Curve Estimation for Corporate Bond Risk Forecasts - RiskMetrics ...

ContentsContents ..................................................................................... 21. Introduction ........................................................................... 32. Estimation Analytics .............................................................. 32.1. Optimization ..................................................................................................... 42.2. Grid Search ....................................................................................................... 62.3. Positive forward and positive spread constraints ........................................ 62.4. Filtering of bonds ............................................................................................. 62.5. Stickiness adjustments .................................................................................... 72.6. Inverse yield volatility weight winsorization ................................................. 72.7. Flat spread filing ............................................................................................... 83. Universe Selection ................................................................. 83.1. Merrill Lynch Indices Used for the Curve Universe ....................................... 83.2. Sector and Ratings Curves ........................................................................... 103.3. Issuer Selection .............................................................................................. 144. Conclusion ........................................................................... 14Appendix A: Figures ................................................................. 15APPENDIX B: Barra rating calculation ...................................... 29Client Service Information is Available 24 Hours a Day ....................................... 30Notice and Disclaimer .............................................................................................. 30About MSCI ............................................................................................................... 30MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 2msci.com

1. IntroductionMSCI curve estimation methodology is designed to provide discount curves to estimate risk forecasts forcorporate bonds. The methodology tries to satisfy two main objectives at the same time1. Fit the daily market prices of the bonds used in the estimation of the curve2. Reduce jumps in rates from day to day that are caused by the estimation method and not bybond pricesThese objectives are not always easy to meet at the same time. In our model, the risk of corporatebonds is driven by the historical evolution of spot rates at the maturity nodes (as an example currentGBP nodes are 1m, 3m, 1y, 2y, 3y, 4y, 5y, 7y, 9y, 10y, 15y, 20y, 30y, 40y, 50y). It is not generally possibleto perfectly fit all the market prices of an estimation universe. The yields of the bonds underlying anestimation curve are heterogeneous; the best discount curve that passes all the nodes might have spikesthrough time to maturity, and also through history. These spiky curves can create unrealistic riskforecasts. For example the spiky behavior can occur when the bonds time to maturity are near thecenters of the maturity nodes, and estimation of curve does not follow any smoothing function, then thespikes will fluctuate with the bonds getting close to the maturity.2. Estimation AnalyticsStability is particularly important for sector-by-rating curves. Risk Manager allows clients to use issueror CDS curves, which have more granularity than sector curves, and for volatile assets, a more accuraterisk measure can be attained by using those curves. But for curves that will be used in the riskattribution of many different bonds, it is important to make sure they do not fluctuate rapidly due toslight yield changes in couple of bonds.We tested several methodologies to fit a discount curve for use in risk forecasts. Parametric curves aresmooth at the maturity nodes, and can also be made stable through time by properly directing theoptimization. We chose four parameter Nelson Siegel (NS) curves for the spread curves, because of theirflexibility and wide usage in pricing curve estimation of fixed income assets.The price of a bond can be written in terms of the expected cash flows at coupon dates t m , maturityat , the risk free (government) discounting function , and a spread discounting function f(t):(1)(2)is the NS spread curve function with the parameters where ( and a decay parameter(the smaller the the faster the decay of spread through time to maturity)(3)MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 3msci.com

On the boundary limits, the NS function approaches its parameters: and .controls the level of the hump in the NS function, and affects the location of the humpWe modify the parametric NS function at the borders of the estimation universe so that a constantspread is used where there are no bonds. The discounting function is(4)(5)is the shortest time to maturity for the bonds in a curve estimationis the longest time to maturity for the bonds in a curve estimation2.1. OptimizationWe use a Levenberg-Marquardt optimization algorithm to fit the market prices. The optimizer targetfunction is given by the following equationis the dirty market price of the assetis the dirty fitted price of the assetis the weight of the assetThe convergence criterion is >0, where the value is 0.01 andis the degrees of freedom (the number of assets minus the number of fit parameters, e.g., for 10assets -4 parameters, )For an equal weighted case, is set to a default value of ; thus the summation becomes(6)(7)If similar error is achieved in all assets, andwill be close to 0.1(10bps relative error), the final(8)Using equal weights in the optimization generates stability issues, since a small change in the yield of asingle bond can move the curve away from the previous day’s fit. If these unstable curves are used, therisk will be over-estimated. In order to avoid this, we use non-equal weights.For these non-equal weights, asset weights areMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 4msci.com

(9)Figure 1 (in the appendix) shows the GBP Financial AA sector curve spot rates for 1y, 10y and 30y nodesin 2008. The short end of the estimated curve is very volatile for the equally weighted case (labeled asEQUAL). The heterogeneous yield distribution can result in small differences in even as the curve ischanging rapidly. The short end has moved more than 1% from 2008/09/23 to 2008/09/24, althoughyields of bonds have not changed much (Figure 2 and Figure 3). Plots like Figure 2 are used in the rest ofthe document. The top graph shows the market yields of the bonds as triangles. The blue curve is theestimated sector curve, the gray line is the risk free curve, and the red circles are the fitted yields. Thebond weights plot displays the normalized weights (in percent) of each asset with their respective timeto maturity on the x axis. They are close to zero in Figure 2, as there are over 70 assets in that curve(1/70 = 1.4%). The history of NS parameters and are shown in the middle four subplots and theparameters for the specific yield curve date are marked with the red circle on each plot. Historical(CHISQ) and 1y, 10y, and 30y node rates are also shown in the 4 lower subplots.The wide distribution of yields causes significant jumps, especially during the 2008 crisis. To avoid thejumps caused by small changes in the yields, we weighted the asset price differences by the inversevolatility of their market yields, where the volatility of yields is calculated by exponentially decayedweighting of the yield differences with a half life of 20 days. As shown in Figure 1, inverse volatility(curve INV. VOL), makes the curve more stable and reduces the jumps by changing the significance ofbonds in the optimizer objective function ( Inverse effective duration ( weighting is applied inaddition to the inverse volatility weights and is replaced withInverse duration weighting defines the error function more in terms of yield:(10)(11)For small relative difference between and , this is an accurate measure of the differencebetween the market and fitted yield. Inverse duration weighting increases the accuracy of the short endof the curve with respect to market yields. Figure 4 displays the GBP Utility A curve. The weights on theshort end decreased significantly as a result of large volatility bonds experienced during late 2008, andthe optimizer can get trapped in a minimum where the short end yields are not fit very well. Inverseduration weighting (Figure 5) resolves this issue.To further ensure curve stability, we added the absolute differences of zero coupon rates from theprevious day to .MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 5msci.com

(12)is today’s estimated issuer curve zero coupon rate for maturity nodeis the previous estimated issuer curve zero coupon rate for maturity nodeis the sticky coefficient used to tune the effect of the stickiness of the spot rates.Figure 6 and Figure 7 show that the GBP Consumer Staples BBB curve is more stable with a stickycoefficient of 10. The sticky coefficient should be chosen carefully: even though the curve becomes verystable with the large sticky coefficient, it can start deviating from the bond yields. Figure 8 shows theeffect of increasing the sticky coefficient on the estimated curves. Our tests have shown thatresults in stable curves without ignoring the effects of yield changes.Sector/issuer curve estimation is a challenging task, as the diversity of the yields in each curve can besubstantial. For example, the GBP Financial High Yield curve included bonds in late 2008 and early 2009with yields from 200% to 10% (see Figure 9). Even after the introduction of custom weighting andstickiness constraints, there are still jumps in the zero coupon rates as the short end bond drops late inthe year and the curve is transformed from an inverse humped shape.2.2. Grid SearchWe use the previous day’s NS parameters as initial values for the estimation. In order to avoid theestimation getting stuck in a local minimum, a grid search on is implemented. Grid search is only doneif the new optimization result is worse than previous day’s (), since the grid searchslows the estimation by approximately 20x.2.3. Positive forward and positive spread constraintsThe estimated curves are not constrained to have positive forward rates or spreads. Addition of apositive forward constraint is not straightforward: there is a nonlinear relationship between theestimated curve forwards, the NS parameters, and the underlying risk free curve. Since positive forwardrates is not a requirement for a curve used for risk modeling, we are not planning to implement it.However, since the estimated curves are derived from assets that are more risky than the riskless bonds,one should expect them to have positive spreads to the riskless bond curve on all nodes. Unfortunately,the standard form of the NS function creates a nonlinear dependency for for . If anegative spread is observed as a result of the optimization, we adjust the parameters constraints touse the previous day’s estimation, and re-estimate the curve. This approach does not always result in afinal positive spread (since the underlying risk free curve, or the estimation universe, might be differentfrom previous day), but it gradually pulls the curve to a positive spread region2.4. Filtering of bondsEven though highly volatile bonds are down-weighted by the inverse yield volatility approach, we haveobserved that extreme yields compared to the other bond yields in a bucket can cause slight moves inMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 6msci.com

the curves. In order to identify these extreme yields, a weighted standard deviation is calculated asbelow(13)(14)is the market yield of bond(15)is the fitted yield of bond , using the previously estimated issuer curve.As default we keepat a large value (50%), so that filtering will only be applied rarely, andfiltering will not cause artificial jumps in the estimated curves.2.5. Stickiness adjustmentsStickiness parameter is adjusted automatically in order to avoid optimization induced jumps, when theconstituents of the curve do not change, and yield differences from the previous day are small. In thestandard setting, a sticky coefficient ofis applied to the curves every day. Resultant zerocoupon curve is compared at each node of the previous zero coupon curve. Moreover the market yielddifferences from the previous day’s market yields are calculated for each bond. Sticky coefficient isincreased from its standard setting, if the maximum absolute zero coupon rate difference is higher thanthe maximum absolute yield difference by a ratio (currently set to 1.1), and maximum absolute zerocoupon rate difference is larger than a floor value (currently set to 10bps). We also check the inverseyield volatility differences of the bonds while deciding on the sticky adjustment, and only increase thesticky coefficient if the maximum absolute weight difference (than a set value (currently set to 1%)) is smaller2.6. Inverse yield volatility weight winsorizationRight after the bonds enter the Merrill indices, we do not have sufficient history to calculate theirvolatilities accurately. While the number of observations in the bond’s yield volatility is smaller than thehalf life (currently set to 20 days), its inverse yield volatility weighting is replaced by the weight of themost volatile bond which has sufficient number of yield observations (> half life). We have observedoccasionally; the day the bond has half life number of observations plus one, its weight can jump tobecome the largest weight in the universe. In order to resolve this; the weights are winsorized from thetop part of their distributions. Winsorized inverse yield volatilitiesand , represent the standard deviation and mean of the inverse yield volatility of the curveconstituents which are truncated from the top and bottom of the cross-sectional inverse yield volatilitydistribution bynumber of elements; is the truncation percentage.(16)MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 7msci.com

2.7. Flat spread filingWe have observed that for some sector buckets, the parametric spread curves did not have anyadvantage over a flat spread curve, since the cross-sectional distribution of yields throughout the historywere large. As a result we have decided to calculate an equally weighted average of option adjustedspreads (OAS) of the bonds after removing the extreme outliers (see section; Filtering of bonds). OASsare calculated over the risk free curve.3. Universe SelectionThe curve universe is based on Merrill Lynch index prices and on Reuters terms and conditions. Usingindex constituents and prices, we minimize the possibility of jumps in the estimation universe from dayto day because index vendors must price all the constituents of the index in order to report daily indexlevels.The bonds are also filtered using their security and schedule types. Only bonds that meet therequirements in the table below are used to estimate the curves. We restrict the sector curve universeto bonds with no options and fixed coupon bonds, since there are many bonds to estimate them from.However issuer curves include bonds with options, fixed to floats, and perpetuals, as there are fewerbonds for each issuer and we require four or more bonds to estimate a curve. The four bond cutoff is aninitial requirement for a curve to be generated, but the curve estimation process will not automaticallydrop a curve when the count declines below four: curves are dropped from the estimation universe onlyafter investigation by the data analyst team.Security typeSector CurvesOnly fixed and zero coupon bonds(no floaters or fixed to floats)Issuer CurvesFixed and zero coupon; fixed to floats asfixed coupon bonds with a modified maturitydate on the fixed to float switch date;perpetuals as fixed coupon bonds maturingon the first call dateSchedule type Bonds with no options Bonds with no options and bonds with calland put schedules (option types Europeanand Bermudan)3.1. Merrill Lynch Indices Used for the Curve UniverseSpecific Merrill Lynch indices are chosen for corporate bond curves so that covered bond orcollateralized assets are not included in the estimation universe. There is an exception for thePfandbrief/Covered sector in Euro market: covered bonds are included through an additional Merrillindex. The issuer and sector curve use a joined estimation universe of all Merrill Index Ids in thefollowing table.MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 8msci.com

Currency Merrill Index Ids# issuers defined by MSCI IssuerIDs as of 2010 AugustGBP UQ00 (Sterling Investment Grade Quasi & ForeignGovernment Index)426 with options, 315 with nooptions,HL00 - Sterling High Yield IndexUR00 - Sterling Investment Grade CorporateSecurities IndexUSD C0A0 (Corporate Master) 2440 with options, 1357 with nooptionsG0P0 (Agency Master)H0A0 (High Yield Master)GS00 (US Foreign Govt and Supra National)EMUEQ00 - EMU Investment Grade Quasi-GovernmentIndexER00 - EMU Investment Grade Corporate IndexEP00 - EMU Pfandbrief Index (only used forPfandbrief sector curve and rating curves)HE00 -Euro High Yield Index884 with options, 678 with nooptionsMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 9msci.com

3.2. Sector and Ratings CurvesSector curves are assigned based on Barra model sectors and subsectors, which are primarily based onGICS sector classifications 1 . For sector curves, we use the level one GICS sectors (only for Transportationsector, we use level two GICS), and generate additional curves for Agency, Covered, Local/Provincial,Sovereign, and Supranational Barra Sectors. We calculate a Pfandbrief/Covered curve only available forthe Euro, using the EP00 Merrill index.Barra SectorGICSsector NotesLevelAgencyNACovered (Pfandbrief) NA EP00 Merrill index for Euro PfandbriefGovernment NA used for treasuriesLocal/Provincial NA any country outside the US; RM has separate USD Muni curvesSovereignNASupranationalNAConsumer Discretionary 1Consumer Staples 1Energy 1Financials 1Health Care 1Industrials 1Information Technology 1Materials 1Telecommunications 1Transportation 2Utility 1Rating assignment to curves are based on Barra ratings (see APPENDIX B: Barra rating calculation) whichare an average of S&P and Moody’s except in Japan, where JNR and RNI ratings are also used togenerate the Barra rating. There are not always enough bonds to calculate seven ratings categories foreach individual Barra sectors. Finding the set of rating by industry universes with enough bonds togenerate stable curves through time requires detailed investigation. We follow the Barra IntegratedModel version 301 (BIM301) factors to assign the sector by rating curves: BIM301 credit factors aredefined on Barra sector/subsector pairs with at least 5 bonds in recent years. BIM301 credit factors aremore granular since they also use the GICS subsectors, so wherever we have a BIM301 factor we shouldbe able to generate a sector by rating curve.We also generate rating only curves for each market by using all the bonds (including Pfandbriefe).These curves will be used for bonds for which a sector by industry curve is not available. For example,USD Transportation A, BBB, B-BB will be generated, but the other Transportation by rating curves willnot (this is denoted by NA in the following tables), so a Transportation bond with a AAA rating will beexposed to the USD_AAA curve. This logic guarantees that each sector by rating curve has enough bondsand that all corporate bonds with a rating can at least be assigned to a rating only curve. Note that somesector curves span more than one rating, e.g., USD Transportation B-BB, to increase the number ofbonds in the estimation.Examples of USD sector curves, and how they improve with the volatility weighting can be seen in Figure10 and Figure 11.GICS Sector definitions are described in S&P document 1 http://www2.standardandpoors.com/spf/pdf/index/GICSDef.pdfMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 10msci.com

1. USD proposed sector curvesGICS Level 1 & BarraSectors AAA AA A BBB BB B CCCAgencyAgencyAAA NA NA NA NA NA NACovered (Pfandbrief) NA NA NA NA NA NA NALocal/ProvincialSovereignSupranationalSovereign &Supranational AA-AAAConsumer Discretionary NA NA Cons. Disc. AConsumer Staples NA NA Cons. Stap. ANo curve to be built since RiskServer has separate curves for USD MunisSovereign & SupranationalBBB-ACons. Disc.BBBCons. Stap.BBBSovereign & Supranational CCC-BBCons. Disc.BBCons. Disc.BCons. Stap. B-BBCons. Disc.CCCCons. Stap.CCCEnergy Energy AA-AAA Energy A Energy BBB Energy BB Energy B Energy CCCFinancialsFinancialAAAFinancialAA Financial A Financial BBB Financial BB Financial B NAHealth Care Health AA-AAA Health A Health BBB Health BB Health B Health CCCIndustrial Industrial Industrial IndustrialIndustrials NA NA Industrial A BBBBBBCCCInformation Technology NA NATechnologyATechnologyBBBTechnologyBBTechnology BNAMaterials NA NA Materials AMaterialsBBBMaterialsBBMaterialsBMaterialsCCCTelecommunications NA NA Telco. A Telco. BBB Telco. BB Telco. B Telco. CCCTransportation NA NATransportation ATransportation BBB Transportation B-BB NAUtility NA NA Utility A Utility BBB Utility BB Utility B NAMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 11msci.com

2. EUR proposed sector curvesGICS Level 1 & BarraSectors AAA AA A BBB BB B CCCAgency Agency AAA Agency AA Agency A NA NA NA NACovered Bonds Covered BondsCovered (Pfandbrief)AAAAA NA NA NA NA NALocal/Provincial Muni AAA Muni AA NA NA NA NA NASovereignSovereignSovereign AA-AAAA NA NA NA NASupranationalSupranationalAAA NA NA NA NA NA NAConsumer Discretionary NA NACons. Disc.ACons. Disc.BBBCons. Disc.BBCons. Disc.CCC-BCons. Stap. Cons. Stap.Consumer Staples NA NAABBB NA NA NAEnergy Energy AA-AAA Energy BBB-A NA NA NAFinancials Financial AAA Financial AA Financial A Financial BBB Financial BB Financial CCC-BHealth Care NA NA Health BBB-A NA NA NAIndustrials NA NA Industrial AIndustrialBBBIndustrialBBIndustrial CCC-BInformation Technology NA NA NA NA NA NA NAMaterialsMaterials NA NA Materials A BBBMaterials CCC-BBTelecommunications NA NA Telco. A Telco. BBB Telco. CCC-BBTransportation Transport AA-AAA Transport BBB-A Transport CCC-BBUtility NA NA Utility A Utility BBB NA NA NAMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 12msci.com

3. GBP proposed sector curvesGICS Level 1 & Barra Sectors AAA AA A BBB BB B CCCAgency Agency AAA NA NA NA NA NA NACovered (Pfandbrief) NA NA NA NA NA NA NALocal/Provincial NA NA NA NA NA NA NASovereign NA Sovereign AA NA NA NA NA NASupranational Supranational AAA NA NA NA NA NA NAConsumer Discretionary NA NA Cons. Disc. BBB-A Cons. Disc.BB- CCCConsumer Staples NA NA Cons. Staples A Cons. Staples BBB NA NA NAEnergy Energy AA-AAA Energy BBB-A NA NA NAFinancials Financial AAA Financial AA Financial A Financial BBB Financial CCC-BBHealth Care NA NA NA NA NA NA NAIndustrials NA NA Industrial BBB-A NA NA NAInformation Technology NA NA NA NA NA NA NAMaterials NA NA Materials BBB-A NA NA NATelecommunications NA NA Telco. A Telco. BBB NA NA NATransportation Transport AA-AAA NA NA NA NA NAUtility NA NA Utility A Utility BBB NA NA NAMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 13msci.com

3.3. Issuer SelectionReuters issuer classifications are used to identify the issuers of a given asset. Reuters defines parent andsubsidiary relation between companies: the subsidiary information is used to create the most granularissuer curves. We also calculate parent curves using the bonds of all subsidiaries. For example, in GBP,there will be an HSBC Bank Curve and a curve for its ultimate parent, HSBC Holdings. Subordinationlevels and ratings are not used to create further granularity in the issuer curves, since the number ofbonds per curve can drop substantially.4. ConclusionThe new MSCI curve estimation methodology improves on the previous RiskManager curves in analyticsand estimation universe. The new sector curves will be more granular, and stable through history. Issuercurves will also improve with the Merrill prices and the new estimation methodology as shown in Figure12 and Figure 13. A detailed analysis of how the improvements in issuer curve affects historical VARforecasts can be found in a prior study. 2We are committed to improving the corporate curve methodology further through client feedback andwill have beta releases of curves estimated with the new methodology.2 “Spread Based Issuer Curve Estimation” E.Ultanir, J.Fox, January 2011, MSCIMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 14msci.com

Appendix A: FiguresMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 15msci.com

Figure 1 Equal Weighting versus Inverse VolatilityMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 16msci.com

Figure 2 Equal Weighted Curve on 2008/09/22MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 17msci.com

Figure 3 Equal Weighted Curve on 2008/09/23MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 18msci.com

Figure 4 GBP Utility A with inverse volatility weightingMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 19msci.com

Figure 5 GBP Utility A with inverse volatility and inverse duration weightingMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 20msci.com

Figure 6 GBP Consumer Staples BBB on 2009/07/21 with no sticky coefficientMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 21msci.com

Figure 7 GBP Consumer Staples BBB with sticky coefficient of 10MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 22msci.com

Figure 8 Increased sticky coefficientMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 23msci.com

Figure 9 GBP Financial High YieldMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 24msci.com

Figure 10 USD Financial A 2008-2009MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 25msci.com

Figure 11 USD Industrial BBB 2008-2009MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 26msci.com

Figure 12 GBP Tesco curve in 2008MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 27msci.com

Figure 13 France Telecom curve in 2008MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 28msci.com

APPENDIX B: Barra rating calculationBarra rating is the arithmetic mean of S&P and Moody’s ratings. A precise calculation is as follows:• Convert letter-based ratings into equivalent integer ratings using the S&P and Moody equivalencetables (see below).• If there are ratings from both agencies, take the (arithmetic) average of S&P and Moody equivalentinteger ratings. If this average is not an integer, round up to the nearest largest integer. If only onerating is available use that rating.• Convert the result back into a letter based Barra rating.ExampleBond B is rated AA+ by S&P and Aa2 by Moody’s. S&P equivalent integer rating is 1. Moody’s equivalentinteger rating is 2. The average integer rating is 1.5. The model integer rating is 2. B’s model rating is AA.Table 1 Rating Equivalence TablesInteger Rating S&P Rating Integer Rating Moody's Rating Integer Rating Barra Rating0 AAA 0 Aaa 0 AAA1 AA+ 1 Aa1 1 AA2 AA 2 Aa2 2 AA3 AA- 3 Aa3 3 AA4 A+ 4 A1 4 A5 A 5 A2 5 A6 A- 6 A3 6 A7 BBB+ 7 Baa1 7 BBB8 BBB 8 Baa2 8 BBB9 BBB- 9 Baa3 9 BBB10 BB+ 10 Ba1 10 BB11 BB 11 Ba2 11 BB12 BB- 12 Ba3 12 BB13 B+ 13 B1 13 B14 B 14 B2 14 B15 B- 15 B3 15 B16 CCC+ 16 Caa1 16 CCC17 CCC 17 Caa2 17 CCC18 CCC- 17 Caa 18 CCC19 CC+ 18 Caa3 19 CCC20 CC 19 Ca1 20 CCC21 CC- 20 Ca2 21 CCC22 C+ 20 Ca 22 CCC23 C 21 Ca3 23 CCC24 C- 22 Ca1 24 CCC25 D 23 C2 25 CCC23 C24 C325 DMSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 29msci.com

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MSCIproducts and services include indices, portfolio risk and performance analytics, and governance tools.The company’s flagship product offerings are: the MSCI indices which include over 148,000 daily indices covering more than 70 countries; Barra portfolio risk andperformance analytics covering global equity and fixed income markets; RiskMetrics market and credit risk analytics; ISS governance research and outsourced proxyvoting and reporting services; FEA valuation models and risk management software for the energy and commodities markets; and CFRA forensic accounting riskresearch, legal/regulatory risk assessment, and due-diligence. MSCI is headquartered in New York, with research and commercial offices around the world.MSCI Fixed Income Research© 2011 MSCI Inc. All rights reserved.Please refer to the disclaimer at the end of this document 30msci.com