>de</strong>bt instruments 11 . The risk seller transfers<br />
the risk implying that the risk buyer takes the risk. Of course, the risk seller has to pay<br />
a fee to the risk buyer. The CDO became a successful product by allowing the credit risk<br />
division among di¤erent tranches. Synthetic CDOs 12 , in particular, were booming, improving<br />
liquidity, and allowing corporate bonds to be sliced and diced on the basis of risk. Investors<br />
were able to choose di¤erent levels of risk and returns 13 . The growth was so huge that it had a<br />
global macroeconomic impact, <strong>de</strong>creasing the risk of <strong>de</strong>fault impact, in‡ating asset prices and<br />
narrowing credit spreads 14 . Prior to summer 2007, there was up to 30% of banking investment<br />
pro…t.<br />
From that time, all products have slumped sud<strong>de</strong>nly in value due to fraud, and low quality<br />
loan un<strong>de</strong>rwriting. The "credit crunch" allowed i<strong>de</strong>nti…cation of several weaknesses in the in-<br />
dustry of loan securitization. Severing the link between borrowers and risk takers, it promoted<br />
a lack of accountability. In addition, market protagonists contributed to a credit bubble 15 . In-<br />
vestors did not fully un<strong>de</strong>rstand the products and had an over reliance on ratings provi<strong>de</strong>d by<br />
specialized agencies. Moreover, some securities were poorly structured. Thereby, on a cleared<br />
market with more incentives, some experts are hoping for a recovery. Fortunately, securitization<br />
is not con…ned to consumer or corporate loans.<br />
Residual value risk and credit risk have a clear analogy, constituting of units that are more<br />
or less risky. A lease portfolio is similar to a loan portfolio, both could be divi<strong>de</strong>d into systematic<br />
and idiosyncratic risks. Losses occur when certain events happen, and again, the correlation<br />
risk has a huge impact. Hedging a portfolio of leasing equipment using <strong>de</strong>rivative securities is<br />
11 Collateralized <strong>de</strong>bt obligations divi<strong>de</strong> the credit risk among di¤erent tranches : First senior tranches (rated<br />
AAA), second mezzanine tranches (AA to BB), and …nally equity tranches (unrated). Losses are applied in<br />
reverse or<strong>de</strong>r of seniority. Therefore junior tranches o¤er higher coupons to compensate for the ad<strong>de</strong>d risk.<br />
12 Synthetic CDOs do not own cash assets like bonds or loans. Using credit <strong>de</strong>fault swaps (a <strong>de</strong>rivatives<br />
instrument), synthetic CDOs gain credit exposure to a portfolio of …xed income assets without owning those<br />
assets.<br />
13 See Hull (2005).<br />
14 « La multiplication <strong>de</strong>s émissions <strong>de</strong> CDO semble avoir contribué au resserrement prononcé <strong>de</strong> spreads<br />
intervenu au cours <strong>de</strong> ces <strong>de</strong>ux <strong>de</strong>rnières années sur l’ensemble <strong>de</strong>s marchés <strong>de</strong> crédit » . Cousseran and Rahmouni<br />
(2006). See also “At the risky end of …nance”The economist (April 21st 2007).<br />
15 “Fear and loathing, and a hint of hope”The economist (February 14th 2008).
2.1. INTRODUCTION 41<br />
attractive, and the i<strong>de</strong>a to use some of the signi…cant <strong>de</strong>velopments in Credit risk mo<strong>de</strong>lling is<br />
attractive as well.<br />
Therefore the aim of this chapter is to transfer a mo<strong>de</strong>l from the credit risk to the residual<br />
risk. The one factor mo<strong>de</strong>l is presented and modi…ed. This modi…cation allows the creation<br />
of a new product, the Collateralized Residual Value. Pykhtin and Dev (2003), …rst applied<br />
the one factor mo<strong>de</strong>l to auto lease. They calculated the economic loss associated to residual<br />
risk, leading to an estimate on economic capital. The mo<strong>de</strong>l was constructed and modi…ed for<br />
…nancial lease with the option to buy out (the lessee has a purchase option at the end of the<br />
contract). Moreover, loss distribution was calculated for a …ne grained portfolio (speci…c to<br />
large portfolio without signi…cant individual exposure), as a result, the mo<strong>de</strong>l was only driven<br />
by the systematic factor.<br />
Our study is somewhat di¤erent, as we aim to hedge residual risk using a <strong>de</strong>rivative …nancial<br />
product. This second chapter is inten<strong>de</strong>d for people within the leasing industry interested by<br />
an innovative …nancial product, as well as people from the …nancial market concerned by<br />
leasing risk opportunities. More speci…cally, we aim to hedge risk for a classical European<br />
contract. The product should cover operating lease contracts on a <strong>de</strong>…ned number of units and<br />
<strong>de</strong>…ned characteristics equipment parameters. We complete this theoretical <strong>de</strong>velopment by an<br />
empirical analysis in which we confront this new <strong>de</strong>rivative with market reality. The rest of the<br />
chapter is organized as follows : Sections 2 and 3 provi<strong>de</strong> some backgrounds on residual value<br />
risk and CDO pricing ; Section 4 <strong>de</strong>scribes the mo<strong>de</strong>l and the …nancial product ; Section 5 is<br />
<strong>de</strong>voted to the empirical analysis and Section 6 conclu<strong>de</strong>s.
42 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
2.2 <strong>Le</strong>asing<br />
The initial i<strong>de</strong>a of leasing is that it is the use of equipment in a business which produces<br />
bene…ts, not the ownership. One characteristic of ownership in leasing contract is the residual<br />
value risk that generates competitiveness or losses.<br />
2.2.1 Main characteristics<br />
As previously mentioned, a lease 16 is a contract between two parties where a party (the<br />
lessor) provi<strong>de</strong>s equipment for usage on a speci…c period of time to another party (the lessee)<br />
for speci…ed payment. Three parties are involved in the process : equipment suppliers, lessors<br />
and lessees. The lessor is the party that grants the use of the asset to the lessee. The lessee is<br />
the party that obtains the use of the asset from the lessor. The lessor purchases the equipment<br />
to the supplier. All along the contract, the lessor has the legal ownership of the asset. To use<br />
the asset, the lessee makes periodic payments to the lessor at an agreed rate of interest.<br />
There are two families of lease contracts. An operating lease can be consi<strong>de</strong>red as a typical<br />
rental allowing the lessee to use an asset without owning it. A …nancial lease aims to transfer<br />
all risks and rewards of ownership to the lessee.<br />
A lease is <strong>de</strong>…ned as a …nancial lease if it contains one of the following elements :<br />
- The ownership of the asset is transferred to the lessee by the end of the lease term.<br />
- The lessee has an end of contract option to buy the asset lower than the fair market value.<br />
- Whether the asset is transferred or not, the lease period is for a majority of the asset<br />
useful life.<br />
- Because of the specialized nature of the asset, the lessee only can use the equipment<br />
16 <strong>Le</strong>asing <strong>de</strong>…nitions and legislations are quite di¤erent from a country to another. As we do not wish to focus<br />
on a speci…c legislation, <strong>de</strong>…nitions are ma<strong>de</strong> on an international common perspective.
2.2. LEASING 43<br />
without major modi…cation.<br />
Otherwise, it is an operating lease 17 .<br />
A lease is a …nancial instrument for the procurement of equipment. Recovery rate on a lease<br />
is higher than on a standard loan. But why do enterprises lease ? Regarding large …rms, leasing<br />
minimizes the after tax cost of their capital. For small asset base companies, leasing increases<br />
access to equipment …nance. The inherent value of the purchased asset acts as collateral. The<br />
lessor is the owner of the equipment, and then is secured by the collateral. Another attractive-<br />
ness is the leasing companies expertise. <strong>Le</strong>asing companies are not only intermediaries. Their<br />
expertise is a real ad<strong>de</strong>d value in the leasing process. They have knowledge of the asset. They<br />
select the appropriate equipment based on the ability of the asset to contribute to cash ‡ow<br />
(through various parameters like equipment characteristics, economic life of the asset, taxes or<br />
residual value risk). <strong>Le</strong>asing companies have also skills in …nance, credit, equipment acquisition<br />
and <strong>de</strong>aling. All things consi<strong>de</strong>red, they facilitate the ‡ow between equipment suppliers and<br />
equipment users.<br />
On lessor si<strong>de</strong>, there are several key elements :<br />
- Asset leased : Used by the lessee for business purpose, it could be any kind of equipment<br />
(i.e. printers, trucks...)<br />
- Asset list price : The lessor is usually able to negotiate rebates and the lessee could be<br />
part of the acquisition process.<br />
- <strong>Le</strong>ase period : It is a pre requisite agreement between the parties. According to the contract,<br />
it could be ‡exible.<br />
- End of term options : At the end of the contract, there are options allowed to the lessee ;<br />
<strong>Le</strong>ase period can be exten<strong>de</strong>d, lease can be renewed, equipment can be bought or returned.<br />
17 In the next sections, we propose a mo<strong>de</strong>l to hedge residual value risk on an operating lease that is the most<br />
common contract in Europe for Auto <strong>Le</strong>ase. The mo<strong>de</strong>l can be exten<strong>de</strong>d and modi…ed for a …nancial lease (see<br />
Pykhtin and Dev (2003)).
44 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
- Residual value : The lessor forecasts the market value of the asset at the end of the contract.<br />
- Depreciation : It might be seen as the variance between the List price and the Residual<br />
value all along the lease period.<br />
- <strong>Le</strong>ase payment : As illustrated by Figure 1, several features are inclu<strong>de</strong>d in payments ma<strong>de</strong><br />
by the lessee during the contract : <strong>de</strong>preciation of the asset (usually the larger component),<br />
interests on the lessor investment, servicing charges (including operation cost, insurances, coun-<br />
selling, repairs...).<br />
Figure 1 : <strong>Le</strong>ase rental calculation<br />
2.2.2 Residual value risk versus competitiveness<br />
The residual value risk corresponds to the fact that the lessor faces the risk to not being<br />
able to recover su¢ cient capital value from the resale or disposal of the asset. As illustrated by<br />
Figure 2, the fair market value curve implies a gain on sale or a loss on sale <strong>de</strong>pending on the
2.2. LEASING 45<br />
level of the residual value.<br />
Figure 2 : Depreciation curve<br />
Therefore the lessor faces a dilemma : The higher the residual value, the higher the risk of<br />
loss on sale. But the higher the residual value, the higher the rental payment. At the same time,<br />
the higher the rental payment, the worse the competitiveness. Conversely the higher the residual<br />
value risk, the better the competitiveness. Figure 3 displays the mechanism of competitiveness<br />
and sales results at the end of the contract.
46 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
Figure 3 : Dynamical bene…ts<br />
In others words, the lessor has to set a residual value to minimizing residual value risk<br />
and maximizing competitiveness. A solution would be the use of a …nancial product. Hedging<br />
residual value risk could be done through a security <strong>de</strong>rivative. Security <strong>de</strong>…nition inclu<strong>de</strong>s<br />
…nancial security (bond, stock) but also capital market securities (mortgage, long-term bonds).<br />
It is an investment instrument which o¤ers evi<strong>de</strong>nce of <strong>de</strong>bt or equity. A security <strong>de</strong>rivative is<br />
a …nancial security whose value is <strong>de</strong>rived in part from the value and characteristics of another<br />
security, the un<strong>de</strong>rlying asset 18 . It would allow the lessor to transfer the risk to a fourth party<br />
(i.e. insurance company, …nancial market...).<br />
18 Securitization is the process of aggregating similar securities that can be transferred or <strong>de</strong>livered to another<br />
party.
2.3. MODEL PRE REQUISITES 47<br />
2.3 Mo<strong>de</strong>l pre requisites<br />
Because it allows to create a link of two survival functions, Gaussian Copula is a key element<br />
in our analysis. CDO pricing, <strong>de</strong>fault mo<strong>de</strong>ling, and the one factor mo<strong>de</strong>l are also inherent to<br />
the …nancial product presented in Section 4.<br />
2.3.1 CDO are a subclass of ABS<br />
Asset Backed Securities are securities backed by a pool of assets. ABS inclu<strong>de</strong> various<br />
subclasses ( Commercial Mortgage Backed Securities (CMBS) or credit card ABS...), <strong>de</strong>pending<br />
on the un<strong>de</strong>rlying asset class. Obligations are usually un<strong>de</strong>rlying Collateral Debt Obligations<br />
(CDO). The basic i<strong>de</strong>a of CDO is to pool corporate bonds and selling o¤ pieces of the pool.<br />
A synthetic CDO replaces pool’s bonds by speci…c credit <strong>de</strong>rivatives, Credit Default Swaps<br />
(CDS).<br />
All in all, CDS are triggered by a credit event. A credit event increases the likelihood that<br />
the rating of a bond <strong>de</strong>creases. Consequently, a credit event increases the risk that a bond<br />
issuer will <strong>de</strong>fault, by failing to repay principal and interest in a timely manner. The events<br />
triggering a credit <strong>de</strong>rivative are <strong>de</strong>…ned in a bilateral swap con…rmation. It is a document that<br />
refers to an agreement between the two swap counterparts. There are several standard credit<br />
events that could be referred to in credit <strong>de</strong>rivative transactions : Bankruptcy, Failure to Pay,<br />
Restructuring, Repudiation, Moratorium.<br />
By selling a CDS, an investor can take exposure to an individual credit. He is receiving<br />
periodic payment from his client. At the same time, however, he has to pay contigent payment<br />
when <strong>de</strong>fault occurs. The client, conversely, can hedge individual credit by buying a CDS. He<br />
provi<strong>de</strong>s periodic payment to the client and receives contingent when <strong>de</strong>fault occurs.
48 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
2.3.2 Default, <strong>de</strong>fault, <strong>de</strong>fault....<br />
Default mo<strong>de</strong>ling is about the expected <strong>de</strong>fault payment of an obligor in a bank credit port-<br />
folio. The obligor (or <strong>de</strong>btor) is an individual or company that owes <strong>de</strong>bt to another individual<br />
or company (the creditor). The obligor borrows or issues bonds.<br />
The following framework <strong>de</strong>…nes our mo<strong>de</strong>l. The mo<strong>de</strong>l is un<strong>de</strong>rlaid by a probability space.<br />
This probability space is constituted of three parts. F, a Algebra, is the information available<br />
into a sample space called . Elements of F are the measurable events of the mo<strong>de</strong>l. Events<br />
of <strong>de</strong>fault are measurable. For instance, the event that an obligor survives or <strong>de</strong>faults is a<br />
measurable event. The last element is Pr, a probability measure. Pr(<strong>de</strong>fault) is the probability<br />
of <strong>de</strong>fault. Finally, to summarize, the probability space ( ; F; Pr) is un<strong>de</strong>rlying our mo<strong>de</strong>l.<br />
In survival analysis, T is a random variable <strong>de</strong>noting the time of <strong>de</strong>fault and t are other<br />
di¤erent times. If T > t, then the obligor <strong>de</strong>faults. The survival function, usually <strong>de</strong>noted S is<br />
<strong>de</strong>…ned as S(t) = Pr(T > t). This function must be non increasing : S(t + 1) S(t).<br />
We can now <strong>de</strong>…ne the complement of the survival function. Usually <strong>de</strong>noted F , it is a<br />
lifetime distribution function : F (t) = P r(T t) = 1 S(t). From this concept a <strong>de</strong>fault<br />
rate per unit time can be calculated, the event <strong>de</strong>nsity. Usually <strong>de</strong>noted f, it is the <strong>de</strong>rivative<br />
f(t) = d F (t). dt<br />
All of this allows the <strong>de</strong>…nition of an advanced function, the hazard function. The hazard<br />
function, usually <strong>de</strong>noted , is the event rate at time t conditional until time t or later. It is<br />
given by (t)dt = Pr(t T < t + dt j T > t) = f(t)dt<br />
S(t) = S0 (t)dt<br />
( (t) 0 and S(t) R 1<br />
(t)dt = 1<br />
0<br />
with no continuous or monotonic constraints).<br />
A cumulative hazard function is (t) = R t<br />
0 (u)du.<br />
Because (t) = S0 (t) d , then (t) = S(t) dt S0 (t)<br />
S(t)<br />
and (t) = log S(t).<br />
Several distributions can be used in duration mo<strong>de</strong>ling (usually <strong>de</strong>…ned on R + ), the most<br />
common one being the exponential distribution (S(t) = e t<br />
).
2.3. MODEL PRE REQUISITES 49<br />
2.3.3 Basic elements on Copulas<br />
Why do we use copula ? In a portfolio, credit risks are non in<strong>de</strong>pen<strong>de</strong>nt. Copulas are a<br />
convenient approach to specify a joint distribution of survival times. Using a copula function,<br />
we are able to link the survival function of an obligor to the survival function of another obligor<br />
in a portfolio .<br />
In our mo<strong>de</strong>l, we use copula on a three dimensional perspective. For simpli…cation pur-<br />
pose, we will focus on the bivariate distribution function and the two dimensional copula. The<br />
following results, however, can be exten<strong>de</strong>d to the multivariate case (see Nelsen (2006) and<br />
Vershuere (2006)).<br />
For a "rigorous" copula <strong>de</strong>…nition, we …rst have to <strong>de</strong>…ne the unit square and the concept<br />
of subcopula.<br />
– The unit square I 2 is the product I I where I = [0; 1].<br />
– A two dimensional subcopula is a function C 0 <strong>de</strong>…ned through the four following proper-<br />
ties :<br />
1_ DomC0 = S1 S2 (with S1and S2 are subsets of I containing 0 and 1).<br />
2_ C0 is groun<strong>de</strong>d 19 .<br />
3_ C0 is 2-increasing (for every x1 x2 and y1 y2 , H(x1; y1) H(x2; y2)).<br />
4_ For every u in S1 and every v in S2, C0(u; 1) = u and C0(1; v) = v.<br />
We are now able to <strong>de</strong>…ne a two dimensional copula : It is a two dimensional subcopula C<br />
whose domain is I 2 .<br />
Figure 4 gives an intuitive notion of a two dimensional copula. The graph of a two dimen-<br />
sional copula is a continuous surface within the unit cube I 3 .<br />
19 A function H from S1 S2 is groun<strong>de</strong>d if H(x; a2) = 0 = H(a1; y) for all (x; y) in S1 S2 with a1 and a2<br />
being the last elements of S1 and S2.
50 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
Figure 4 : Two dimensional copula<br />
Two others elements are fundamental in our analysis ; the joint bivariate distribution func-<br />
tion and the Sklar Theorem.<br />
A joint bivariate distribution function is a function H with domain R 2 such that H is<br />
2-increasing :<br />
H(x; 1) = H( 1; y) = 0, and H(+1; +1) = 1. The joint bivariate distribution func-<br />
tion is a key element of the Sklar Theorem : <strong>Le</strong>t H be a joint distribution function with margins<br />
F and G. Then there exists a copula C, such that for all x; y in R, H(x; y) = C(F (x); G(y)):<br />
Furthermore, if F and G are continuous, the copula C is unique. Otherwise C is uniquely <strong>de</strong>ter-<br />
mined on RanF RanG. Conversely, if C is a copula and F and G are distribution functions,<br />
then H is a joint distribution function with margins F and G:<br />
We can now inclu<strong>de</strong> random variables. <strong>Le</strong>t X and Y be random variables with distribution<br />
functions F and G, and joint distribution function H. Then there exists a copula C with<br />
H(x; y) = C(F (x); G(y)). If F and G are continuous, C is unique. Otherwise, C is uniquely
2.3. MODEL PRE REQUISITES 51<br />
<strong>de</strong>termined on RanF RanG.<br />
In a few words, a copula function is a function that links univariate marginal to their full<br />
multivariate distribution : C(u; v) = Pr(u U; v V ). Therefore, using a copula function, we<br />
are able to link the survival function of a credit risk to the survival function of another credit<br />
risk in a portfolio.<br />
2.3.4 Speci…c pre requisites, the Gaussian copula<br />
In the mo<strong>de</strong>l presented in this chapter, we use the Gaussian copula. <strong>Le</strong>t be the bivariate<br />
normal distribution function with correlation coe¢ cient (0 1). The bivariate normal is<br />
a member of the family of elliptically contoured distributions.<br />
1<br />
The <strong>de</strong>nsity function of is (x; y) = p<br />
2 1 2 e(<br />
1<br />
2(1 2 ) (x 2 +y 2 2 xy)) .<br />
The <strong>de</strong>nsities for such distributions have contours that are concentric ellipses with constant<br />
eccentricity.<br />
1 is the inverse of a normal distribution function.<br />
Finally the Gaussian copula is C(u; v) = ( 1 (u); 1 (v); ).<br />
Consequently, variables are jointly elliptically distributed and we can set using a linear<br />
correlation as a measure of <strong>de</strong>pen<strong>de</strong>nce : <strong>Le</strong>t X and Y follow, respectively, the distribution F<br />
and G. They jointly follow the distribution function H. Then the linear correlation for X and<br />
Y is <strong>de</strong>…ned, using u = F (x) and v = G(y) as<br />
= (X; Y ) =<br />
p 1p<br />
V ar(X) V ar(Y )<br />
R 1 R 1<br />
0 0 [C(u; v) uv]dF 1 (u)dG 1 (v).<br />
Another property of the bivariate normal distribution is radially symmetry. A bivariate<br />
normal distribution with parameters x, y, 2 x, 2 y and is radially symmetric about the point<br />
( x, y). It means that H( x + x; y + y) = H( x x; y y).<br />
Using copula, we are able to work on survival function. In<strong>de</strong>ed, for a pair of random variable<br />
with joint distribution function H(H(x; y) = P [X < x; Y < y]), the joint survival function
52 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
copula is given by H(x; y) = P [X > x; Y > y] = 1 H(x; y). The relationship is<br />
H(x; y) = 1 F (x) G(y) + H(x; y) = 1 + F (x) + G(y) + C(1 F (x); 1 G(y)).<br />
In the next section, we assume that the correlation of <strong>de</strong>fault is driven by a common factor<br />
through a Gaussian copula.<br />
2.3.5 The initial one factor mo<strong>de</strong>l is used for CDO pricing<br />
To resume the mo<strong>de</strong>l in one sentence, a …rm <strong>de</strong>faults when its “asset value-like”stochastic<br />
process X, falls below a barrier. X is commonly i<strong>de</strong>nti…ed as the amount of assets and X<br />
the barrier as the amount of liabilities. The …rm <strong>de</strong>faults when the amount of assets is below<br />
the amount of liabilities. The i<strong>de</strong>a was …rst introduced by Merton (1974). He transferred an<br />
option pricing mo<strong>de</strong>l to the credit risk market. Then he applied the Black and Scholes mo<strong>de</strong>l to<br />
credit risk. We present an alternative mo<strong>de</strong>l using copula. Value ad<strong>de</strong>d is in copula ‡exibility to<br />
<strong>de</strong>pen<strong>de</strong>nt variables and copula ability to provi<strong>de</strong> scale invariant measure of association between<br />
random variables. The intuitive aspect of this mo<strong>de</strong>l contributed to the growth of credit risk<br />
market.<br />
The mo<strong>de</strong>l <strong>de</strong>scribed below is the famous standard Gaussian copula <strong>de</strong>veloped by Li (2000)<br />
and exposed 20 by Gibson(2004).<br />
In a reference portfolio of i = 1; :::N credits, for each obligor, <strong>de</strong>fault payment occurs when<br />
xi (reference credit normalized asset value) falls below xi (the threshold).<br />
xi = aiM +<br />
xi has three main components : M, Zi, and ai.<br />
q<br />
(1 a 2 i )Zi (2.1)<br />
M is the common factors a¤ecting all the credits, the systematic risk. Zi is the factor a¤ec-<br />
20 See also Meneguzzo and Vecchiato (2004) for an empirical study of credit <strong>de</strong>rivatives within the copula<br />
framework. Cherubini, Luciano, and Vecchiato (2004) give an overview of copula applications in Finance.
2.3. MODEL PRE REQUISITES 53<br />
ting only credit i. ai is the correlation parameter (0 6 ai 6 1) and <strong>de</strong>…nes <strong>de</strong>fault <strong>de</strong>pen<strong>de</strong>ncy<br />
between companies in the economy. The correlation of asset values between credits i and j is<br />
equal to aiaj. The random variables are assumed to be in<strong>de</strong>pen<strong>de</strong>ntly distributed. Therefore<br />
unconditionally on the systematic risk, <strong>de</strong>fault payments are correlated but conditionally there<br />
are in<strong>de</strong>pen<strong>de</strong>nt.<br />
M, Zi, and xi are zero-mean, unit variance random variables with distribution functions<br />
G(0; 1), Hi(0; 1), and Fi(0; 1). qi(t) is a risk neutral probability that credit i <strong>de</strong>faults before t.<br />
The <strong>de</strong>fault threshold xi is equal to F -1<br />
i (qi(t)).<br />
When does a <strong>de</strong>fault happen ?<br />
A <strong>de</strong>fault happens when xi falls below xi.<br />
But xi falls below xi if F (xi) < qi(t) , xi < F -1<br />
i (qi(t)) , aiM + p 1 a 2 i Zi < F 1 (qi(t))<br />
and …nally Zi < F 1 (qi(t)) aiM p<br />
1 a2 i<br />
Conditional on the value of the factor M, the probability of <strong>de</strong>fault is therefore<br />
qi(t=M) = H 1 ( F 1 (qi(t)) aiM<br />
p ) (2.2)<br />
2 1 ai For any number of <strong>de</strong>faults in a portfolio of N obligors, we have to estimate the probability<br />
of <strong>de</strong>fault on time t and conditional on the common factor M.<br />
Therefore, we set the number of <strong>de</strong>fault distribution using a binomial function 21 .<br />
P N(l; t=M) = l<br />
N qi(t=M) (2.3)<br />
Once we have the conditional <strong>de</strong>fault distribution, we estimate the distribution according<br />
the distribution of M.<br />
21 The number of <strong>de</strong>fault distribution is usually computed through a recursion method (An<strong>de</strong>rsen, Si<strong>de</strong>nius<br />
and Basu (2003) or Hull and White (2004)). In the case of homogeneous credits and for simpli…cation purpose,<br />
a binomial function is simpler and lead to similar results.
54 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
The unconditional <strong>de</strong>fault distribution P N (l; t) can be calculated as<br />
P N (l; t) =<br />
Z 1<br />
1<br />
P N (l; t=M)g(M)dM: (2.4)<br />
In a CDO, the investor is responsible for the interval of loss [L; H]. The expected loss of a<br />
CDO is <strong>de</strong>…ned on [L; H]. We <strong>de</strong>…ne the loss for any <strong>de</strong>fault as A(1 R) with A the notional<br />
amount of credit and R the recovery rate.<br />
The expected loss is<br />
ELi =<br />
NX<br />
P N (l; Ti) max(min(lA (1 R); H) L; 0) (2.5)<br />
l=0<br />
with T i, i = 1; :::; n the periodic payment.<br />
Now, how to price a CDO ?<br />
A CDO contract speci…es two potential cash ‡ow streams : a Contingent leg and Fee leg.<br />
– On the contingent leg si<strong>de</strong>, the protection seller makes one payment only if the reference<br />
credit <strong>de</strong>faults. The amount of a contigent payment is the notional amount multiplied by<br />
(1 R).<br />
The contigent leg is<br />
contigent =<br />
nX<br />
Di(ELi ELi 1) (2.6)<br />
i=1<br />
with Di the risk free discount factor for payment date i (e rt , with r the risk free rate). The<br />
risk free discount factor is usually <strong>de</strong>rived from the risk free interest rate.<br />
– On the …xed leg si<strong>de</strong>, the buyer of protection makes a series of …xed, periodic payments<br />
of CDO premium until the maturity, or until the reference credit <strong>de</strong>faults.
2.4. A MODIFIED MODEL : THE LEASING MODEL 55<br />
The expected present value of the Fee leg is<br />
F ee = s<br />
nX<br />
Di i [(H L) ELi)] (2.7)<br />
i=1<br />
i is the accrual factor for payment date i and s is the spread per annum paid to the tranche<br />
investor ( i Ti Ti 1).<br />
The value of the CDO contract to the tranche investor at any given point of time is the<br />
di¤erence between the present value of the contigent leg and the present value of the …xed leg.<br />
It is the di¤erence between the protection the buyer expects to pay, and the amount he expects<br />
to receive.<br />
– The Mark To Market value of the tranche, from the perspective of the tranche investor is<br />
MT M = F ee Contigent (2.8)<br />
At inception the mark to market is equal to 0, therefore the spread is<br />
s =<br />
nP<br />
Contigent<br />
Di i [(H L) ELi)]<br />
i=1<br />
2.4 A modi…ed mo<strong>de</strong>l : The leasing mo<strong>de</strong>l<br />
(2.9)<br />
From equipment leasing speci…cities and the one factor mo<strong>de</strong>l, we create a residual value<br />
risk mo<strong>de</strong>l. A new product called Collateralized Residual Value (CRV) is adjusted through the<br />
leasing contract parameters.
56 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
2.4.1 There is a similarity between credit risk and residual value<br />
risk. But there are also dissimilarities and speci…cally in Auto<br />
<strong>Le</strong>ase.<br />
The main i<strong>de</strong>a of the leasing mo<strong>de</strong>l is that a portfolio of leased equipment is comparable to<br />
a portfolio of credit. A portfolio with losses on resales is equivalent to a portfolio of credit with<br />
companies <strong>de</strong>faulting.<br />
– As in a CDO, every unit into the lease portfolio, has an idiosyncratic and a systematic<br />
risk ; asset speci…c characteristic impact is resale price (mo<strong>de</strong>l type, obsolescence. . . ). At<br />
the same time, resale price of other assets has a signi…cant impact (bid and ask e¤ect,<br />
downturn on the resale price market, in‡ation etc.. . . ).<br />
There are also dissimilarities :<br />
– First of all, equipment units are resold only one time at the end of the contract, although<br />
for a CDO, there is a risk of <strong>de</strong>fault throughout the contract. Therefore, the mo<strong>de</strong>l<br />
presented in the next section is set for only one period.<br />
– Another dissimilarity (and not the least) is on correlation estimation. Di¤erence is not on<br />
calculation but on data source.<br />
In credit risk, they are four main data sources available :<br />
-Default events that are obviously concrete realization of credit risk. They are rare events<br />
and as a result there are usually few data available. Approximations and aggregation have to<br />
be ma<strong>de</strong> to constitute data bases.<br />
-Companies credit ratings : They are provi<strong>de</strong>d by credit agencies and re‡ect the credit risk<br />
of a company according to experts points of views. By and large, they are ma<strong>de</strong> through balance<br />
sheet and macroeconomic analysis.<br />
-Credit spreads : They re‡ect market perception of credit risk. A large amount of data is<br />
available. But spreads could be impacted by external elements like liquidity
2.4. A MODIFIED MODEL : THE LEASING MODEL 57<br />
-Equity correlation : The factor mo<strong>de</strong>l (cf Section 3), assumes a theoretical link between<br />
equity and credit risk. Correlations are then more easy to compute.<br />
In residual risk, there is one main data source available : for a residual value calculation,<br />
inputs are observations from second hand markets. Correlation estimation of residual value is<br />
based on resale market statistics. Resale prices, asset characteristics and price in<strong>de</strong>x are used<br />
to set mo<strong>de</strong>lization variables. A large amount of data is available.<br />
– The last dissimilarity is on standard <strong>de</strong>…nitions. As multiple factors <strong>de</strong>…ne a resale, there<br />
are issues to <strong>de</strong>…ne resale asset classes or homogeneity prices.<br />
Auto lease is an extreme illustration. The high price level in the automotive second hand<br />
market involves a high residual value level. Combined to a competitive leasing market, the level<br />
of price leads to high risks of loss on sale.<br />
At the same time, automotive is a singular equipment. A car is not only a tool to go<br />
from a place to another. It is also a living place and a symbol. Automotive often re‡ects<br />
driver’s sociological characteristics. The purchase of a vehicle is a sensitive act, even in business.<br />
Therefore, Auto lease is a wi<strong>de</strong> area to analyze. In automotive market multiple factors in‡uence<br />
resale price. A second hand vehicle price is impacted by age (time between registration date<br />
and resale date), mileage (number of kilometers at the end of the contract), damages (i.e.<br />
amount and type ), product life cycle (i.e. new mo<strong>de</strong>l...), make (i.e. Toyota, Renault...), mo<strong>de</strong>l<br />
(i.e. Yaris, Laguna...), version, body type (i.e. break, pick-up...), segment (i.e. small cars...) or<br />
external color. Figure 5 gives an overview. Choices have to be ma<strong>de</strong> to <strong>de</strong>…ne similar assets and<br />
prices (c.f Section 5).
58 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
Figure 5 : Multiple factors of automotive market<br />
2.4.2 Homogeneous equipment type mo<strong>de</strong>l<br />
The initial i<strong>de</strong>a is simple : we use the equipment resale value as the asset value-like xi and<br />
the probability of resale value below residual value (xi
2.4. A MODIFIED MODEL : THE LEASING MODEL 59<br />
loss on resales on unit i<br />
-Xi, M, and Zi are zero-mean, unit variance random variables with distribution functions<br />
Fi(0; 1), G(0; 1), and Hi(0; 1).The random variables are assumed to be in<strong>de</strong>pen<strong>de</strong>ntly distribu-<br />
ted.<br />
At that point, the construction is similar to the credit mo<strong>de</strong>l, but we inclu<strong>de</strong> residual risk.<br />
Resale’s value can be lower than residual value. There is a risk of loss on sale.<br />
Three new elements will have an impact on the leasing adjustment of the mo<strong>de</strong>l.<br />
Vi is the residual value or in other words the expected fair market value. mF MVi is the<br />
historical average fair market value, eF MVi is the historical standard <strong>de</strong>viation.<br />
mF MVi, eF MVi, and Vi are set on a percentage of Lp, List price by unit. As an example,<br />
an asset bought e 10000 and leased for a Residual value of e 5000 has Vi= 50%.<br />
Then residual risk is ad<strong>de</strong>d : Probability of loss at the end of the contract is qi(t). qi(t) is a<br />
variable with mean mF MVi, variance eF MVi, and distribution function Ei(mF MVi; eF MVi)<br />
The probability of loss <strong>de</strong>pends on residual value : qi = Ei(Vi). So <strong>de</strong>fault threshold xi is equal<br />
to F -1<br />
i (qi).<br />
Conditional on the value of the sectorial factor M, the probability of <strong>de</strong>fault is therefore<br />
qi(M) = H 1 ( F 1 (qi) aiM<br />
p ) (2.11)<br />
2 1 ai Again, conditional probability is P N (l; M) = l<br />
N qi(M) and the unconditional probability<br />
can be calculated as P N (l) = R 1<br />
1 P N (l)g(M)dM.<br />
As a result the recovery rate is equal to the probability of loss. By construction the recovery<br />
rate is R = qi. The loss on sale for any unit is (1 R)Lp. Finally, resale price becomes RLp.<br />
Previous elements allow the creation of a …nancial product, inspired by Collateral <strong>de</strong>bts<br />
obligations :
60 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
The Expected loss is<br />
The contigent leg is<br />
EL =<br />
NX<br />
P N(l) max(min(Lpl (1 R); H) L; 0) (2.12)<br />
l=0<br />
The premium leg is again<br />
The spread is again<br />
F ee = s<br />
s =<br />
contigent =<br />
nP<br />
nX<br />
Di(EL) (2.13)<br />
i=1<br />
nX<br />
Di i [(H L) ELi)] (2.7)<br />
i=1<br />
Contigent<br />
Di i [(H L) ELi)]<br />
i=1<br />
(2.9)<br />
2.4.3 Heterogeneous equipment type mo<strong>de</strong>l : a portfolio of three dif-<br />
ferent assets<br />
The mo<strong>de</strong>l is exten<strong>de</strong>d to a portfolio with non similar units. A company ‡eet is commonly<br />
constituted of various car mo<strong>de</strong>ls. In an European leasing contract for medium size European<br />
company, lessee usually request di¤erent categories of cars for an auto lease contract. The ‡eet<br />
is usually divi<strong>de</strong>d into three groups : Executives’cars (usually high brand car), Employee cars<br />
(medium level cars) and Small cars.<br />
4.2).<br />
Basically the construction is similar to the homogeneous equipment type mo<strong>de</strong>l (cf Section
2.4. A MODIFIED MODEL : THE LEASING MODEL 61<br />
Three representative’s vehicles constitute the mo<strong>de</strong>l : Ex, Em and Sm.<br />
Now there are di¤erent types of asset residual values, number of units, List price etc....<br />
V 1i, V 2i,V 3i are residual values for groups 1, 2, 3,<br />
mF MV 1i,mF MV 2i, mF MV 3i, are fair market values historical averages,<br />
eF MV 1i,eF MV 2i,eF MV 3i are historical standard <strong>de</strong>viation historical averages.<br />
mF MV 1i, eF MV 1i, and V 1i are set on a percentage of List price. The recovery rate for<br />
group 1 is R1 = q1i, the loss on sale for any unit is R1(1 Lp1) with Lp1 unit list price. In<strong>de</strong>ed,<br />
resale price is R1Lp1. The principle is the same for others groups.<br />
For each vehicle, asset value is still xi = aiM + p (1 a 2 i )Zi:<br />
For group 1, <strong>de</strong>fault threshold xi is equal to F -1<br />
i (qi) with q1i = Ei(V 1i) and Ei(mF MV 1i; eF MV 1i).<br />
The principle is the same for other groups.<br />
The distribution of the number of <strong>de</strong>faults, conditional on the common factor M, is com-<br />
puted for each group as P N1 (u; M) = u<br />
N1 q1i(M), P N2 (v; M) = v<br />
N2 q2i(M) , P N3 (w; M) =<br />
w<br />
N3 q3i(M) with N1; N2; N3 number of units, P N1 ; P N2 ; P N3 the conditional probabilities, and<br />
u; v; w number of <strong>de</strong>faults for group 1, 2, 3.<br />
EL =<br />
The probability of <strong>de</strong>fault is computed on the whole portfolio.<br />
P N (u; v; w; M) = P N1 (u; M)P N2 (v; M)P N3 (w; M)<br />
The Expected loss is :<br />
NX<br />
P N (u; v; w; M) max(min((Lp1u (1 R1))+(Lp2u (1 R2))+(Lp3u (1 R3)); H) L; 0)<br />
l=0<br />
Premium leg, contigent leg and spread are calculated like in 4.2.<br />
(2.14)
62 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
It is straightforward to generalize this approach to more than three vehicle types.<br />
2.4.4 Collateralized Residual Values<br />
We propose a …nancial product, the Collateralized Residual Value, that covers residual value<br />
risk. We display a sensitivity analysis of the CRV to the main characteristics of the leased asset.<br />
A CRV is a new class of ABS<br />
The Collateralized Residual Values (CRV) is a new class of Asset Backed Securities (ABS).<br />
The CRV is inspired by synthetic Collateralized Debt Obligations (CDO) structure. Like a<br />
CDO, CRV can be sliced and diced, and tranches can be sold. But CRV is not about credit<br />
risk. The purpose is to hedge residual value risk on a portfolio of leases. A credit <strong>de</strong>rivatives,<br />
obviously, is more accurate to hedge credit risk in a portfolio of contract.<br />
Sensitivity Analysis on a CRV<br />
What is the sensitivity of a CRV to size, residual value, and fair market variance ?<br />
In the following sensibility analysis, all un<strong>de</strong>rlying reference assets are cars. The portfolio is<br />
homogeneous. List price (e 15000), Fair market value (e 4500) and Correlation ( p 0:3) by car<br />
are equal. Cars are leased on a three years contract.<br />
We value four tranches of the CRV. The …rst tranche absorbs all losses until the …rst 25%<br />
of the portfolio, the second tranche until 50%, the third tranche until 75% and the fourth until<br />
100%.
2.4. A MODIFIED MODEL : THE LEASING MODEL 63<br />
Impact of Fleet Size<br />
Table 1 : Sensitivity to ‡eet size<br />
Table 1 shows that the buyer of protection on a ‡eet of 600 units should be willing to pay<br />
125,21 basis points to hedge the …rst 50% losses using a CRV. According to our results, the<br />
spread is stable until 500 units. Then the increasing size reduces the cost of protection. An<br />
increase in size reduces idiosyncratic e¤ects. There is a diversi…cation of risk.
64 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
Impact of Residual Value level<br />
Table 2 : Sensitivity to residual value<br />
The higher the residual value, the higher the pricing of CRV (Table 2). As illustrated in<br />
Section 2.2, <strong>de</strong>creasing residual value reduces the risk of loss on sales.
2.4. A MODIFIED MODEL : THE LEASING MODEL 65<br />
Impact of Fair Market Value variance<br />
Table 3 : Sensitivity to fair market value variance<br />
Fair market value distribution tails <strong>de</strong>pends of FMV variance (Table 3). For an higher<br />
variance, tail are larger. As a result, the spread is an increasing function of the variance.
66 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
2.5 Empirical analysis<br />
The mo<strong>de</strong>l is applied to a six years historic resale’s portfolio. The observations, between 2000<br />
and 2008, are from a major European leasing company (General Electric Capital Solutions). We<br />
…rst estimate the correlation of assets to a common factor. Then fair market value parameters<br />
and residual value are estimated.<br />
2.5.1 Correlation to the one sector factor<br />
According to section 4.2, we have to set the linear correlation (ai) between the portfolio<br />
and a sectorial factor a¤ecting equipment units on resale’s market (M). The sectorial factor is<br />
assessed using Eurostat Harmonized Consumer Price in<strong>de</strong>x (HCPI 22 ). The in<strong>de</strong>x Purchase of<br />
vehicles price allows comparison within European markets. Additionally, a portfolio in<strong>de</strong>x has<br />
to be created. The portfolio in<strong>de</strong>x provi<strong>de</strong>s a non-biased historical trend analysis and exposes<br />
portfolio sale price at di¤erent times.<br />
Automotive Price In<strong>de</strong>x<br />
To set a common factor that would a¤ect the whole portfolio, several HCPIs are available ;<br />
HCPI all items, HCPI Energy, HCPI Petroleum products, HCPI Road transport equipment.<br />
The In<strong>de</strong>x "Purchase of vehicle" (Figure 6) appears to be the most relevant. It covers purchases<br />
of new vehicles and purchases of second-hand vehicles from other institutional sectors. It is<br />
available by country and on European level. This in<strong>de</strong>x is inclu<strong>de</strong>d in the mo<strong>de</strong>lization as the<br />
sectorial factor indicator (M). Vehicle customers have to choose between resale market and new<br />
market. As a consequence, resale market is strongly impacted by new vehicle market. Therefore,<br />
a positive or a negative correlation of the sectorial in<strong>de</strong>x with the portfolio can be expected.<br />
22 Graphics of HCPI series are reported in Appendix.
2.5. EMPIRICAL ANALYSIS 67<br />
Figure 6 : European HCPI<br />
Portfolio In<strong>de</strong>x Creation and Computation<br />
A large amount of parameters impacts resale price and there is a non homogeneity of<br />
the portfolio mix from one month to another. As a consequence, average price never re‡ects<br />
accurately portfolio sales price variance through time. Therefore a consistent price variable<br />
is created through an in<strong>de</strong>x replicating a same arti…cial portfolio. The i<strong>de</strong>a is to replicate a<br />
portfolio mix to allow time series analysis.<br />
Portfolio In<strong>de</strong>x Creation The information comes from resale vehicles statistics from 01/2000<br />
to 01/2008 including France, Germany, Italy, Portugal, Spain and Swe<strong>de</strong>n. We only inclu<strong>de</strong> nor-<br />
mal termination sales (sales types like wrecks or litigations are exclu<strong>de</strong>d). Observations with<br />
extreme and incorrect values are cleaned. High damages (95th <strong>de</strong>cile by country) that would<br />
alter resale’s price and therefore are …ltered.<br />
Calculation is a …ve-steps process :<br />
1. Creation of buckets for Age and Mileage (<strong>de</strong>tails in appendix).
68 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
2. Keys are created including the following components :<br />
age=mileage=mo<strong>de</strong>l=fiscalclass=fueltype=country.<br />
3. Keys with population of less than 100 units on the whole history are exclu<strong>de</strong>d.<br />
(e.g.GBR=T oyota=previa=private=lightgoods=petrol=_6:33; 39month=_3:75000; 105000km<br />
is exclu<strong>de</strong>d. During the last 8 years, less than 100 units in this bucket have been sold.)<br />
4. Representative and similar samples are created all along the history using the historical<br />
key frequency. A Random selection is processed by month through the following criteria : -1%<br />
of units by bucket are selected (e.g. for a bucket of 200 units, then 2 units are selected), -<br />
Restricted random sampling with replacement (SAS proc survey), -Priority levels : The sample<br />
is replicated on a monthly basis according to key frequency and by or<strong>de</strong>r of priority ; selected<br />
month, semester of the selected month, whole history (e.g. If data are not available in the<br />
current month, then data are selected in the current quarter etc...).<br />
is<br />
5. A monthly resale percentage is computed from the sample. The percentage of resale<br />
resaleprice<br />
. It allows a comparison of resale performance between vehicles with<br />
Listprice+OptionListprice<br />
di¤erent levels of price and option price.<br />
The process is replicated several time to create several sample. 1000 random samples are<br />
created by month.
2.5. EMPIRICAL ANALYSIS 69<br />
Portfolio In<strong>de</strong>x Computation and results 565 representative buckets are selected from<br />
an initial pool of 38257 units. 97000 samples are calculated (97 periods).<br />
Among other perspective, it provi<strong>de</strong>s a graph distribution by month. Results are available<br />
by country and on European level. For instance, Figure 7 displays the simulation result for<br />
Portugal on January 2001. The percentage of resale distribution is on a range of [49%-72%].<br />
Figure 7 : Portugal <strong>de</strong>preciation distribution on January 2001<br />
Estimation of the correlation between the sectorial factor and the portfolio price<br />
Time series are seasonally adjusted using the TRAMO-SEATS methodology 23 . Graphical results<br />
by countries are displayed in Appendix.<br />
23 TRAMO-SEATS : They consist of new versions of programs TRAMO, "Time series Regression with ARIMA<br />
noise, Missing values and Outliers", and SEATS, "Signal Extraction in ARIMA Time Series", created by Gómez<br />
and Maravall in 1996, of program TERROR, "TRAMO for Errors", and program TSW, a Windows version<br />
of TRAMO-SEATS with some modi…cations and additions, <strong>de</strong>veloped by G. Caporello and A. Maravall at the<br />
Banco <strong>de</strong> España.
70 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
Figure 8 : European HCPI and European portfolio YoY variance<br />
Figure 8 illustrates results for Europe. The European HCPI is more stable than the European<br />
Portfolio YoY variance value.<br />
A Pearson’s product moment is computed on a year on year annual variance, and results<br />
are given in table 4.<br />
Table 4 : Pearson Product moment on year on year annual variance<br />
As expected, results are di¤erent by country. Correlation are negative or positive with<br />
di¤erent levels of intensity. Impacts are negative for Germany, France and Italy. If "Purchase<br />
of vehicle" HCPI increases, then the resale portfolio performance <strong>de</strong>creases. Therefore unlike<br />
the initial credit mo<strong>de</strong>l, the correlation parameter could be negative ( 1 6 ai 6 1).
2.5. EMPIRICAL ANALYSIS 71<br />
2.5.2 Fair Market Value and Residual Value setting<br />
mF MVi, average fair market value, eF MVi, standard <strong>de</strong>viation and residual value (Vi) are<br />
parameters to inclu<strong>de</strong> in the mo<strong>de</strong>l.<br />
Fair Market Value estimation is complex We assess the Fair Market value at the end of<br />
the contract. In others words, we estimate the <strong>de</strong>preciation of the asset for the next years.<br />
Resale percentage Mean and Variance of resale percentage are calculated from historical<br />
statistics. For simpli…cation purpose, resale price is computed through a percentage of List<br />
resaleprice<br />
Price ( Listprice+OptionListprice ).<br />
FMV subtlety To illustrate our presentation we focus on a speci…c Key : PEUGEOT 307<br />
Tourisme Diesel _6.]33,39]month _4.]105000,145000]km _FRA.<br />
Figure 9 : 36 months contracts / Peugeot 307 <strong>de</strong>preciation and historical average<br />
Figure 9 shows the time series <strong>de</strong>preciation of the key. It also shows the historical average<br />
<strong>de</strong>preciation. Since January 2004, the key average <strong>de</strong>preciation is 37.26% and the standard<br />
<strong>de</strong>viation is 46.76%.
72 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
Figure 10 : 24 months contracts and 36 months contracts <strong>de</strong>preciations<br />
Figure 10 compares the <strong>de</strong>preciation with a 24 months Key : PEUGEOT 307 Tourisme<br />
Diesel _6.]21,27]month _4.]105000,145000]km _FRA .<br />
Figure 11 : Peugeot 306 and Peugeot 307<br />
Figure 11 is a graphic of Peugeot 306 24 and Peugeot 307 <strong>de</strong>preciation : PEUGEOT 306<br />
Tourisme Diesel _6.]33,39]month _4.]105000,145000]km _FRA.<br />
Previous graphics illustrate the fact that FMV is not a constant value. There are trends and<br />
cycles that are not straightforward to i<strong>de</strong>ntify. Depreciation in the value of a car occurs based<br />
24 Peugeot 306 is the previous mo<strong>de</strong>l version of Peugeot 307.
2.5. EMPIRICAL ANALYSIS 73<br />
on a range of factors. The factors inclu<strong>de</strong> cars condition, kilometers traveled and brand repu-<br />
tation. Moreover, brand reputation contains mechanics and popularity. Consequently, di¤erent<br />
methodologies are possible to forecast average fair market value.<br />
<strong>Le</strong>asing industry usually works with internal mo<strong>de</strong>lization. Standard mo<strong>de</strong>ls have insi<strong>de</strong> a<br />
mo<strong>de</strong>l life cycle and a segment analysis. New legislations or macroeconomic impacts also are<br />
sometime inclu<strong>de</strong>d. Additionally, external companies (Eurotax, X-ray, Cap) provi<strong>de</strong>s forecasted<br />
FMV. Forecasts are based on market data, mo<strong>de</strong>lization and expertise.
74 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
RV and FMV, a new perspective<br />
In an operating lease contract, Residual value is <strong>de</strong>…ned as the forecasted fair market value.<br />
It is an input in rental calculation. It also drives the risk of loss on sales at the end of the<br />
contract. What is the impact of a CRV ?<br />
Elements of the contract become di¤erent. Using securitization product, elements of the<br />
contract have to be re<strong>de</strong>…ned. The fair market value still has to be forecasted. But residual<br />
value is now a threshold. As illustrated in Figure 12, the threshold is a level of risk chosen by<br />
the lessor and the lessee. In the mo<strong>de</strong>l, mF MV is a forecasted average of fair market value at<br />
the end of the contract. And eF MVi is the estimated standard <strong>de</strong>viation of fair market value.<br />
So the consi<strong>de</strong>red residual value is now an adjustment variable. Therefore the securitization<br />
product allows several choices within di¤erent levels of risk, di¤erent levels of rents, di¤erent<br />
market spreads, and di¤erent fair market value variances. Additionally, hedging can be ma<strong>de</strong><br />
on speci…c tranches.<br />
Figure 12 : Sale results through fair market value and residual value level
2.5. EMPIRICAL ANALYSIS 75<br />
For simpli…cation purpose, the threshold is set at mF MV value in the next illustration. It<br />
means that the contract position is neither conservative or risk taking.<br />
Six CRV<br />
Table 5 : Pricing of six CRV<br />
A CRV is built accordingly to leasing contract characteristic. As illustrated in Table 5 for<br />
six CRV, inputs in pricing are population size, list price, fair market value mean, fair market<br />
value variance and residual value. Through the selected residual value level and tranches limits,<br />
lessor and lessee can choose a level of risk. Moreover, in case of negative correlation parameter,<br />
CRV could go against a downturn in the sectorial market and create opportunities for risk<br />
diversi…cation. Like standards <strong>de</strong>rivatives, CRV allows insurance or hedging for the lessor and,<br />
for the buyer taking opposite position in the …nancial market, speculation or arbitrary.
76 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
2.6 Conclusion<br />
Li Gaussian copula mo<strong>de</strong>l, initially used for credit risk, is transposed in residual value risk<br />
of the leasing industry. The Collateralized Residual Value (CRV), a new <strong>de</strong>rivative product, is<br />
proposed. Pooling together a large portfolio of equipment that has been leased, the <strong>de</strong>rivative<br />
converts end of contract risks into an instrument that may be sold in the capital market. As a<br />
standard <strong>de</strong>rivative, it is a tool that transfers risk, and can be used for hedging or speculation.<br />
Moreover, it allows the lessor and lessee to select their <strong>de</strong>gree of exposure to residual value risk<br />
and to improve competitiveness. As a result, the mo<strong>de</strong>l is a contribution geared for people from<br />
the leasing industry interested by an innovative …nancial product, as well as people from the<br />
…nancial market concerned by leasing risk opportunities.<br />
The present analysis could be exten<strong>de</strong>d in various ways. The accuracy of the correlation<br />
parameter can be improved by a complete macroeconomic analysis, and the fair market value<br />
parameter can also be improved. Finally, other families of copula could be tested.
2.7. APPENDIX 77<br />
2.7 Appendix<br />
Figure 13<br />
Figure 14
78 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES<br />
Figure 15 : HCPI YoY variance<br />
Figure 16 : HCPI YoY variance
2.7. APPENDIX 79<br />
Figure 17 : Age and Mileage buckets
80 CHAPITRE 2. HEDGING RESIDUAL VALUE RISK USING DERIVATIVES
Chapitre 3<br />
A Family Hitch<br />
Econometrics of the New and the Used Car Markets<br />
81
82 CHAPITRE 3. A FAMILY HITCH<br />
3.1 Introduction<br />
Apples are non-durable goods. Out of the new market, they have no value. On the contrary,<br />
cars are durable goods. They are usually bought with the intention to be used for a limited<br />
time and then re-sold. A car owner can choose for a duration, and then re-sell the vehicle<br />
on a well <strong>de</strong>veloped secondary market. Thanks to the durability of the car, drivers can re-<br />
sell cars to each other, and buy new or used vehicles. Durability creates speci…c dynamics of<br />
overlapping generations of durable goods that are not present in non-durable markets, and<br />
brings the question of the interaction between primary and secondary markets.<br />
We aim to i<strong>de</strong>ntify the relationship between new and used car markets in or<strong>de</strong>r to forecast<br />
car prices. For various industries the future car prices are of special interest. In<strong>de</strong>ed, among<br />
other things, used car market prices directly a¤ect leasing companies losses and bene…ts.<br />
The third chapter is organized as follows. Section 2 reviews the literature related to the<br />
inter<strong>de</strong>pen<strong>de</strong>nce between primary and secondary markets, speci…cally in the automotive sector.<br />
Section 3 presents the data and our empirical setting. In Section 4, we empirically evaluate<br />
the inter<strong>de</strong>pen<strong>de</strong>nce between new and used cars for three major markets (France, the United<br />
Kingdom and the U.S.). Section 5 conclu<strong>de</strong>s.<br />
3.2 Aca<strong>de</strong>mic researches in the second-hand market are<br />
legion.<br />
There has been a signi…cant amount of aca<strong>de</strong>mic researches on the subject of durable goods<br />
in the second-hand market. The literature discusses why second-hand markets exist and high-<br />
lights some mechanisms of inter<strong>de</strong>pen<strong>de</strong>nce between new and used markets, especially in the<br />
microeconomy area. It mainly focuses on three related axes of research : the Akerlof e¤ect, the<br />
optimal durability and the time inconsistency. Some researches, like Scitovsky (1994), also exist<br />
into a Keynesian system.
3.2. ACADEMIC RESEARCHES IN THE SECOND-HAND MARKET ARE LEGION. 83<br />
3.2.1 Why secondary markets exist ?<br />
Van Cayseel (1993) provi<strong>de</strong>s a framework : Second-hand markets are institutions <strong>de</strong>aling<br />
with transactions of durable goods 1 , and the durability constitutes their …rst condition of exis-<br />
tence. As a second condition, the good utility needs su¢ cient volatility. For instance, an eco-<br />
nomic <strong>de</strong>preciation 2 could appear if the consumer has no further need of the good or because<br />
the maintenance cost of the car increases 3 . Consequently, the second-hand market re-allocates<br />
goods from agents extracting a low utility to agents extracting a higher one. Mixing the condi-<br />
tion of durability and a possible variance of utility, we can state that the longer the durability,<br />
the higher the probability for an asset to change of valuation. The longer the durability, the<br />
higher the probability for a consumer to drop the asset, and buy another one. The secondary<br />
market could also be a way for some users to drop goods with malfunctions and no functiona-<br />
lity 4 . But dropping ‘lemons’could only be an incentive for a minority of agents, otherwise the<br />
secondary market would collapse.<br />
According to Van Cayseel (1993), the possibility of simultaneity of new and used markets<br />
constitutes the last condition, raising the question of bene…ts and constraints in the second-<br />
hand market for producers. In or<strong>de</strong>r to reduce the risk of competition with new products 5 ,<br />
producers would try to prevent the existence of a secondary market (i.e. by only renting their<br />
equipment or reducing the substitutability between new and used markets). Fortunately, some<br />
incentives to tolerate and to even support a second- hand market, additionally exist for the<br />
producer. The …rst incentive would be the pressure created by other competitors with similar<br />
goods. Following researches on industrial regulation and anti-trust policies, a large amount of<br />
aca<strong>de</strong>mic papers have studied durable goods in a monopolistic market 6 . The incentive could be<br />
a law committing the monopoly to sell his products. The existence of asymmetric information<br />
1 On a broa<strong>de</strong>r <strong>de</strong>…nition of Van Cayseel, the key concept should be not used goods but resales.<br />
2 We are focusing on second-hand markets for automobiles. Most of the time there is a <strong>de</strong>preciation of the<br />
good over time. However, in some markets like art or …nancial product, the secondary market has a higher<br />
valuation than the primary market. Speci…c cars (luxury ones) could also gain value after some years because<br />
of collectors interests.<br />
3 Regarding maintenance, the second hand market could be a way to reallocate used goods with high main-<br />
tenance cost to users who have a better maintenance technology or skills.<br />
4 It brings the problem of adverse selection discussed in the next section.<br />
5 The problem of Time Inconsistency is discussed in section 2.2.<br />
6 See Waldman (2003) for a large review in the microeconomy area.
84 CHAPITRE 3. A FAMILY HITCH<br />
could also restrain the opportunity of leasing, because users are less careful with goods they<br />
do not own. An<strong>de</strong>rson and Ginsburgh (1994), through a microeconomic analysis and un<strong>de</strong>r<br />
a monopolistic assumption, show a bene…cial e¤ect of secondary markets for the producers :<br />
consumer heterogeneous tastes result in a segmented secondary market allowing producers to<br />
establish a system of indirect price discrimination (by setting higher prices, a producer extracts<br />
higher surplus from consumers with higher willingness to pay). In the automotive industry,<br />
manufacturers are selling both new and used cars 7 . They also rent and provi<strong>de</strong> services of<br />
maintenance in or<strong>de</strong>r to bene…t most of the needs related to their products (i.e. …nancing car<br />
ownership through their …nancial branch). Manufacturers aim to collect various revenues from<br />
all available channels.<br />
De…ning the automotive industry as a monopoly would be a strong assumption. Accor-<br />
ding to the ACEA 8 in 2008, more than 15 manufacturers (through more than 43 brands) were<br />
sharing the market in Western Europe, and none of them had more than 21 percent of the<br />
market share. In the US, more than 15 automotive makers are competing and none of them<br />
had more than 15 percent of market share 9 . Pare<strong>de</strong>s (2006) argues that cars are ‘durable ex-<br />
perience goods’. Before buying a car, a consumer can’t evaluate all of its characteristics. As a<br />
consequence, Pare<strong>de</strong>s states that a link exists between consumer loyalty, satisfaction and reten-<br />
tion value. The existence of consumer loyalty (and non loyalty) implies that consumers are able<br />
to choose di¤erent manufacturers and that car markets are not monopolistic. As a conclusion,<br />
an automotive company could only be <strong>de</strong>…ned as a monopoly during the introduction of new<br />
vehicles (i.e. minivans in the US market 10 ). Although we reject a monopolistic assumption, we<br />
take these studies into account by focusing on the highlighted mechanisms of inter<strong>de</strong>pen<strong>de</strong>nce.<br />
Scitovsky (1994) adopts a macroeconomic approach to explain the existence of secondary<br />
markets. He argues that durable goods are valued by the services they provi<strong>de</strong> to the consu-<br />
mers. Because of time and obsolescence, the amount of services inclu<strong>de</strong>d <strong>de</strong>creases. Therefore<br />
the secondary market has two functions : …rst, it mitigates the inequalities by allowing poor<br />
customers to buy a cheaper bundle of services to richer ones. Second, it stimulates the economy<br />
7 usually through franchise <strong>de</strong>aler.<br />
8 European Automobile Manufacturers’Association :<br />
www.acea.be/in<strong>de</strong>x.php/news/news_<strong>de</strong>tail/new_vehicle_registrations_by_manufacturer/<br />
9 Source : CRS report for congress.<br />
10 See Petrin (2002).
3.2. ACADEMIC RESEARCHES IN THE SECOND-HAND MARKET ARE LEGION. 85<br />
by facilitating the replacement of obsolete durable goods. Scitovsky’s theory explains why there<br />
are bigger proportions of second-hand markets (i.e. clothes, household appliances) in <strong>de</strong>veloping<br />
countries. But used car markets have a signi…cant size in countries with high standard of living.<br />
In<strong>de</strong>ed, automobiles are relatively expensive and, by increasing the price span, the second-hand<br />
market allows most of people to a¤ord a car. The empirical analysis of Cleri<strong>de</strong>s (1998) on the<br />
welfare e¤ects of tra<strong>de</strong> liberalization 11 in 1993 (by permitting the importation of Japanese cars<br />
in Cyprius second-hand market) con…rms Scitovsky’s opinion. Cleri<strong>de</strong>s conclu<strong>de</strong>s of signi…cant<br />
gains that bene…ted predominantly for low-income consumers because of an increase in product<br />
variety.<br />
3.2.2 The Akerlof e¤ect and the car durability are linked.<br />
The main area of research on durable goods comes from the most famous analysis on auto-<br />
motive second-hand market. Akerlof (1970) explained why used car valuation is so much lower<br />
than new car valuation. The automotive resale market is a¤ected by something called the ’le-<br />
mon e¤ect’. A used car has a probability to be of a good quality or a bad one (i.e. lemon), and<br />
the uncertainty on quality implies a price adjustment. In the resale market, there is an asym-<br />
metry of information ; the car owner has a better knowledge of the probability of bad lemons. If<br />
second-hand vehicles were valued like as new vehicles, then it would attract lemons (sellers of<br />
lemons would have the opportunity to sale their vehicles and buy a new one on the new vehicle<br />
market) and it would create an arbitraging opportunity. Akerlof used the automotive market<br />
as a best illustration and exten<strong>de</strong>d his i<strong>de</strong>a to other markets (the cost of dishonesty...).<br />
The Akerlof’s article helps to un<strong>de</strong>rstand why an adverse selection happens, as well as the<br />
large variance and the trends between new and second-hand prices. But some elements of the<br />
article have to be discussed.<br />
First, the in‡uence of new markets misses in the analysis. Hen<strong>de</strong>l and Lizzeri (1999a) built a<br />
microeconomic mo<strong>de</strong>l including a primary market and according to their conclusions, a su¢ cient<br />
level of tra<strong>de</strong> could reduce the adverse selection. Moreover, buying new cars and selling used<br />
cars are complementary activities : even if they give higher valuation to their used units, owners<br />
11 In spite of the limitation of the study focusing on a country without a national automotive industry.
86 CHAPITRE 3. A FAMILY HITCH<br />
…nd optimal to sell their good quality cars ; once their used car has been sold, owners place a<br />
higher value on purchasing a new car. Finally, Hen<strong>de</strong>l and Lizzeri argue that new market prices<br />
could be increased thanks to the adverse selection. The …rst explanation would be that a used<br />
good becomes a worse substitute than a new one (in case of an average quality reduction on the<br />
used market). The second reason would be that the buyer of new goods gets an option value<br />
and he or she can <strong>de</strong>ci<strong>de</strong> to keep the high quality realization of the used car.<br />
Empirical analyses give a second perspective. Winand and George (2002) provi<strong>de</strong>d a large<br />
review of empirical tests on the Akerlof e¤ect and in various markets, as well as a speci…c<br />
analysis, in the second-hand car market of a Swiss canton. According to their conclusions,<br />
adverse selections are not always observed or could occur un<strong>de</strong>r a mitigated and non wi<strong>de</strong>spread<br />
form.<br />
Car durability constitutes a third element. An increase of average durability, through the<br />
Akerlof analysis, could have either a negative or a positive e¤ect. A better durability implies<br />
a better quality of cars producing a lower probability of ’lemons’on the second-hand market.<br />
On the other hand, consumers would keep their car longer and it would increase the proportion<br />
of ’lemons’. Whatever the consequence (positive or negative for pro…ts), a manufacturer can<br />
impact the adverse selection e¤ect through guaranteed warranties, buyback or by improving<br />
information on the second-hand vehicles. Similarly, by the beginning of the 90’s, Peach et al.<br />
(1996) noticed an improvement of the information availability on the US second-hand market<br />
and an increase of car durability. At the same time, the used car market experienced an increase<br />
of sales and a¤ordability. All in all, it suggests a positive correlation between quality, durability,<br />
and non-adverse selection.<br />
To conclu<strong>de</strong>, the Akerlof e¤ect and the durability could explain the price trends through<br />
the structure of the market and the inner quality of cars. The questions of quality and optimal<br />
durability are <strong>de</strong>veloped in the next section.
3.2. ACADEMIC RESEARCHES IN THE SECOND-HAND MARKET ARE LEGION. 87<br />
3.2.3 Optimal durability and Time inconsistency are two areas of<br />
research.<br />
Optimal durability constitutes another main area of research in the microeconomic analysis<br />
of durable goods. A non-competitive market might lead to a lower socially e¢ cient durability of<br />
goods in or<strong>de</strong>r to constraint consumers to increase purchase frequency. Sieper and Swan (1973),<br />
however, argue for an absence of durability distortion : monopoly market and competitive<br />
markets will always produce at minimum cost and then consi<strong>de</strong>r the durability as a minor<br />
problem. Some articles, like Hen<strong>de</strong>l and Lizzeri (1999b), contest these outcomes : although used<br />
goods create competition for new goods, a manufacturer would bene…t from a well functioning<br />
used-goods market increasing the willingness of consumer to buy new goods easy to resale.<br />
At the same time, the producer could slightly reduce the durability (by un<strong>de</strong>r investing in<br />
durability, by directly reducing new units durability, by introducing frequent style changes and<br />
new products...) : it alters the substitutability of new and used market and allows the …rm<br />
to increase the price of new units. The maintenance market could also interfere. Rust (1986)<br />
argues that, in case of a competitive maintenance market and a monopolistic new market, most<br />
of consumers would prefer over maintained used goods.<br />
Durability could have a positive impact on prices for both new and used market by increasing<br />
the quality of cars and therefore the utility of the consumer. At the same time, it has a negative<br />
impact on prices in the new market by improving the competition with the second-hand market.<br />
In the US market, by the beginning of the nineties, Peach and al (1996) observed that cars<br />
reliability, survival rate, and warranties durations have been rising simultaneously with car<br />
prices. Acknowledging that durability has not been the only factor impacting the level of price,<br />
graphical analyses show similar trends, from 1990 to 2008, of the median age and the average<br />
sale price of new cars. But their conclusions have to be strongly quali…ed : for used cars and<br />
light truck markets, similar trends are less visible 12 . Furthermore the Consumer Prices In<strong>de</strong>x<br />
for cars (new and used), that adjust prices through obsolescence and representative constant<br />
mixes of vehicles, has been <strong>de</strong>creasing since 1990 in the US 13 .<br />
A third large area of research on durable goods discusses the Time inconsistency. Optimal<br />
12 See graphs in Appendix 2.<br />
13 See graphs in Appendix 2.
88 CHAPITRE 3. A FAMILY HITCH<br />
durability and the Time inconsistency problem are embed<strong>de</strong>d. According to Coase (1972) a<br />
monopolist has to manage the dilemma that the price of units sold in the future will be a¤ected<br />
by the characteristics of the units sold today. The Time inconsistency constitutes an issue for<br />
producers across planned obsolescence, R&D, and the introduction of new products on the<br />
market. Waldman (1996) argues that R&D could have a negative impact on new products<br />
because consumers expect a technological improvement in a later period. As a consequence,<br />
a monopolist should un<strong>de</strong>r invest in R&D and reduce the availability of the used goods (i.e.<br />
by reducing the durability of new unit, by repurchasing and scrapping the used units...) to<br />
maximize his pro…t. On the other hand, Fu<strong>de</strong>nberg and Tirole (1998) argue that new and used<br />
units could become imperfect substitutes after the improvement of new goods. They conclu<strong>de</strong><br />
that R&D could have a positive impact on new goods prices, as well as a negative impact<br />
on second-hand cars 14 . As already mentioned, microeconomic studies usually make the strong<br />
assumption of a monopolistic market. But Schiraldi (2009) proposed a microeconomic mo<strong>de</strong>l in<br />
an oligopolistic car market. She conclu<strong>de</strong>d on a possible collusion of manufacturers to increase<br />
prices on second-hand markets through leasing policy, warranty policy and buy-back policy in<br />
or<strong>de</strong>r to increase prices on new markets. By and large, microeconomic results lead to various<br />
conclusions, but they always bring the i<strong>de</strong>a that new and used markets impact each other prices<br />
(and volumes) on a short and a long time perspective.<br />
3.2.4 Scitovsky’s mechanisms are part of a Keynesian framework.<br />
Most of mentioned articles assume a neoclassical economy driven by real factors and where<br />
money supply has no impact. Agents are optimizing their purchase and know the function<br />
to optimize. Scitovsky (1994) adopts a Keynesian approach that inclu<strong>de</strong>s uncertainty and the<br />
impact of disposable incomes on the overall economy.<br />
Scitovsky investigates the <strong>de</strong>stabilizing impact of secondary markets on the overall economy.<br />
They strengthen both recessions and recoveries. He …rst focuses on speci…c movements of prices :<br />
14 Petrin(2002)’s empirical analysis on the impact of introduction of the minivan in the US market does<br />
not inclu<strong>de</strong> the second-hand market, but the study con…rms the positive impact of innovation in a competitive<br />
market. When automotive …rms are introducing new products, they are cannibalizing each other pro…ts ignoring<br />
the externalities they create. In the end, new products can bring large pro…ts to the innovator and substantial<br />
gains for the consumer.
3.2. ACADEMIC RESEARCHES IN THE SECOND-HAND MARKET ARE LEGION. 89<br />
consumers often react to a modi…cation of their income by shifting their <strong>de</strong>mand between new<br />
markets and cheaper secondary ones. As a result, in case of a su¢ cient elasticity of goods<br />
substitution, new and second-hand markets become inter<strong>de</strong>pen<strong>de</strong>nt. A shock or a disequilibrium<br />
in each market impacts prices, <strong>de</strong>mand and supply in the same direction. Additionally, both<br />
markets o¤set one another. The disturbed market excess <strong>de</strong>mand (or supply) becomes equal to<br />
the other market excess supply (or <strong>de</strong>mand) and prices are stabilized accordingly. Unfortunately,<br />
prices are stabilized only for a while.<br />
A gap between <strong>de</strong>mand and supply still exist in both markets and an opposite e¤ect soon<br />
appears because of a slow adjustment of stock in the second-hand market. In the automotive<br />
sector, for instance, owners of used vehicles are more or less willing to hold their vehicles<br />
according to increases and <strong>de</strong>creases of prices. The slow variation of stock has the following<br />
consequences : the used market volume rises and reduces the level of price in the new market.<br />
So the inter<strong>de</strong>pen<strong>de</strong>nce disrupts the equilibrium in both markets.<br />
To summarize, following disturbance disequilibrium in one market, a short-term e¤ect of<br />
arbitraging creates a temporary obstacle to price movement and a move on the other market on<br />
the same direction. Then, on a second period, the second-hand market’s disequilibrium slowly<br />
liberates constraints of an equilibrating price movement.<br />
Scitovsky extends the discussion to the impact on the overall US economy. The e¤ect <strong>de</strong>-<br />
pends of the size of the used market. It <strong>de</strong>pends also on the length of time the secondary market<br />
is able to compensate the variation of the new market without impacting prices. Automobiles<br />
are exceptional durable goods because of the size of the second-hand market, but Scitovsky<br />
assumes that the in‡uence of stocks would be limited to two months only 15 (Car owners are<br />
rarely relinquish and <strong>de</strong>alers stocks are quite limited).<br />
From an empirical perspective, Peach et al (1996) also conclu<strong>de</strong> that used markets intensify<br />
economic cycles. But they have another explanation : there has been a long-term shift of the US<br />
consumer <strong>de</strong>mand from new to used car markets 16 . Franchised new car <strong>de</strong>alers have captured<br />
15 According to Scitovsky, …nancial assets are the only exception. The <strong>de</strong>stabilizing impact of …anacial se-<br />
condary market would have no limit. Their sizes and shocks duration would signi…cantly impact the overall<br />
economy.<br />
16 There has been a shift, as mentioned in the previous section, consequently to an increase of durability and
90 CHAPITRE 3. A FAMILY HITCH<br />
much of the second-hand market growth. They are collecting most of their pro…ts from used<br />
cars and are less aggressive bid<strong>de</strong>rs on the <strong>de</strong>mand si<strong>de</strong> of auctions. Regarding the supply si<strong>de</strong>,<br />
when <strong>de</strong>mand for new cars increases, they accelerate the used car price reduction by sending<br />
more used cars to auctions. The mechanism become reversed when the <strong>de</strong>mand for new cars<br />
<strong>de</strong>crease. At the end, car markets have more volatility. Pashigan (2001) observed that US used<br />
car prices in<strong>de</strong>x has much more volatility than the new car in<strong>de</strong>x. The supply curves are less<br />
elastic for used than for new cars and, as a consequence, contribute to a higher volatility.<br />
3.2.5 There are implied mechanisms behind the aca<strong>de</strong>mic theories.<br />
Other mechanisms do not come from a speci…c literature and are implied in the previous<br />
contributions. We mention them for clari…cation purposes and to facilitate their i<strong>de</strong>nti…cations<br />
in the econometric analysis that will be implemented in the next section.<br />
"The new market feeds the used market" : as a result, volume and prices of today’s used<br />
car market might be positively correlated with volume and prices of the past new market. The<br />
mechanism also interacts with renewals on the used and the new markets.<br />
"Renewals" : after some years, drivers have to renew their vehicles. Concentrations of re-<br />
newals create cycles on both markets. Additionally, concentrations on the new market could<br />
create future concentrations on the used market.<br />
"Volume e¤ect" : an increase of transaction volumes, if caused by a greater o¤er, could<br />
have a positive impact on the prices. An increase of transaction volumes, if caused by a greater<br />
<strong>de</strong>mand, could have a negative impact on the prices.<br />
"Price e¤ect" : a price increase could have a positive impact on the volume of transactions<br />
by improving o¤er, or a negative impact by <strong>de</strong>creasing <strong>de</strong>mand.<br />
"Arbitration" : a driver can buy a car on the used market or on the new market. A car<br />
bought from one market cannot be bought from another market at the same time. When most<br />
a¤ordability of cars, as well as a higher level of available information for consumers.
3.3. THE MACROECONOMIC TIMES SERIES NEED CLARIFICATIONS. 91<br />
of drivers choose to buy used vehicles, volumes (and prices) improve in the used market and,<br />
as a consequence, <strong>de</strong>crease in the new market.<br />
"Reallocation" : when prices are too high in the new market, the buyers move to the second-<br />
hand market. Consequently, used car prices increase. In other words, prices and volumes move<br />
in the same direction in both markets on a short term perspective. Scitovsky analyzed the<br />
reallocation mechanism by insisting on the threshold e¤ects (due to stocks) on volumes and the<br />
lags creating constant disequilibrium.<br />
The "Income e¤ect" : a <strong>de</strong>crease of income (or consumption or con…<strong>de</strong>nce) creates a <strong>de</strong>-<br />
crease of <strong>de</strong>mand, a <strong>de</strong>crease of transaction volumes, and a fall of prices in both markets 17 .<br />
Alternatively, it could create a shift of consumption from the new market to the used market.<br />
As a consequence, volumes and prices go down in the new market while they are increasing in<br />
the used market.<br />
3.3 The macroeconomic times series need clari…cations.<br />
We aim to check the accuracy of the mechanisms mentioned in the previous sections using<br />
econometric tools. The interactions of the consumer price in<strong>de</strong>xes and the volume of transactions<br />
of new and second-hand cars are analyzed in three countries. Following an interpretation of the<br />
relations between the aca<strong>de</strong>mic theories on durables goods and the time series behavior, we<br />
<strong>de</strong>…ne the limit of our macro-economic perspective.<br />
3.3.1 Three countries are compared through four time series.<br />
We study the automotive markets of France, the United Kingdom and the United States of<br />
America. We consi<strong>de</strong>r observations related to the Consumer Price In<strong>de</strong>x (CPI) and the volume<br />
of registrations (or sales) for new and used cars 18 . The US volumes make the di¤erence : in<br />
2007, used car sales volume was more than 41,4 millions for the US market. By comparison, it<br />
17 According to Scitovsky (1994), the Income e¤ect causes cycles.<br />
18 See Appendix 1 for data sources.
92 CHAPITRE 3. A FAMILY HITCH<br />
was 5.3 millions and 7 millions for France and the UK. Moreover, the passenger car populations<br />
in use for France, the UK, and the US were 30.7 millions, 30.1 millions, and 135.4 millions 19 .<br />
We aim to analyze the inter<strong>de</strong>pen<strong>de</strong>nce between primary and secondary markets on a ma-<br />
croeconomic perspective. The quality of the car (to account for the Akerlof e¤ect), informations<br />
regarding <strong>de</strong>mand (i.e. consumer con…<strong>de</strong>nce) and o¤er (i.e. business con…<strong>de</strong>nce), the level of<br />
R&D (for the Time inconsistency), the mix of vehicles or the level of stocks constitute relevant<br />
explanatory variables. However, we only inclu<strong>de</strong>d four time series in our analysis (prices and<br />
volumes) because of the di¢ culty to collect standardized information and to allow a comparison<br />
from a country to another.<br />
The National Statistical Institutes (INSEE for France, ONS for the UK, BLS for the US)<br />
provi<strong>de</strong> the automotive Consumer Price In<strong>de</strong>xes. They re‡ect the general movement of prices on<br />
the new and the used car markets. The statistical institutes do not communicate a precise list<br />
of the items inclu<strong>de</strong>d in the samples used to construct the in<strong>de</strong>xes. And the precise locations,<br />
where the observations are collected, are neither provi<strong>de</strong>d. They communicate, however, a<br />
general setting of their methodologies 20 . The frameworks are not always similar from a country<br />
to another, but share the same objectives. First, the CPI has to re‡ect the cost of life and to<br />
give an overview of price variation of the general expenditure across the country. Then prices<br />
are collected from various areas and the selected samples of cars aim to be representative of<br />
what people buy in these areas. Second, although goods and services are changing through<br />
time in their characteristics, the statistical institutes intend to measure the e¤ects of price<br />
changes by keeping constant the other economic factors. The processes by which prices are<br />
adjusted to account for changes in product quality constitute an important subject of research<br />
and discussions in the automotive sector. The US applies the Grilitch methodology 21 for the<br />
quality adjustment of automotive observations : the Hedonic approach estimates the price of a<br />
19 The number of new passenger car registrations in 2007 for France and UK was 2.0 millions and 2.4 millions.<br />
New vehicles sales in US were more than 13,6 millions. The average car age is 8.1 and 6.7 years for France and<br />
for UK. In US, the median age for automobiles is 9.2 years. See data sources in Appendix 1.<br />
20 See Caillaud (98) for France<br />
See www.statistics.gov.uk/articles/nojournal/CPISQR.pdf for UK.<br />
See Reinsdorf and Triplett (2008) and also Pashigan (2001) who provi<strong>de</strong>s critical elements on the US CPI for<br />
used cars.<br />
21 See Otha and Grilitch (1976) for additional <strong>de</strong>tails the Hedonic methodology in the automotive area and<br />
also Fixler et al (1999). See Prado (2009) for an application on the European used car market.
3.3. THE MACROECONOMIC TIMES SERIES NEED CLARIFICATIONS. 93<br />
good through the valuation of its attributes. France and the UK apply another methodology,<br />
the ’option costing’, that can be used when a product changes in speci…cation and when it is<br />
possible to value separately the components that have changed.<br />
We use the volumes of registrations (for France and the UK) and sales volumes (for the<br />
US) as proxies of the total amount of transactions. They do not allow a distinction between<br />
the variations of o¤ers and the variations of <strong>de</strong>mands, and provi<strong>de</strong> a slightly more ambiguous<br />
information than the CPI : an increase of sales could be either the consequence of an increase<br />
of <strong>de</strong>mand, or an increase of o¤er, or a reduction of prices. The impacts of volumes on prices<br />
are also ambiguous. An increase of the volumes could cause either a reduction or an increase of<br />
prices. Following an improvement of the market size, for instance, the <strong>de</strong>alers could reduce their<br />
prices in or<strong>de</strong>r to increase their market share or to reduce …xed costs. They could also consi<strong>de</strong>r<br />
a high level of <strong>de</strong>mand as an opportunity to improve their bene…ts by increasing prices.<br />
3.3.2 How to connect the aca<strong>de</strong>mic literature with a time series<br />
analysis ?<br />
We divi<strong>de</strong> the economic literature, surveyed in Section 2, in three groups : the advanced<br />
mechanisms (Table 1), the Scitovsky theory (Table 2) and, the basic mechanisms (Table 3).<br />
Their consequences on the time series analyzed in our article are synthesized in the column<br />
’Impact on Prices and Volumes’. The arrows ( =) () ) indicate that a parameter a¤ects or<br />
causes another one. In or<strong>de</strong>r to avoid any misun<strong>de</strong>rstanding, we have to mention that we do not<br />
assume mechanical relations similar to a clockwork (or <strong>de</strong>terministic links), but we expect to<br />
i<strong>de</strong>ntify probable inter<strong>de</strong>pen<strong>de</strong>nce between the new and the used markets (or stochastic links).
94 CHAPITRE 3. A FAMILY HITCH<br />
Mechanisms Descriptions Impact on Prices and Volumes<br />
Akerlo¤ e¤ect 1 An increase of quality or information in<br />
the Used Car Market creates an increase<br />
in price and <strong>de</strong>mand on the used mar-<br />
ket.<br />
Akerlo¤ e¤ect 2 An increase of quality or information in<br />
the Used Car Market creates an increase<br />
in price and <strong>de</strong>mand on the Used Car<br />
Market and the New Market.<br />
Optimal durability An increase of durability creates a <strong>de</strong>-<br />
crease of <strong>de</strong>mand of new cars ; there-<br />
fore, a <strong>de</strong>crease of prices in the New Car<br />
Market as well as a <strong>de</strong>crease of o¤ers in<br />
the Used Car Market and an increase of<br />
prices.<br />
Time Inconsistency An increase of durability creates a <strong>de</strong>-<br />
crease of <strong>de</strong>mand of new cars ; there-<br />
fore, a <strong>de</strong>crease of prices in the New Car<br />
Market as well as a <strong>de</strong>crease of o¤ers in<br />
the Used Car Market and an increase of<br />
prices.<br />
Table 1 : Advanced Mechanisms.<br />
Quality " or Information " =) Volumes<br />
Used " and/or Prices Used "<br />
Quality " or Information " =) Volumes<br />
Used " and/or Prices Used " and Vo-<br />
lumes New " and/or Prices New "<br />
Durability " =) Volumes New # =)<br />
Prices New # and Volumes Used # =)<br />
Prices Used "<br />
R&D " =) Volumes Used " and/or<br />
Prices Used " and Volumes New #<br />
and/or Prices New #<br />
Mechanisms Descriptions Impact on Prices and Volumes<br />
Scitovsky Theory Interactions creating constant disequi-<br />
librium in the primary and secondary<br />
markets.<br />
Table 2 : Scitovsky Theory.<br />
Volumes New # (insu¢ cient stocks) =)<br />
Prices New " =) Volumes Used " =)<br />
Prices Used " =) Volumes New ! =)<br />
Prices New ! =) Volumes Used # (in-<br />
su¢ cient stocks) =) Prices Used " =)<br />
Volumes New " =) Prices New " and<br />
again =) Volumes Used " =) Prices<br />
Used ". . . .
3.3. THE MACROECONOMIC TIMES SERIES NEED CLARIFICATIONS. 95<br />
Mechanisms Descriptions Impact on Prices and Volumes<br />
New market feeds<br />
used market<br />
Past volumes of new sales transac-<br />
tions correlated positively with the cur-<br />
rent volumes of Used Sales transactions.<br />
Past prices of New Sales transactions<br />
correlated positively with current prices<br />
of Used Sales transactions<br />
Reallocation Prices and volumes of New sales<br />
transactions correlated positively with<br />
prices and volumes of Used Sales tran-<br />
sactions<br />
Arbitration A car bought in one market can’t be<br />
bought, at the same time, in another<br />
market.<br />
Renewals Concentrations of renewals create cycles<br />
in both markets. Concentrations in the<br />
new market could create future concen-<br />
trations on the used market.<br />
Price e¤ect A price increase could have a positive<br />
impact on the volume of transactions by<br />
improving o¤ers/sales, or a negative im-<br />
pact by <strong>de</strong>creasing <strong>de</strong>mand.<br />
Volume e¤ect A volume increase could have a positive<br />
impact on the prices if caused by a grea-<br />
ter o¤er or a negative impact, if caused<br />
by a greater <strong>de</strong>mand.<br />
Income e¤ect 1 A <strong>de</strong>crease of consumers’ income (or<br />
business activity or con…<strong>de</strong>nce) reduces<br />
the <strong>de</strong>mand for new cars and used cars<br />
<strong>de</strong>creasing in prices and volume in both<br />
markets.<br />
Income e¤ect 2 A <strong>de</strong>crease of consumers income (or bu-<br />
siness activity or con…<strong>de</strong>nce) reduces<br />
the <strong>de</strong>mand for new cars and creates a<br />
shift to the used car market It’s <strong>de</strong>crea-<br />
sing prices and volumes in the new mar-<br />
ket and an increase in the used market<br />
Table 3 : Basic Mechanisms.<br />
Positive Correlation : Past New Vo-<br />
lumes () Current Used Volumes / Past<br />
New Prices () Current Used Prices<br />
Positive Correlation : New Volumes<br />
() Used Volumes / New Prices ()<br />
Used Prices<br />
Negative Correlation : New Volumes ,<br />
Used Volumes / New Prices , Used<br />
Prices<br />
Cycles of Prices and volumes : Past<br />
New Volumes " =) Current Used<br />
Volumes " and Past New Prices " =)<br />
Current Used Prices "<br />
Prices " =) O¤er " =) Volume " or<br />
Demand # =) Volume #<br />
Volume " =) Prices # or Prices "<br />
Income # =) Demand # =) Volumes #<br />
and/or Prices #<br />
Income # =) Demand New # =) Vo-<br />
lumes New # and/or Prices New # and<br />
Demand Used " =) Volumes Used "<br />
and/or Prices Used "
96 CHAPITRE 3. A FAMILY HITCH<br />
As discussed in section 2.2, the new market could experience di¤erent consequences from<br />
the Akerlo¤ e¤ect. Therefore we ma<strong>de</strong> a distinction between the Akerlo¤ e¤ect 1 having only<br />
an impact on the used market and the Akerlo¤ e¤ect 2 impacting both markets. There was a<br />
similar issue with the Income e¤ect driving both markets in the same direction or in di¤erent<br />
ones. Another roadblock exists regarding the e¤ect of <strong>de</strong>mand. As an example, for the Time<br />
inconsistency e¤ect, an increase of <strong>de</strong>mand would create either an higher volume of transactions,<br />
or only an increase of prices, or both 22 .<br />
The Akerlo¤, the Optimal durability and the Time inconsistency e¤ects are di¢ cult to<br />
investigate because they involve additional information (quality, durability, R&D...). They could<br />
be invalidated, however, when series move in di¤erent directions than the ones listed in the<br />
tables. For instance, the improvement of quality in the Akerlo¤ e¤ect would take some time to<br />
spread across the population of cars and therefore could be i<strong>de</strong>nti…ed by an increasing trend<br />
on volumes, or prices, or both. If the trends are <strong>de</strong>creasing, then the theory should be refuted.<br />
Our attempt to translate the theoretical economic literature un<strong>de</strong>r an econometric analysis<br />
highlights a critical point : the timing. In most of aca<strong>de</strong>mics papers, except the Scitovsky<br />
(1994)’s article, the period in which the mechanism has an e¤ect was never explicit and the<br />
lags are not precisely <strong>de</strong>…ned. For instance, are the adjustments simultaneous in the Arbitration<br />
e¤ect ? Or are they lagged ? Do they last for the next six months ? Do they last for a year ?<br />
The econometrics of the next section will provi<strong>de</strong> an insight on timing.<br />
3.3.3 We work on macroeconomic time series, a limited information.<br />
The macroeconomic perspective presents four limits : the cross bor<strong>de</strong>r sales, the availability<br />
of the historical observations, the usual critics on Consumer Prices In<strong>de</strong>xes, and the heteroge-<br />
neity of the markets.<br />
As a …rst concern, the cross bor<strong>de</strong>r sales might a¤ect the national prices and transactions<br />
of cars : the imported vehicles, for instance, could increase the competitiveness and reduce car<br />
prices. In the European market (including France) the existence of signi…cant cross bor<strong>de</strong>ring<br />
22 It is i<strong>de</strong>nti…ed every time there is an "and/or" in the table.
3.3. THE MACROECONOMIC TIMES SERIES NEED CLARIFICATIONS. 97<br />
transactions should lead to a price convergence. Gaullier and Haller (2000), however, did not<br />
notice mechanisms creating an automobile price convergence in European countries. They argue<br />
that exchange rate ‡uctuations explain a large share of the price dispersion dynamics 23 . Parities<br />
between Euro-land countries were …xed in May 1998, so their study was too early to assess the<br />
long-term e¤ects implied by the implementation of the single currency. Prado (2009), through<br />
an Hedonic analysis on the 2005-2009 period, shows that even with the Euro implementation,<br />
distinct national markets still constitute the European second-hand car market. Thanks to the<br />
right wheel vehicles, we have few concerns for the UK market regarding a possible interaction,<br />
on prices and volumes, with the other countries. As a conclusion, the impact seems limited for<br />
France and the UK. The US car market has a size dramatically higher than the Mexican and<br />
the Canadian markets and we also expect a limited cross bor<strong>de</strong>ring impact.<br />
As a second concern, we have to keep in mind that our results might be altered by the<br />
limited period of available observations. All in all, knowing that cars longevity can run up to<br />
20 years, the study would hardly provi<strong>de</strong> a long-term perspective. In France, the used car CPI<br />
is available since January 1998, while, in the UK, the used car In<strong>de</strong>x is available since January<br />
1996. In the US, the BLS has published the used car in<strong>de</strong>x since 1952 and, in or<strong>de</strong>r to re‡ect the<br />
cost of living of a representative household, light truck vehicles have only been inclu<strong>de</strong>d in the<br />
CPI since 1998. To standardize the analyses (for the UK), for consistency purpose (for the US),<br />
and to allow a comparison of the three countries, we selected the CPI samples from January<br />
1998. Regarding the times series of volumes (number of registrations, number of sales), we did<br />
not apply the same criteria for the selection of the period : we inclu<strong>de</strong>d as much information<br />
as possible, regarding the number of registrations and sales, maximizing the opportunity to<br />
i<strong>de</strong>ntify a relation between prices and past volumes (i.e. correlation between used cars and<br />
previous …ve years used cars sales). Most of the time, the volume of transactions has been<br />
inclu<strong>de</strong>d according to the series provi<strong>de</strong>d by the statistical institutes and, as a result, series<br />
of volumes are longer than CPI series 24 (except for the UK used car registrations). The time<br />
series for France, the UK and the US are presented in Appendix 3.<br />
The relevance of the variables constitutes our third concern. Like any other statistical indi-<br />
23 They con…rm the conclusion of Goldberg and Verboven (1998) that prices follow exchange rates closely.<br />
24 France : New registrations and used car registrations since January 1987.<br />
UK : New registrations since January 1987/ Used car registrations since January 2001.<br />
US : New sales since January 1987/ Used car sales since January 1997.
98 CHAPITRE 3. A FAMILY HITCH<br />
cator, the Consumer Price In<strong>de</strong>x has been the subject of several critics. In addition, because of<br />
the political and economical impacts on citizen (i.e. wage negotiations), there has always been<br />
a suspicion regarding the CPI accuracy. Two main critics show up : in the automotive area,<br />
people complain that Hedonic adjustments over <strong>de</strong>‡ate the movement of prices and that CPI<br />
does not re‡ect their ’feeling’of increasing prices. Greenlees and McClelland (2008) discussed<br />
the limits of those critics. They <strong>de</strong>monstrated the limited impact of Hedonic adjustment on<br />
CPI results 25 . And a well known psychological ’loss aversion’could increase the sensibility to<br />
increasing prices than to <strong>de</strong>creasing prices ; because the CPI cannot re‡ect the consumption of<br />
a particular group of customers, they are <strong>de</strong>…ned as an average of the in‡ation rate. Consumers<br />
are always members of a speci…c group and they always have the feeling that the CPI is not in<br />
line with their speci…c consumption.<br />
Fourth, speaking of di¤erent groups of customers, we have to clarify that, although we work<br />
at a country level, we do not assume heterogeneity of the markets : a national car market could<br />
be the sum of several sub markets involving very di¤erent populations of customers. A sub<br />
market might strongly impact the whole car market through a signi…cant size or a high level of<br />
volatility. But we aim to provi<strong>de</strong> a macro-economic perspective and intra market interactions<br />
do not constitute the subject of our study.<br />
3.3.4 What do the series look like ?<br />
The period of analysis has been standardized from January 1998 to June 2009. The French<br />
market seems rather stable, whereas the UK 26 and the US prices follow a negative trend and<br />
display a high volatility 27 . For the last ten years the trends of the US series look negative and<br />
illustrate the crisis of the automotive sector in North America. All these characteristics remain<br />
through a growth rate perspective and after a seasonal adjustment 28 .<br />
25 Although there is no European study that would corroborate these results, we also assume a limited impact<br />
regarding the quality adjustment methodologies applied on the French and the UK Consumer Price In<strong>de</strong>x.<br />
26 For UK, they are two big variances after 1999. There has been a change in the car registrations process<br />
after 1999. Prior to 1999, new plates were introduced in August. From 1999 onwards, there has been two plate<br />
changes, in March and September.<br />
27 See graphs in Appendix 3.<br />
28 Series are seasonally adjusted using X11 methodology. See graphs in Appendix 4.
3.4. THE ECONOMETRIC ANALYSIS SHOWS DIFFERENT RESULTS BY COUNTRY.99<br />
At a glance, new car CPI are always more stable than used car CPI. Prices on the used<br />
market are the result of <strong>de</strong>mands and o¤ers, while new car prices are set by the <strong>de</strong>alers and<br />
manufacturers according to constraints of production and maximization of pro…ts. If new car<br />
prices become too high, the number of sales <strong>de</strong>creases because of prices rigidity on the new<br />
market and the adjustment operates mainly by the volume of transaction 29 . As a result, regis-<br />
tration (or sale) volumes are more volatile for new cars than second-hand cars, and new car<br />
prices are quite stable. The market readjustment through volumes explains why some econo-<br />
mic institutions (i.e. OECD) use new car transactions as a short-term economic indicator. In<br />
contrast, prices in the second-hand market are set through o¤er and <strong>de</strong>mand. As a result, used<br />
car prices display more volatility than new car prices.<br />
By the beginning of 2008, the time series falled sharply. The subprime crisis, a global<br />
economical event, appears as an opportunity to compare the reaction on the di¤erent markets<br />
and to con…rm the previous statements. The new cars registrations (or sales for the US) are<br />
more impacted (by a stronger drop) than the used car registrations (or sales), and used car<br />
CPI is more impacted than new car CPI. As a …rst conclusion, it suggests that, in the case<br />
of an Income e¤ect, the used car market has an higher probability to be impacted on a price<br />
perspective, whereas the new market would rather be impacted on a volume perspective because<br />
of a relative price rigidity from car manufacturers. The mechanisms mentioned as the Feeds<br />
e¤ect, Arbitration, Prices e¤ect and Volume e¤ect might be similarly a¤ected.<br />
All in all, new car markets in the UK and the US have been <strong>de</strong>clining for the last 10 years,<br />
while France has been a stable market.<br />
3.4 The econometric analysis shows di¤erent results by<br />
country.<br />
The econometric tools i<strong>de</strong>ntify trends, cycles and correlations through various durations<br />
(short-term, very short-term, the whole ten years period). At the same time, we evaluate if the<br />
29 These conclusions should be con…rmed by an analysis of the automotive production (does the manufacturers<br />
adjust the production according to prices ?) and stocks available (how the stocks impact the markets ?).
100 CHAPITRE 3. A FAMILY HITCH<br />
outcomes are in line with the aca<strong>de</strong>mic theories. At the end of the section, we estimate the<br />
VAR mo<strong>de</strong>ls to investigate the relations between the markets and the possible forecasts 30 .<br />
3.4.1 The unit root tests un<strong>de</strong>rmine the advanced mechanisms.<br />
As previously stated, France appears as a stable market. To check this intuition, we apply<br />
the Augmented Dickey Fuller unit root test to the growth rate of the series. The results are<br />
reported in Table 4 and show that the French volumes and in<strong>de</strong>x prices have been stationary<br />
for the last ten years. On the contrary, the UK and the US have trends : new cars CPI in the<br />
UK, as well as the volume of new car and used car sales in the US, have a unit root (Di¤erence<br />
Stationnarity or DS). According to the econometric theory, it means that a macroeconomic<br />
shock would have an impact on the trend series forever. In contrast, a trend stationnarity (TS)<br />
has been i<strong>de</strong>nti…ed for the new car prices in<strong>de</strong>x in the US, implying that a macroeconomic<br />
shock would have a temporary e¤ect on the prices. Finally, the used car CPI has no trend in<br />
every country.<br />
France Used cars CPI S<br />
New cars CPI S<br />
Used cars Registrations S<br />
New cars Registrations S<br />
UK Used cars CPI S<br />
New cars CPI DS<br />
Used cars Registrations S<br />
New cars Registrations S<br />
US Used cars and light trucks CPI S<br />
New cars and light trucks CPI TS<br />
Used cars and light trucks Sales DS<br />
New cars and light trucks Sales DS<br />
Stationarity (S)<br />
Di¤erence Stationarity (DS)<br />
Trend Stationarity (TS)<br />
Table 4 : Augmented Dickey Fuller Results.<br />
30 The econometrical analysis is inspired by Chazi (2007) and <strong>Le</strong>scaroux and Mignon (2008).
3.4. THE ECONOMETRIC ANALYSIS SHOWS DIFFERENT RESULTS BY COUNTRY.101<br />
The unit root test invalidates the assumption that, for the last ten years, prices and volumes<br />
have been moving in the same direction in the UK new car market (the new car CPI follows<br />
a DS process while the volume of used car sales was stable), and in the US new market (sale<br />
volumes and prices follow a di¤erent trend, a TS and a DS). Turning to the economic theories,<br />
it rejects the presence of mechanisms involving similar long-term trend on prices and volumes<br />
(like the Akerlo¤ e¤ect, the Time inconsistency....). As an example, the <strong>de</strong>creasing trend in<br />
the US might be explained by the Optimal durability e¤ect : the <strong>de</strong>mand for vehicles <strong>de</strong>creases<br />
because cars durability has improved. Drivers do not have to renew their vehicles as often as<br />
in the past. An improvement of cars quality should also lead to an expansion of the second-<br />
hand market, and in the same manner, an increase of used cars prices (and volumes). But the<br />
Optimal durability mechanism is invalidated by the stationnarity of the used car prices (and<br />
the <strong>de</strong>crease of used car volumes).<br />
Focusing on car prices, the estimated trends refute several mechanisms and illustrate the<br />
absence of a long term relation between prices. The stability in France and the trends moving<br />
in the same direction in the UK invalidate the existence of a strong Akerlo¤ e¤ect 2, or an<br />
Optimal durability e¤ect.<br />
Regarding the sale volumes, the trend analysis on the whole period illustrates the well known<br />
fact that the new cars of today are the used cars of tomorrow. In France and the UK, the new<br />
and the used car registrations share a similar stationnarity. In the US market, a cointegration<br />
test i<strong>de</strong>nti…es a common long-term trend between new car and used car sales 31 : for the last ten<br />
years, the new and used US sales have been <strong>de</strong>clining. These results also weaken the mechanisms<br />
reported in Table 1. It is highly unlikely that the stability in France and the UK, as well as the<br />
<strong>de</strong>cline in the US, would be due to a global <strong>de</strong>crease of cars quality 32 (according to the Akerlo¤<br />
e¤ect, the Time inconsistency....).<br />
31 See cointegration test <strong>de</strong>tails in Appendix 9. The construction of an Error Correction Mo<strong>de</strong>l (ECM) including<br />
the US volumes series did not provi<strong>de</strong> a good adjustment. As a result, the mo<strong>de</strong>l did not constitute a useful tool<br />
to forecast the volumes and we did not keep it in the study. Moreover, the US market only has two i<strong>de</strong>nti…ed<br />
Di¤erentiated Stationnnarity (DS) time series. As a consequence, there is no possibility of a cointegration test<br />
and an ECM for France and the UK.<br />
32 We can’t believe, as well, that it would be due to a <strong>de</strong>creasing quality of information available for buyers.
102 CHAPITRE 3. A FAMILY HITCH<br />
3.4.2 The correlation analysis provi<strong>de</strong>s a one-month period perspec-<br />
tive.<br />
The correlation calculation provi<strong>de</strong>s a …rst insight on the simultaneity of market evolutions 33 .<br />
For France, a negative correlation between new CPI and used CPI suggests an arbitrage<br />
on prices (i.e. when prices <strong>de</strong>crease on the new market, they improve on the used market).<br />
The signi…cant correlation between new and used registrations has a positive sign that might<br />
be caused by an Income e¤ect on the volume of transactions. In other words, when drivers<br />
incomes (and <strong>de</strong>mand) improve, the volume of sales increases on both markets.<br />
For the UK, there is a positive correlation between the new car registrations and the used<br />
car prices. These results are in line with the graphical analysis : Market adjustments are ma<strong>de</strong><br />
through new volumes and used prices whereas constraints exist on new car prices and on the<br />
volumes of used car transactions ; following an economic crisis, new sales and second-hand prices<br />
fall sharply while new prices and second-hand volumes remain relatively stable.<br />
For the US, a strong positive correlation exists between new and used prices (r = 0:54) as<br />
well as a negative correlation between new and used transactions. The US market dynamics<br />
are converse to the French ones ; it suggests an Income e¤ect on a price perspective and an<br />
Arbitraging e¤ect on a volume perspective. These results evoke a Scitovsky’s framework : in<br />
the new and the second-hand markets, prices move in the same direction but the variation of<br />
bid, o¤er and stocks in both markets lead to a constant disequilibrium.<br />
3.4.3 The Granger causality tests elaborate the assessments of the<br />
correlation analysis.<br />
To investigate the inter<strong>de</strong>pen<strong>de</strong>nce between new and used car markets, we …rst apply the<br />
Granger causality test 34 evaluating how much the previous six month information contained in<br />
33 Details are given in Appendix 6. The econometrics tools are applied on the seasonally adjusted growth rates<br />
and stationnary time series.<br />
34 The Granger test has been set with six months lags.
3.4. THE ECONOMETRIC ANALYSIS SHOWS DIFFERENT RESULTS BY COUNTRY.103<br />
a variable could improve the prediction of another variable. Results are given in Table 5.<br />
France<br />
Used cars CPI =) Used cars Registrations<br />
Used cars CPI =) New cars Registrations<br />
Used cars Registrations () New cars Registrations<br />
UK<br />
Used cars CPI =) New cars Registrations<br />
New cars CPI () New cars Registrations<br />
US<br />
Used cars CPI () New cars CPI<br />
New cars CPI =) Used cars Sales<br />
New cars Sales =) New cars CPI<br />
New cars Sales =) Used cars Sales<br />
=) : Signi…cant Causality<br />
() : Signi…cant causality in both directions.<br />
Table 5 : Granger test Results.<br />
In the French market, new and used cars registrations are interrelated : the null hypothe-<br />
sis, that the volume of used car registrations does not Granger cause the volume of new car<br />
registrations, has not been rejected at the 5% signi…cante level. In addition, the volume of new<br />
car registrations Granger causes the volume of used car registrations 35 . It con…rms the Income<br />
e¤ect mentioned in the correlation analysis. Furthermore, the Granger test indicates that the<br />
used car CPI helps to predict used car registrations and new cars registrations : rising used car<br />
prices improve drivers willingness to resale their cars and to buy a new one, as a result, the<br />
number of registrations goes up.<br />
For the UK, the used car CPI helps also to predict new cars registrations. The results<br />
corroborate the graphical and the correlation analyses and emphasize that the adjustments on<br />
the new market are more on volumes than on prices. Nevertheless, it seems that <strong>de</strong>alers and<br />
manufacturers try to adjust prices and volumes according to the state of the market, because<br />
new car registrations and new car prices also help to predict each other.<br />
35 See the <strong>de</strong>tailed Granger test results in Appendix 5.
104 CHAPITRE 3. A FAMILY HITCH<br />
The causalities are more numerous in the US market : new car prices and used car prices<br />
help to predict each other ; new car sales and new car prices help to predict used sales ; at the<br />
same time, the new car sales help also to forecast new car prices. The test suggests the existence<br />
of multiple relations between new and second-hand cars and shows a strong inter<strong>de</strong>pen<strong>de</strong>nce<br />
in the US markets by comparison to France and the UK. To be speci…c, the Scitosky’s theory,<br />
of constant disequilibrium from one market to another, constitutes a possible explanation.<br />
3.4.4 The Hodrick-Prescott …lter reveals economic cycles.<br />
In or<strong>de</strong>r to i<strong>de</strong>ntify long-term trends of the series, we calculate Hodrick-Prescott …ltered<br />
series 36 . The …lter produces a smoothed non-linear representation of the time series that is<br />
more sensitive to long-term than to short-term ‡uctuations 37 .<br />
For France, the graphs show larger cycles (of 2 years) for used car prices in<strong>de</strong>x by comparison<br />
to new car prices (6 months) and the volume of transactions. Similarly, second-hand price follows<br />
a longer and more visible cycles in the UK and the US car markets. The distinct pattern of the<br />
used car prices mitigates the validation of mechanisms involving prices and volumes moving in<br />
harmony (Akerlo¤ e¤ect, Time inconsistency).<br />
We evaluate the synchronizations of prices and volumes ‡uctuations. Following Fiorito and<br />
Kollintzas (1994), we measure the <strong>de</strong>gree of co-movement of the series’ cyclical components<br />
through the correlation coe¢ cient . If the correlation between the cyclical components of two<br />
series is positive, null or negative the series cycles are i<strong>de</strong>nti…ed as procyclical, acyclical, or<br />
countercyclical. If 0:1 j j < 0:23 or 0:23 j j < 1:0 the cycles are classi…ed as weakly correlated<br />
or strongly correlated. We also calculate (j) with j 2 f 3; 6; 9; 12; 24; 36g in or<strong>de</strong>r<br />
to i<strong>de</strong>ntify lagged correlations. We report the strong correlations 38 on Table 6.<br />
36 See HP …lter cycle and trend graphs in Appendix 7.<br />
37 The sensitivity of the trend to short-term ‡uctuations is adjusted through a multiplier . From an Empirical<br />
perspective the suggested is equal to 14,400 for monthly data. See Hodrick and Prescott (1997).<br />
38 The complete results are reported in Appendix 8.
3.4. THE ECONOMETRIC ANALYSIS SHOWS DIFFERENT RESULTS BY COUNTRY.105<br />
France<br />
New Car CPI Used Car CPI (+9, +36 months)<br />
Used Car Registrations New Car registrations<br />
New Car CPI (-12) New Car registrations<br />
Used Car Registrations (-24) Used Car Registrations<br />
New Car registrations (-12) Used Car Registrations<br />
Used Car CPI Used Car CPI (+12, +18)<br />
Used Car CPI (-3) Used Car CPI<br />
New Car CPI (-36) Used Car CPI<br />
Used Car Registrations (-36) Used Car Registrations<br />
New Car Registrations (-36) New Car Registrations<br />
UK<br />
New Car CPI Used Car CPI (+3, +6, +9,+12)<br />
Used Car CPI (-3, -6, -9, -12, -36) New Car CPI<br />
New Car CPI (-12) New Car CPI<br />
New Car CPI (-36) Used Car CPI<br />
Used Car Registrations Used Car Registrations (-12)<br />
US<br />
New Car CPI Used car CPI (0, +3, +9)<br />
Used Car CPI (-9, -12) Used Sales Volume<br />
Used Sales Volume New Car CPI<br />
New Car CPI (-24) New Car CPI<br />
Used Sales Volume (-12, -36) Used Sales Volume<br />
New Car CPI (-24) New Sales Volume<br />
New Sales Volume (-24) New Sales Volume<br />
New Sales Volume (-36) New Sales Volume<br />
Strong Pro-cyclic Correlation<br />
Strong Counter-cyclic Correlation<br />
Table 6 : Cycles Correlations.<br />
The …lter, applied to the French car prices series, allows the assumption of a Feed e¤ect :<br />
there is a 36 month pro-cyclical movement of new prices with used prices 39 . The new prices of<br />
the past 36 months impact the second-hand prices of today. Furthermore, the …lter indicates<br />
a critical correlation between new cars and used cars registrations 40 : the cycles of new and<br />
second-hand transactions increase and <strong>de</strong>crease simultaneously. As a result, like the correlation<br />
39 = 0:34<br />
40 = 0:42
106 CHAPITRE 3. A FAMILY HITCH<br />
analysis of Section 4.2, the Hodrick-Prescott …lter i<strong>de</strong>nti…es an Income e¤ect on a volume<br />
perspective.<br />
On the UK market, the …lter also con…rms the existence of a Feed e¤ect : used car prices<br />
cycles are pro-cyclical to new car prices through lags of 3 to 12 and 36 months 41 . The absence of<br />
strong correlations on registrations cycles with other series reduces the probability of a Scitovsky<br />
mechanism.<br />
For the US, markets cycles are well interrelated. There are several pro-cyclical and counter-<br />
cyclical relations between prices and volumes. First of all, we i<strong>de</strong>ntify a positive correlation<br />
between new car CPI and the used car CPI. In addition, the used car CPI, with 9 months<br />
and 12 month lags, appears countercyclical to the volume of used sales. Finally, the used sales<br />
volumes have a cyclical relation with new car prices. These results are in line with the Scitovsky<br />
theory.<br />
3.4.5 Vector Autoregressive (VAR) mo<strong>de</strong>ls clarify the previous re-<br />
sults.<br />
A Vector Autoregressive mo<strong>de</strong>l gives a straight perspective of the relation between prices<br />
and volumes in both markets. We selected the best mo<strong>de</strong>l using the Akaike and the Schwarz<br />
criteria. The results are reported in Appendix 10 and show the usual greater interaction between<br />
the primary and the secondary markets for the US. <strong>Le</strong>t us discuss the outcomes for each country.<br />
For France, the used car prices mainly <strong>de</strong>pend on their own lagged values 42 . The equation<br />
is in line with the Hodrick Prescott results displaying that used CPI cycles are di¤erent to<br />
other series cycles. For the new car prices equation, the mo<strong>de</strong>l has a good …t to the data<br />
thanks to the relevant information from the previous month new prices and the constant.<br />
These results corroborate the graphical analysis revealing rigidity of new car prices by showing<br />
few ‡uctuations of the new car CPI.<br />
41 At the same time, new car prices with a lag of 3 to 12 and 36 months are counter-cyclical to used car prices.<br />
42 Previous months of used CPI variables have a high statistical signi…cativity according to the stu<strong>de</strong>nt test.
3.4. THE ECONOMETRIC ANALYSIS SHOWS DIFFERENT RESULTS BY COUNTRY.107<br />
Regarding the French volume equations, the new and the used cars registration mo<strong>de</strong>ls<br />
have a poor adjustment to the historical observations and none of the variables are statistically<br />
signi…cant. In other words, none of the variables from one market are relevant to mo<strong>de</strong>l the other<br />
market, and the VAR methodology does not i<strong>de</strong>ntify the suggested relations of the previous<br />
section (correlation and arbitraging). Gautier (1995) attempted to i<strong>de</strong>ntify new car registration<br />
cycles, which would be a characteristic of durable goods in the French market since 1945. He<br />
conclu<strong>de</strong>d that registration cycles are more the result of the economic activity (with additional<br />
volatility and sectorial events) than to the internal dynamics of car markets. It means that, in<br />
or<strong>de</strong>r to forecast the registrations in France, a mo<strong>de</strong>l including variables related to the economic<br />
activity would be more relevant.<br />
For the UK, the used car CPI equation shows that, in a similar way to France having dis-<br />
tinct cycles for used car CPI, the previous months used car prices information is statistically<br />
signi…cant. The new market variables are also crucial, but they have smaller coe¢ cients com-<br />
pared to used car prices lagged values. To be more speci…c, the coe¢ cients of the variables from<br />
the new market have a positive e¤ect and therefore reinforce the conclusions of the graphical<br />
and the correlation analyses (the new CPI coe¢ cient is less important because of the rigidity<br />
of new car prices created by production constraints), as well as the Granger causality test (in<br />
spite of the rigidity, <strong>de</strong>alers try to modify the prices according to the state of the economy).<br />
Regarding the new cars CPI equation, although the adjustment is poor, two variables appear<br />
signi…cant (the used car price in<strong>de</strong>x and the used car registrations). But even with a new car<br />
CPI series positively correlated to the used car market, the weakness of the relation suggests<br />
that any involved mechanism would be quite limited.<br />
For the British used cars registrations equation, the mo<strong>de</strong>l has also a poor adjustment and<br />
registrations seem slightly and positively impacted by the used car prices : when prices go up,<br />
<strong>de</strong>alers and privates get an opportunity and they increase the volumes of sales, but stocks are<br />
limited and the evolution remains limited as well. Into the new cars registrations equation,<br />
though the used cars CPI and the constant constitute the only relevant information, the mo<strong>de</strong>l<br />
adjustment is quite good. Again, it strengthens the previous conclusions that economic read-<br />
justments are mainly ma<strong>de</strong> on the new market by volume (and on the used market by price) :<br />
when the state of the economy improves, for instance, the volume of new cars and the prices<br />
of used cars react …rst and increase. The new car volumes are, however, limited by production
108 CHAPITRE 3. A FAMILY HITCH<br />
constraints and consequently, the constant in the equations appears highly signi…cant. The po-<br />
sitive coe¢ cient of the new car volume variable would only allow the existence of mechanisms<br />
with similar co-movements in both markets (Income e¤ect, Akerlo¤ e¤ect...) on a short period.<br />
From the previous results in the US market, we know that the used CPI follows speci…c<br />
cycles and, at the same time, was positively correlated to new car prices. Accordingly, in the<br />
used CPI equation, the lagged used car prices and the new car CPI (with a positive sign) are<br />
statistically signi…cant. On the contrary to France and the UK, the new CPI equation is well<br />
…tted to the historical observations. New car prices are explained by the previous used car CPI<br />
and the previous new CPI. They are also positively impacted by the volume of transactions of<br />
the new market. Therefore the US car prices are connected in various ways with the new and<br />
the used market.<br />
The explained variance of US volume equations are not as good : R 2 are equal to 20% and<br />
47% for new and used sale equations. In the new sales equation the only important variables<br />
are the previous new sales ; in the used sales equation the new and the used sales are signi…cant<br />
variables. Scitovsky (1994) mentioned that the market adjustments were altered by the limited<br />
variation of volumes. He argued that used car market volumes were limited by stocks. In<br />
addition, we argue that new car volumes are limited by production constraints, and that the<br />
VAR results on volumes are fully in line with his theory.<br />
3.5 To conclu<strong>de</strong>, an inter<strong>de</strong>pen<strong>de</strong>nce ?<br />
To conclu<strong>de</strong>, what kind of inter<strong>de</strong>pen<strong>de</strong>nce exists between the new and the second-hand car<br />
markets ?<br />
The aim of this chapter was to investigate the inter<strong>de</strong>pen<strong>de</strong>nces between the new and<br />
the second-hand car markets in three countries : France, the UK and the US. The analysis<br />
was limited to a ten year period ; since cars are durable goods that can be used for more<br />
than 20 years, it might have restricted the results to inter<strong>de</strong>pen<strong>de</strong>nces shorter than a <strong>de</strong>ca<strong>de</strong>.<br />
The econometric tools, however, show consistent outcomes all along the study. Results are<br />
synthesized in Tables 7, 8, and 9.
3.5. TO CONCLUDE, AN INTERDEPENDENCE ? 109<br />
Mechanisms Results and Comments<br />
Akerlo¤ e¤ect 1 /<br />
Akerlo¤ e¤ect 2 /<br />
Optimal durability /<br />
Time Inconsistency<br />
All these mechanisms might be altered by rigidity on the new car prices<br />
and constraints on the used car transaction volumes. However, we can’t<br />
validate any of them : The main reasons are the stable prices and volumes<br />
in France, as well as the <strong>de</strong>crease of used car prices in UK and US.<br />
Table 7 : General Results on Advanced Mechanisms.<br />
Scitovsky Theory Links are too weak in the French and the UK markets to allow the possibility<br />
of a situation similar to the one <strong>de</strong>scribed by Scitovsky article. In contrast,<br />
most of the statistical analyses i<strong>de</strong>nti…ed multiple and signi…cant relations<br />
between new and used cars in the US market and therefore, are in line with<br />
the assumption of a Scitovsky mechanism.<br />
Table 8 : General Results on Scitovsky Theory.<br />
Mechanisms Results and Comments<br />
New market feeds<br />
used market<br />
The trend analysis illustrates a feed e¤ect on a volume perspective in all<br />
markets. For the US market, new and used car sales time series are coin-<br />
tegrated. Additionally, the Hodrick-Prescott …lter suggests that used car<br />
prices of today are related to new car prices of yesterday.<br />
Reallocation Correlation calculations suggest an instantaneous Reallocation e¤ect, bet-<br />
ween the new and the used market, on volumes in France and on prices in<br />
the US<br />
Arbitration Correlation calculations suggest an instantaneous Arbitration e¤ect, bet-<br />
ween the new and the used market, on prices in France and on volumes in<br />
the US.<br />
Renewals The Hodrick-Prescott …lter did not allow a clear i<strong>de</strong>nti…cation of a renewal<br />
Price e¤ect / Volume<br />
e¤ect<br />
Income e¤ect 1 / In-<br />
come e¤ect 2<br />
e¤ect in any of the three countries, neither in the new or the used market.<br />
It is may be due the limited sample (ten years) used in the study.<br />
They are no signi…cant results for France and the UK. Regarding the US<br />
market, we noticed that in line with Scitovsky theory, prices impact volumes<br />
in both directions.<br />
Although our results suggest some income e¤ects, it needs to be con…rmed<br />
through a proper analysis of the relations between disposables incomes and<br />
car market volatility.<br />
Table 9 : General Results on Basic Mecanisms.<br />
Initially, we argue that in all countries the new market of the past is linked to the used
110 CHAPITRE 3. A FAMILY HITCH<br />
market of today, through volumes and prices. Secondly, the interrelations appear limited for<br />
France and the UK, whereas the US market is characterized by a Scitovsky dynamics, <strong>de</strong>…ned<br />
by constant disequilibrium and multiple interactions between primary and secondary markets.<br />
Our contribution also highlighted that, <strong>de</strong>pending of a short-term or a long-term perspective,<br />
interactions are di¤erent. Thirdly, theories implying volumes and prices moving in the same<br />
direction (Akerlo¤ e¤ect, Optimal durability, Time Inconsistency) are di¢ cult to con…rm. Fi-<br />
nally, for France, the UK, and the US the connections between primary and secondary car<br />
markets are not similar, but all markets experience a characteristic rarely mentioned in the<br />
literature : a rigidity of both the new car prices and the used car volumes of transactions.<br />
Another similar characteristic is that, for all countries, used car prices follow distinct cycles.<br />
All things consi<strong>de</strong>red, our results illustrate that the interrelations between the new and used<br />
car markets are not strong enough to fully explain and forecast the market patterns. The use<br />
of macroeconomic variables related to the disposable income of buyers or the general state of<br />
the economy might improve the forecast accuracy, and is left for future research.
3.6. APPENDIX 111<br />
3.6 Appendix<br />
3.6.1 Appendix 1 : Data sources<br />
The Time series 43 :<br />
CPI FR Www.bdm.insee.fr/bdm2/serie/A¢ chRechDirecte.do I<strong>de</strong>nti…ant : 000638803 000638804<br />
CPI UK Www.statistics.gov.uk/statbase/tsdtimezone.asp Consumer prices indices DE78 DE79<br />
CPI US Www.data.bls.gov/cgi-bin/srgate Series Id : CUSR0000SS45011 CUSR0000SETA02<br />
New Car Reg FR Www.statistiques.<strong>de</strong>veloppement-durable.gouv.fr/rubrique.php3 ?id_rubrique=122<br />
New Car Reg UK Www.smmt.co.uk/dataservices/vehicleregistrations.cfm<br />
New car sales US Www.bea.gov/national/xls/gap_hist.xls<br />
Used car Reg FR Www.statistiques.<strong>de</strong>veloppement-durable.gouv.fr/rubrique.php3 ?id_rubrique=122<br />
Used car Reg UK Driver and Vehicle Licensing Agency Www.dvla.gov.uk/<br />
Used car sales US CNW Marketing Research Www.cnwmr.com/<br />
France and UK, new registra-<br />
tions and vehicles in use<br />
France second-hand registra-<br />
tions<br />
Others Statistics :<br />
ACEA Www.acea.be/in<strong>de</strong>x.php/collection/statistics<br />
Fichier central <strong>de</strong>s automobiles Www.statistiques.<strong>de</strong>veloppement-<br />
durable.gouv.fr/rubrique.php3 ?id_rubrique=32<br />
UK second-hand registrations British Car Auctions Used Car Market Report Www.bca-europe.com/<br />
US new and used average sale<br />
price<br />
National Transportation Statistics from the US <strong>de</strong>partment of statistics.<br />
Www.bts.gov/publications/national_transportation_statistics/<br />
US car on use National Automobile Dealers Association Www.nada.org/NR/ rdonlyres/0FE75B2C-<br />
69F0-4039-89FE-1366B5B86C97/0/NADAData08_no.pdf<br />
US median age Www.nada.org/NR/rdonlyres/0FE75B2C-69F0-4039-89FE-1366B5B86C97/0/ NADA-<br />
Data08_no.pdf<br />
43 A special thanks to Tom Webb (Www.manheimconsulting.com/) for his support on US data.
112 CHAPITRE 3. A FAMILY HITCH<br />
3.6.2 Appendix 2 : Median Age and Average Sales price in the US<br />
(see data source in Appendix 1)<br />
Median Age in US market<br />
Average Sale Price Real US $
3.6. APPENDIX 113<br />
3.6.3 Appendix 3 : Raw data<br />
(see data source in Appendix 1)<br />
FR
114 CHAPITRE 3. A FAMILY HITCH<br />
UK<br />
US (CPI data provi<strong>de</strong>d by the BLS are seasonally adjusted.)
3.6. APPENDIX 115<br />
3.6.4 Appendix 4 : Growth rate and seasonally adjusted times series<br />
FR<br />
UK
116 CHAPITRE 3. A FAMILY HITCH<br />
US<br />
FR
3.6. APPENDIX 117<br />
UK<br />
US
118 CHAPITRE 3. A FAMILY HITCH<br />
3.6.5 Appendix 5 : Granger Test<br />
Pairwise Granger Causality Tests<br />
Lags : 6<br />
Null Hypothesis : Obs F-Statistic Probability<br />
NEW_CARS_CPI does not Granger Cause USED_CARS_CPI 120 1.0125 0.4212<br />
USED_CARS_CPI does not Granger Cause NEW_CARS_CPI 0.3615 0.9017<br />
USED_CARS_VOL does not Granger Cause USED_CARS_CPI 120 0.5774 0.7476<br />
USED_CARS_CPI does not Granger Cause USED_CARS_VOL 2.5318 0.0248<br />
NEW_CARS_VOL does not Granger Cause USED_CARS_CPI 120 0.8105 0.5640<br />
USED_CARS_CPI does not Granger Cause NEW_CARS_VOL 2.6519 0.0194<br />
USED_CARS_VOL does not Granger Cause NEW_CARS_CPI 120 0.8364 0.5444<br />
NEW_CARS_CPI does not Granger Cause USED_CARS_VOL 0.9842 0.4397<br />
NEW_CARS_VOL does not Granger Cause NEW_CARS_CPI 120 1.0053 0.4258<br />
NEW_CARS_CPI does not Granger Cause NEW_CARS_VOL 0.8752 0.5158<br />
NEW_CARS_VOL does not Granger Cause USED_CARS_VOL 252 2.1592 0.0477<br />
USED_CARS_VOL does not Granger Cause NEW_CARS_VOL 3.8416 0.0011<br />
France<br />
Pairwise Granger Causality Tests<br />
Lags : 6<br />
Null Hypothesis : Obs F-Statistic Probability<br />
NEW_CARS_CPI does not Granger Cause USED_CARS_CPI 119 0.5688 0.7543<br />
USED_CARS_CPI does not Granger Cause NEW_CARS_CPI 0.8581 0.5283<br />
USED_CARS_VOL does not Granger Cause USED_CARS_CPI 84 1.5144 0.1859<br />
USED_CARS_CPI does not Granger Cause USED_CARS_VOL 1.7610 0.1196<br />
NEW_CARS_VOL does not Granger Cause USED_CARS_CPI 120 0.7487 0.6117<br />
USED_CARS_CPI does not Granger Cause NEW_CARS_VOL 3.5091 0.0033<br />
USED_CARS_VOL does not Granger Cause NEW_CARS_CPI 84 0.8961 0.5027<br />
NEW_CARS_CPI does not Granger Cause USED_CARS_VOL 0.4179 0.8648<br />
NEW_CARS_VOL does not Granger Cause NEW_CARS_CPI 119 10.6495 0.0000<br />
NEW_CARS_CPI does not Granger Cause NEW_CARS_VOL 0.3673 0.8982<br />
NEW_CARS_VOL does not Granger Cause USED_CARS_VOL 84 1.5057 0.1888<br />
USED_CARS_VOL does not Granger Cause NEW_CARS_VOL 0.7780 0.5899<br />
UK
3.6. APPENDIX 119<br />
Pairwise Granger Causality Tests<br />
Lags : 6<br />
Null Hypothesis : Obs F-Statistic Probability<br />
NEW_CARS_CPI does not Granger Cause USED_CARS_CPI 120 3.2097 0.0062<br />
USED_CARS_CPI does not Granger Cause NEW_CARS_CPI 2.3908 0.0331<br />
USED_CARS_VOL does not Granger Cause USED_CARS_CPI 120 1.6204 0.1485<br />
USED_CARS_CPI does not Granger Cause USED_CARS_VOL 1.7257 0.1219<br />
NEW_CARS_VOL does not Granger Cause USED_CARS_CPI 120 0.7601 0.6028<br />
USED_CARS_CPI does not Granger Cause NEW_CARS_VOL 0.4233 0.8621<br />
USED_CARS_VOL does not Granger Cause NEW_CARS_CPI 120 0.3855 0.8869<br />
NEW_CARS_CPI does not Granger Cause USED_CARS_VOL 2.5894 0.0221<br />
NEW_CARS_VOL does not Granger Cause NEW_CARS_CPI 120 2.0814 0.0613<br />
NEW_CARS_CPI does not Granger Cause NEW_CARS_VOL 1.2774 0.2738<br />
NEW_CARS_VOL does not Granger Cause USED_CARS_VOL 134 4.2343 0.0007<br />
USED_CARS_VOL does not Granger Cause NEW_CARS_VOL 1.7096 0.1244<br />
US
120 CHAPITRE 3. A FAMILY HITCH<br />
3.6.6 Appendix 6 : Correlation Analysis<br />
USED_CARS_CPI NEW_CARS_CPI USED_CARS_VOL NEW_CARS_VOL<br />
USED_CARS_CPI 1.00 -0.31 -0.03 0.10<br />
NEW_CARS_CPI -0.31 1.00 -0.13 -0.17<br />
USED_CARS_VOL -0.03 -0.13 1.00 0.44<br />
NEW_CARS_VOL 0.10 -0.17 0.44 1.00<br />
France<br />
USED_CARS_CPI NEW_CARS_CPI USED_CARS_VOL NEW_CARS_VOL<br />
USED_CARS_CPI 1.00 0.16 0.05 0.35<br />
NEW_CARS_CPI 0.16 1.00 -0.09 0.01<br />
USED_CARS_VOL 0.05 -0.09 1.00 0.16<br />
NEW_CARS_VOL 0.35 0.01 0.16 1.00<br />
UK<br />
USED_CARS_CPI NEW_CARS_CPI USED_CARS_VOL NEW_CARS_VOL<br />
USED_CARS_CPI 1.00 0.54 -0.01 -0.01<br />
NEW_CARS_CPI 0.54 1.00 0.02 0.04<br />
USED_CARS_VOL -0.01 0.02 1.00 -0.28<br />
NEW_CARS_VOL -0.01 0.04 -0.28 1.00<br />
US
3.6. APPENDIX 121<br />
3.6.7 Appendix 7 : Hodrick-Prescott Filter, cycles and trends<br />
France France<br />
France France
122 CHAPITRE 3. A FAMILY HITCH<br />
UK UK<br />
UK UK
3.6. APPENDIX 123<br />
US US<br />
US US
124 CHAPITRE 3. A FAMILY HITCH<br />
3.6.8 Appendix 8 : Hodrick-Prescott Cycles Correlations<br />
France NEW_CARS_CPI USED_CARS_VOL NEW_CARS_VOL USED_CARS_CPI<br />
NEW_CARS_CPI 1.000 0.082 0.058 0.087<br />
USED_CARS_VOL 0.082 1 0.421 0.14<br />
NEW_CARS_VOL 0.058 0.421 1 0.179<br />
USED_CARS_CPI 0.087 0.14 0.179 1<br />
USED_CARS_CPI(36) 0.341 0.068 0.206 -0.158<br />
USED_CARS_CPI(24) -0.137 -0.068 -0.005 -0.169<br />
USED_CARS_CPI(18) -0.107 -0.077 -0.065 -0.371<br />
USED_CARS_CPI(12) -0.116 -0.085 -0.223 -0.321<br />
USED_CARS_CPI(9) 0.298 -0.078 -0.145 -0.116<br />
USED_CARS_CPI(6) 0.215 0.128 -0.094 0.101<br />
USED_CARS_CPI(3) 0.049 0.156 0.101 0.513<br />
USED_CARS_CPI(-3) -0.119 0.101 0.018 0.513<br />
USED_CARS_CPI(-6) -0.06 0.011 -0.013 0.101<br />
USED_CARS_CPI(-9) -0.012 0.066 0.04 -0.116<br />
USED_CARS_CPI(-12) 0.008 -0.001 0.058 -0.321<br />
USED_CARS_CPI(-18) -0.019 -0.181 -0.107 -0.371<br />
USED_CARS_CPI(-24) -0.07 -0.084 0.019 -0.169<br />
USED_CARS_CPI(-36) 0.217 0.077 -0.065 -0.158<br />
NEW_CARS_CPI(-6) -0.068 0.116 0.195 0.215<br />
USED_CARS_VOL(-6) 0.041 0.152 0.085 0.128<br />
NEW_CARS_VOL(-6) -0.079 -0.114 0.006 -0.094<br />
NEW_CARS_CPI(-12) -0.392 -0.032 0.035 -0.116<br />
USED_CARS_VOL(-12) -0.038 -0.155 -0.012 -0.085<br />
NEW_CARS_VOL(-12) -0.015 -0.16 -0.447 -0.223<br />
NEW_CARS_CPI(-24) -0.171 0.021 -0.235 -0.137<br />
USED_CARS_VOL(-24) -0.026 -0.299 -0.064 -0.068<br />
NEW_CARS_VOL(-24) 0.047 -0.102 0.045 -0.005<br />
NEW_CARS_CPI(-36) -0.07 -0.131 0.117 0.341<br />
USED_CARS_VOL(-36) 0.047 -0.258 -0.18 0.068<br />
NEW_CARS_VOL(-36) -0.072 -0.067 -0.205 0.206
3.6. APPENDIX 125<br />
UK NEW_CARS_CPI USED_CARS_VOL NEW_CARS_VOL USED_CARS_CPI<br />
NEW_CARS_CPI 1 -0.192 -0.042 0.085<br />
USED_CARS_VOL -0.192 1 0.026 -0.132<br />
NEW_CARS_VOL -0.042 0.026 1 0.176<br />
USED_CARS_CPI 0.085 -0.132 0.176 1<br />
USED_CARS_CPI(36) 0 -0.05 -0.018 -0.158<br />
USED_CARS_CPI(24) 0.1 -0.209 -0.005 -0.169<br />
USED_CARS_CPI(18) -0.043 -0.032 -0.047 -0.371<br />
USED_CARS_CPI(12) -0.283 0.192 -0.059 -0.321<br />
USED_CARS_CPI(9) -0.389 0.117 -0.053 -0.116<br />
USED_CARS_CPI(6) -0.447 0.052 0 0.101<br />
USED_CARS_CPI(3) -0.315 -0.143 0.13 0.513<br />
USED_CARS_CPI(-3) 0.258 0.055 0.132 0.513<br />
USED_CARS_CPI(-6) 0.339 -0.036 0.081 0.101<br />
USED_CARS_CPI(-9) 0.347 0.071 -0.015 -0.116<br />
USED_CARS_CPI(-12) 0.333 0.134 -0.131 -0.321<br />
USED_CARS_CPI(-18) 0.137 0.141 -0.177 -0.371<br />
USED_CARS_CPI(-24) -0.208 -0.067 -0.139 -0.169<br />
USED_CARS_CPI(-36) 0.281 -0.024 -0.144 -0.158<br />
NEW_CARS_CPI(-6) 0.116 0.181 -0.051 -0.447<br />
USED_CARS_VOL(-6) -0.058 -0.007 -0.037 0.052<br />
NEW_CARS_VOL(-6) -0.156 0.069 0.152 0<br />
NEW_CARS_CPI(-12) -0.333 0.146 -0.18 -0.283<br />
USED_CARS_VOL(-12) 0.125 -0.542 0.073 0.192<br />
NEW_CARS_VOL(-12) 0.078 0.035 -0.183 -0.059<br />
NEW_CARS_CPI(-24) -0.224 -0.094 0.039 0.1<br />
USED_CARS_VOL(-24) 0.123 -0.161 -0.179 -0.209<br />
NEW_CARS_VOL(-24) -0.016 -0.132 -0.16 -0.005<br />
NEW_CARS_CPI(-36) -0.066 -0.083 0.15 0<br />
USED_CARS_VOL(-36) -0.263 0.158 -0.011 -0.05<br />
NEW_CARS_VOL(-36) 0.002 0.011 -0.051 -0.018
126 CHAPITRE 3. A FAMILY HITCH<br />
US NEW_CARS_CPI USED_CARS_VOL NEW_CARS_VOL USED_CARS_CPI<br />
NEW_CARS_CPI 1 0.299 0.044 0.421<br />
USED_CARS_VOL 0.299 1 -0.048 0.055<br />
NEW_CARS_VOL 0.044 -0.048 1 0.136<br />
USED_CARS_CPI(36) 0.097 0.139 0.196 0.19<br />
USED_CARS_CPI(24) -0.134 -0.164 -0.171 -0.087<br />
USED_CARS_CPI(18) 0.016 -0.02 0.025 -0.22<br />
USED_CARS_CPI(12) -0.105 0.023 0.096 -0.522<br />
USED_CARS_CPI(9) 0.146 0.054 0.068 -0.213<br />
USED_CARS_CPI(6) 0.369 0.123 0.047 0.201<br />
USED_CARS_CPI(3) 0.445 0.048 0.12 0.69<br />
USED_CARS_CPI 0.421 0.055 0.136 1<br />
USED_CARS_CPI(-3) 0.206 0.024 -0.027 0.69<br />
USED_CARS_CPI(-6) -0.113 -0.034 -0.127 0.201<br />
USED_CARS_CPI(-9) -0.176 0.034 -0.238 -0.213<br />
USED_CARS_CPI(-12) -0.178 0.027 -0.287 -0.522<br />
USED_CARS_CPI(-18) -0.051 -0.082 0.06 -0.22<br />
USED_CARS_CPI(-24) -0.222 -0.006 0.266 -0.087<br />
USED_CARS_CPI(-36) 0.067 -0.15 0.104 0.19<br />
NEW_CARS_CPI(-6) -0.122 -0.09 -0.033 0.369<br />
USED_CARS_VOL(-6) -0.108 -0.037 0.038 0.123<br />
NEW_CARS_VOL(-6) -0.237 -0.137 0.066 0.047<br />
NEW_CARS_CPI(-12) -0.159 0.079 -0.169 -0.105<br />
USED_CARS_VOL(-12) -0.137 -0.289 0.052 0.023<br />
NEW_CARS_VOL(-12) 0.144 -0.05 -0.407 0.096<br />
NEW_CARS_CPI(-24) -0.472 -0.117 0.27 -0.134<br />
USED_CARS_VOL(-24) -0.075 -0.174 0.113 -0.164<br />
NEW_CARS_VOL(-24) -0.054 0.139 -0.256 -0.171<br />
NEW_CARS_CPI(-36) -0.066 -0.215 0.08 0.097<br />
USED_CARS_VOL(-36) 0.098 -0.24 -0.061 0.139<br />
NEW_CARS_VOL(-36) -0.105 0.035 0.245 0.196
3.6. APPENDIX 127<br />
APPENDIX 9 : Cointegration test<br />
us_used_sls_ = C(1) + C(2)* us_new_cars_trk_s_<br />
Null Hypothesis : RES_US_REG has a unit root<br />
Exogenous : None<br />
Lag <strong>Le</strong>ngth : 0 (Automatic based on SIC MAXLAG=13) t-Statistic Prob.*<br />
Augmented Dickey-Fuller test statistic -9.46 0.00<br />
Test critical values : 1 prct level -2.58<br />
*MacKinnon (1996) one-si<strong>de</strong>d p-values.<br />
Augmented Dickey-Fuller Test Equation<br />
Depen<strong>de</strong>nt Variable : D(RESn_USn_REG)<br />
<strong>Le</strong>ast Squares Inclu<strong>de</strong>d observations : 140 after adjustments<br />
Sample (adjusted) : 1997M11 2009M06<br />
5 prct level -1.94<br />
10 prct level -1.62<br />
Variable Coe¢ cient Std. Error t-Statistic Prob.<br />
RES_US_REG(-1) -0.79 0.083 -9.46 0.00<br />
R-squared 0.39 Mean <strong>de</strong>pen<strong>de</strong>nt var 0.00<br />
Adjusted R-squared 0.39 S.D. <strong>de</strong>pen<strong>de</strong>nt var 0.077712394<br />
S.E. of regression 0.06 Akaike info criterion -2.76<br />
Sum squared resid 0.51 Schwarz criterion -2.74<br />
Log likelihood 194.28 Durbin-Watson stat 2.06
128 CHAPITRE 3. A FAMILY HITCH<br />
APPENDIX 10 : Vector AutoRegressions
3.6. APPENDIX 129<br />
Inclu<strong>de</strong>d observations : 124 after adjustm ents FRANCE Sam ple (adjusted) : 1999M 03 2009M 06<br />
Standard errors in ( ) & t-statistics in [ ] U SE D _ C A R S_ C P I N E W _ C A R S_ C P I U SE D _ C A R S_ VO L N E W _ C A R S_ VO L<br />
U SE D _ C A R S_ C P I(-1) 1.4762 0.0239 0.8313 -0.5555<br />
0.0779 0.2139 1.6743 2.5929<br />
[ 18.9538] [ 0.11189] [ 0.49652] [-0.21425]<br />
U SE D _ C A R S_ C P I(-2) -0.5125 -0.1174 -1.1977 0.5550<br />
0.0781 0.2145 1.6787 2.5997<br />
[-6.56302] [-0.54729] [-0.71347] [ 0.21350]<br />
N E W _ C A R S_ C P I(-1) -0.0436 0.5419 -1.2443 -1.8822<br />
0.0328 0.0901 0.7050 1.0919<br />
[-1.32844] [ 6.01583] [-1.76494] [-1.72388]<br />
N E W _ C A R S_ C P I(-2) 0.0543 0.1146 0.7396 0.6650<br />
0.0322 0.0885 0.6926 1.0726<br />
[ 1.68695] [ 1.29516] [ 1.06796] [ 0.61996]<br />
U SE D _ C A R S_ VO L (-1) -0.0002 -0.0231 -0.0297 0.1378<br />
0.0049 0.0135 0.1055 0.1635<br />
[-0.04434] [-1.71260] [-0.28129] [ 0.84324]<br />
U SE D _ C A R S_ VO L (-2) -0.0001 -0.0112 0.0473 -0.1840<br />
0.0051 0.0140 0.1098 0.1700<br />
[-0.02689] [-0.80195] [ 0.43093] [-1.08192]<br />
N E W _ C A R S_ VO L (-1) -0.0030 -0.0004 0.0370 0.0512<br />
0.0032 0.0088 0.0685 0.1061<br />
[-0.94334] [-0.04168] [ 0.53933] [ 0.48245]<br />
N E W _ C A R S_ VO L (-2) 0.0033 -0.0074 0.0361 0.1151<br />
0.0032 0.0088 0.0688 0.1066<br />
[ 1.02733] [-0.84026] [ 0.52384] [ 1.08021]<br />
C 0.0003 0.0044 0.0165 0.0132<br />
0.0005 0.0013 0.0098 0.0152<br />
[ 0.61639] [ 3.48989] [ 1.68583] [ 0.86933]<br />
R -squared 0.9644 0.5524 0.0488 0.0678<br />
A dj. R -squared 0.9619 0.5212 -0.0173 0.0030<br />
Sum sq. resids 0.0012 0.0087 0.5353 1.2838<br />
A kaike inform ation criterion -19.5345 Schwarz criterion -18.7158
130 CHAPITRE 3. A FAMILY HITCH<br />
Inclu<strong>de</strong>d observations : 88 after adjustm ents UK Sam ple (adjusted) : 2002M 03 2009M 06<br />
Standard errors in ( ) & t-statistics in [ ] U SE D _ C A R S_ C P I D _ N E W _ C A R S_ C P I U SE D _ C A R S_ VO L N E W _ C A R S_ VO L<br />
U SE D _ C A R S_ C P I(-1) 1.6667 0.1319 -1.1669 2.3730<br />
0.0837 0.0384 0.8668 1.0948<br />
[ 19.9143] [ 3.43778] [-1.34627] [ 2.16748]<br />
U SE D _ C A R S_ C P I(-2) -0.8040 -0.1377 1.6949 0.0023<br />
0.0814 0.0373 0.8432 1.0650<br />
[-9.87489] [-3.68942] [ 2.01019] [ 0.00218]<br />
D _ N E W _ C A R S_ C P I(-1) 0.4491 0.0432 0.6233 -3.5862<br />
0.2331 0.1068 2.4139 3.0491<br />
[ 1.92667] [ 0.40414] [ 0.25820] [-1.17616]<br />
D _ N E W _ C A R S_ C P I(-2) -0.2309 -0.0620 -0.0753 -3.1484<br />
0.2165 0.0992 2.2418 2.8317<br />
[-1.06681] [-0.62490] [-0.03357] [-1.11182]<br />
U SE D _ C A R S_ VO L (-1) -0.0195 -0.0002 0.0987 -0.1313<br />
0.0108 0.0050 0.1119 0.1414<br />
[-1.80368] [-0.03842] [ 0.88211] [-0.92857]<br />
U SE D _ C A R S_ VO L (-2) 0.0205 0.0138 0.0985 -0.0892<br />
0.0110 0.0050 0.1134 0.1433<br />
[ 1.87362] [ 2.74116] [ 0.86878] [-0.62270]<br />
N E W _ C A R S_ VO L (-1) 0.0196 0.0048 0.0183 0.0546<br />
0.0085 0.0039 0.0883 0.1116<br />
[ 2.29991] [ 1.22077] [ 0.20680] [ 0.48897]<br />
N E W _ C A R S_ VO L (-2) 0.0029 -0.0002 -0.1376 0.1367<br />
0.0086 0.0039 0.0891 0.1126<br />
[ 0.33404] [-0.04041] [-1.54390] [ 1.21433]<br />
C -0.0053] 0.0000 0.0300 0.0798<br />
0.0016 0.0008 0.0170 0.0215<br />
[-3.25706] [ 0.00034] [ 1.76809] [ 3.72193]<br />
R -squared 0.9681 0.2140 0.1032 0.5926<br />
A dj. R -squared 0.9649 0.1344 0.0123 0.5514<br />
Sum sq. resids 0.0030 0.0006 0.3260 0.5202<br />
A kaike inform ation criterion -20.7465 Schwarz criterion -19.7330
3.6. APPENDIX 131<br />
Inclu<strong>de</strong>d observations : 124 after adjustm ents US Sam ple (adjusted) : 1999M 03 2009M 06<br />
Standard errors in ( ) & t-statistics in [ ] U SE D _ C A R S_ C P I T _ N E W _ C A R S_ C P I D _ U SE D _ C A R S_ VO L D _ N E W _ C A R S_ VO L<br />
U SE D _ C A R S_ C P I(-1) 1.7377 0.1028 0.3162 0.0314<br />
0.0563 0.0291 0.4835 0.7147<br />
[ 30.8611] [ 3.53556] [ 0.65400] [ 0.04391]<br />
U SE D _ C A R S_ C P I(-2) -0.8157 -0.0927 -0.3825 -0.3123<br />
0.0567 0.0293 0.4865 0.7192<br />
[-14.3961] [-3.17087] [-0.78621] [-0.43428]<br />
T _ N E W _ C A R S_ C P I(-1) -0.1029 1.2245 1.7836 1.5587<br />
0.1570 0.0810 1.3477 1.9923<br />
[-0.65553] [ 15.1115] [ 1.32336] [ 0.78235]<br />
T _ N E W _ C A R S_ C P I(-2) 0.3920 -0.4502 -1.5271 0.4293<br />
0.1655 0.0854 1.4211 2.1008<br />
[ 2.36873] [-5.26886] [-1.07455] [ 0.20437]<br />
D _ U SE D _ C A R S_ VO L (-1) -0.0090 0.0013 -0.5381 0.0561<br />
0.0104 0.0054 0.0897 0.1326<br />
[-0.85890] [ 0.23630] [-5.99859] [ 0.42267]<br />
D _ U SE D _ C A R S_ VO L (-2) -0.0162 0.0016 -0.3109 0.0176<br />
0.0094 0.0049 0.0811 0.1199<br />
[-1.71557] [ 0.32981] [-3.83257] [ 0.14687]<br />
D _ N E W _ C A R S_ VO L (-1) -0.0067 0.0007 0.2928 -0.4083<br />
0.0075 0.0038 0.0640 0.0946<br />
[-0.90506] [ 0.18388] [ 4.57437] [-4.31499]<br />
D _ N E W _ C A R S_ VO L (-2) 0.0098 0.0079 0.0870 -0.3029<br />
0.0080 0.0041 0.0683 0.1009<br />
[ 1.22991] [ 1.93390] [ 1.27397] [-3.00055]<br />
C -0.0010 0.0003 0.0012 -0.0103<br />
0.0007 0.0003 0.0056 0.0083<br />
[-1.59204] [ 1.02893] [ 0.21004] [-1.23258]<br />
R -squared 0.9832 0.8380 0.4405 0.1968<br />
A dj. R -squared 0.9820 0.8267 0.4016 0.1409<br />
Sum sq. resids 0.0053 0.0014 0.3906 0.8535<br />
A kaike inform ation criterion -20.4271 Schwarz criterion -19.6083
132 CHAPITRE 3. A FAMILY HITCH
Conclusion Générale<br />
Dans un contrat <strong>de</strong> leasing, le bailleur prend le risque <strong>de</strong> subir <strong>de</strong>s pertes …nancières lors <strong>de</strong><br />
la revente <strong>de</strong> l’actif. Il exite un risque <strong>de</strong> valeur résiduelle. L’objectif général <strong>de</strong> cette thèse est<br />
d’apporter une contribution académique à ce problème peu connu mais essentiel dans l’activité<br />
<strong>de</strong> leasing. La thèse traite <strong>de</strong>s di¤érents outils d’analyse quantitative disponibles pour les dé-<br />
partements <strong>de</strong> gestion d’actifs et couvre trois thèmes : la valorisation <strong>de</strong>s équipements par la<br />
métho<strong>de</strong> <strong>de</strong>s prix hédoniques, la couverture du risque <strong>de</strong> valeur résiduelle à l’ai<strong>de</strong> <strong>de</strong> produits<br />
…nanciers dérivés, et en…n les relations macro-économiques entre le marché du neuf et celui <strong>de</strong><br />
l’occasion.<br />
<strong>Le</strong>s modèles statistiques <strong>de</strong> prix hédoniques ont été largement utilisés pour l’analyse du<br />
marché automobile. Dans le premier chapitre, nous exposons la méthodologie et proposons<br />
une application aux véhicules d’occasion dans le secteur du leasing, où la valeur résiduelle<br />
est un paramètre critique. <strong>Le</strong> modèle exploite les caractéristiques techniques <strong>de</strong>s véhicules a…n<br />
d’estimer la distribution <strong>de</strong>s prix <strong>de</strong> revente. Deux autres facteurs, pouvant in‡uencer le marché<br />
automobile, sont inclus : le prix du carburant et l’activité économique (l’indice <strong>de</strong> production<br />
industrielle). La méthodologie, appliquée aux marchés automobiles d’occasion dans quatre pays<br />
européens (l’Allemagne, l’Espagne, la France et la Gran<strong>de</strong> Bretagne) fournit une perspective<br />
nouvelle. En se concentrant sur le comportement <strong>de</strong> dépréciation <strong>de</strong> <strong>de</strong>ux véhicules (Ford Focus<br />
et Audi A4), notre étu<strong>de</strong> révèle les di¤érents niveaux <strong>de</strong> probabilité <strong>de</strong> pertes en utilisant les<br />
informations <strong>de</strong> revente disponibles par les sociétés <strong>de</strong> leasing. A travers une analyse <strong>de</strong>s prix et<br />
du risque, l’approche permet également d’i<strong>de</strong>nti…er les opportunités <strong>de</strong> leasing sur les di¤érents<br />
marchés.<br />
Notre première étu<strong>de</strong> peut être poursuivie <strong>de</strong> plusieurs façons. L’industrie <strong>de</strong> leasing com-<br />
133
134 CONCLUSION GÉNÉRALE<br />
prend tous les types <strong>de</strong> matériel et l’application <strong>de</strong> l’approche hédonique est su¢ samment<br />
‡exible pour être étendue à d’autres actifs que l’automobile. En outre, notre analyse pourrait<br />
également être étendue aux contrats avec option d’achat ou avec une option dite <strong>de</strong> ‘rewrite’sur<br />
l’âge et le kilométrage (le client pouvant, à tout moment, choisir <strong>de</strong> prolonger ou d’interrompre<br />
le contrat.) Deux autres éléments dans le domaine du risque <strong>de</strong> valeur résiduelle pourraient être<br />
ajoutés pour compléter l’analyse : le cycle <strong>de</strong> vie du véhicule et la variation générale du marché.<br />
<strong>Le</strong>s facteurs macro-économiques, en particulier, appellent à une étu<strong>de</strong> plus approfondie.<br />
Dans le <strong>de</strong>uxième chapitre, le modèle <strong>de</strong>s copules gaussien <strong>de</strong> Li, qui a initialement été<br />
utilisé pour l’analyse du risque <strong>de</strong> crédit, est transposé dans le secteur du leasing pour l’étu<strong>de</strong><br />
du risque <strong>de</strong> valeur résiduelle. Un nouveau produit dérivé est proposé, le Collateralized Residual<br />
Value (CRV). <strong>Le</strong> produit dérivé convertit les risques <strong>de</strong> pertes à la revente d’un portefeuille <strong>de</strong><br />
leasing en un instrument qui peut être vendu sur les marchés …nanciers. A l’instar <strong>de</strong>s produits<br />
dérivés classiques, il constitue un outil <strong>de</strong> transfert <strong>de</strong> risque. Ainsi il peut être utilisé à <strong>de</strong>s<br />
…ns <strong>de</strong> couverture <strong>de</strong>s risques ou <strong>de</strong> spéculation. En outre, il permet au bailleur et au locataire<br />
<strong>de</strong> choisir leurs <strong>de</strong>grés d’expositions au risque <strong>de</strong> valeur résiduelle et ainsi d’améliorer leur<br />
compétitivité. En conséquence, le modèle se présente comme un apport pour les professionnels<br />
<strong>de</strong> l’industrie du leasing intéressés par un produit …nancier novateur, ainsi que les acteurs <strong>de</strong>s<br />
marchés …nanciers intéressés par <strong>de</strong> nouvelles possibilités d’investissement.<br />
Notre secon<strong>de</strong> analyse peut être étendue <strong>de</strong> diverses manières. La précision <strong>de</strong>s composants<br />
du modèle pourrait être améliorée, notamment par une analyse macro-économique du paramètre<br />
<strong>de</strong> corrélation. En…n, d’autres familles <strong>de</strong> copules pourraient être appliquées.<br />
Dans le <strong>de</strong>rnier chapitre, nous étudions les interdépendances entre les marchés <strong>de</strong> véhicules<br />
neufs et <strong>de</strong> véhicules d’occasion dans trois pays : la France, le Royaume-Uni et les États-<br />
Unis. L’analyse porte sur une pério<strong>de</strong> <strong>de</strong> dix ans. <strong>Le</strong>s interactions sont donc étudiées sur une<br />
décennie, alors même que l’automobile est un bien durable avec une durée <strong>de</strong> vie qui peut aller<br />
jusqu’à 20 ans. Pourtant, les outils économétriques montrent <strong>de</strong>s résultats uniformes tout au<br />
long <strong>de</strong> l’étu<strong>de</strong>. Nous constatons que pour les trois pays étudiés, le marché du neuf et le marché<br />
<strong>de</strong> l’occasion interagissent par les prix et les volumes. Cependant, les interrelations semblent<br />
limitées pour la France et le Royaume-Uni, alors que le marché américain se caractérise par une<br />
dynamique dite <strong>de</strong> ‘Scitovsky’, dé…nie par un déséquilibre constant et <strong>de</strong> multiples interactions<br />
entre les marchés du neuf et <strong>de</strong> l’occasion. Notre étu<strong>de</strong> a également révélé qu’en fonction <strong>de</strong>
la perspective <strong>de</strong> court ou <strong>de</strong> long terme, les comportements <strong>de</strong>s marchés sont di¤érents et<br />
que certaines théories (Akerlo¤ e¤ect, Optimal durability, Time Inconsistency) impliquant <strong>de</strong>s<br />
volumes et <strong>de</strong>s prix variant dans la même direction sont di¢ ciles à con…rmer. Bien que pour<br />
ces trois pays les relations entre les marchés automobiles du neuf et <strong>de</strong> l’occasion ne soient pas<br />
i<strong>de</strong>ntiques, ils partagent tout <strong>de</strong> même une spéci…cité rarement mentionnée dans la littérature :<br />
les prix pour les voitures neuves et les volumes <strong>de</strong> transaction <strong>de</strong>s voitures d’occasion subissent<br />
<strong>de</strong>s rigidités. <strong>Le</strong> fait que les prix <strong>de</strong>s voitures d’occasion suivent <strong>de</strong>s cycles distincts est un<br />
autre trait commun pour tous les pays. En…n les résultats montrent que les corrélations entre<br />
les marchés <strong>de</strong> voitures neuves et d’occasion ne sont pas su¢ samment fortes pour expliquer<br />
pleinement les variations <strong>de</strong>s marchés.<br />
L’utilisation <strong>de</strong> variables macro-économiques liées au revenu disponible <strong>de</strong>s acheteurs ainsi<br />
que l’état général <strong>de</strong> l’économie pourraient gran<strong>de</strong>ment améliorer la qualité <strong>de</strong>s prévisions, et<br />
faire l’objet <strong>de</strong> futures recherches.<br />
135
136 CONCLUSION GÉNÉRALE
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