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Current Global Equity Market Dynamics
and the Use of Factor Portfolios for Hedging
Effectiveness
Déborah Berebichez, Ph.D.
February 2013
©2013. ©2012. All rights reserved. msci.com

Outline I. Overview of Barra’s
Global Equity Model
II. Is Buying an Index Really
a Country bet?
III. Greece Case Study
IV. Hedging out Undesired
Exposures with a Factor-
Mimicking Portfolio
V. Rebalancing Frequency
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2

I. Overview of our
Global Equity
Model
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Barra Global Equity Model (GEM3) – Characteristics
• Barra Model Factors represent important drivers of both risk and return in
the global equity markets
• Common Factors are grouped into World, Country, Industry, Style, and
Currency components
• Barra Global Equity Model (GEM3) Long & Short Horizons
• Coverage of 77 Country Factors and 66 Currencies
• 74,000+ Assets
• Daily Model Updates (Exposures, Covariance Matrix & Specific Risk)
• Optimization Bias Adjustment improves risk forecasts for optimized portfolios
• Volatility Regime Adjustment calibrates factor volatilities to current levels
• Daily model history back to 1997
• 34 Industry GICS-based and 11 Style Factors
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GEM3 Regression Methodology
GEM3 treats country and industry factors symmetrically:
r
n
f
w
c
X
nc
f
c
i
X
• Every stock has unit exposure to World factor
• Exposures to countries/industries given by (0,1)
• Country and industry returns both net of World factor
• Style exposures cap-weighted mean zero
• Apply constraints to eliminate two-fold collinearity with World
• Regression weighting: square-root of market-cap
• Estimation universe: MSCI ACWI IMI
ni
f
i
s
X
ns
f
s
u
n
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Performance of Country Factors
• USA has outperformed over sample period
• Japan has underperformed, with higher volatility
Cumulative Return (Percent)
40 USA
Japan
20
0
-20
-40
1997 1999 2001 2003 2005 2007 2009 2011
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Year
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Performance of Industry Factors
• Banking factor fared poorly during Internet Bubble and since 2007
• Airlines performed poorly from 1998-2008
Cumulative Return (Percent)
40
20
0
-20
-40
-60
-80
1997 1999 2001 2003 2005 2007 2009 2011
Year
Airlines
Banks
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11 Style Factors in GEM3
• Beta
• Momentum
• Size
• Earnings Yield
• Residual Volatility
• Growth
• Dividend Yield
• Book to Price
• Leverage
• Liquidity
• Non-linear Size
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Descriptors of Residual Volatility Factor
• Residual Volatility
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Descriptor of Momentum Factor
• Momentum
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January 2013 Global Equity Market Watch – Highlights
• The World factor continued its positive performance with a 5% percent
return in January 2013. This marks eight months of non-negative monthly
performance for the World factor
• The Value Factor posted a 1.1 percent return in January 2013. This is the
highest return among the style factors, both by the absolute value and by
z-score
• The Japan factor remained the top contributor to cross-sectional
volatility for the second month in a row
• The Korea and Malaysia factors are among the bottom performers by z-
score, and top contributors to cross-sectional volatility
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Mean trailing 12-month realized volatilities of country, industry
(cap-weighted) and style factors (equal-weighted)
• Country factors dominated in late 1990s
Mean Trailing 12m Volatility
20
15
10
5
• Industries dominated during wake of
Internet Bubble
20
Countries
Industries
Styles
15
10
5
• Systemic
Financial
Crisis
0
1997 1999 2001 2003 2005 2007 2009 2011 2013
Year
0
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II. Is Buying an
Index Really a
Country Bet?
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Is Buying an Index Really a Country Bet?
• When you buy/sell an Index such as MSCI Greece IMI to gain (long or
short) exposure to the country Greece, you are not only getting exposure
to Greece but to many other style and industry factors
• You are getting more (or less) than just the country. The returns (or lack
thereof) depend on the exposure to multiple underlying factors
• A real country bet like a pure Greece exposure can be achieved in two
ways:
• Constructing a factor-mimicking Greece portfolio (very high exposure to Greece and very
low exposure to every other country, style, industry and the world factor)
• Or by hedging out the underlying exposure to all other undesired factors
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2012/02/20
2012/02/29
2012/03/09
2012/03/20
2012/03/29
2012/04/09
2012/04/18
2012/04/27
2012/05/08
2012/05/17
2012/05/28
2012/06/06
2012/06/15
2012/06/26
2012/07/04
2012/07/13
2012/07/24
2012/08/02
2012/08/13
2012/08/22
2012/08/31
2012/09/11
2012/09/20
2012/10/01
2012/10/10
2012/10/19
2012/10/30
2012/11/08
2012/11/19
2012/11/28
2012/12/07
2012/12/18
2012/12/27
2013/01/07
2013/01/16
2013/01/25
2013/02/05
2013/02/14
Malaysia Cumulative Returns 12 Months February 2013
• MSCI Malaysia IMI Daily Cumulative Returns (blue) (-14%)
• Pure Malaysia Market Returns (red) (0.27%)
0.10
0.05
0.00
-0.05
Pure Malaysia Mkt Factor
MSCI Malaysia IMI Index
-0.10
-0.15
-0.20
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III. Greece Case
Study
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2012/02/20
2012/02/29
2012/03/09
2012/03/20
2012/03/29
2012/04/09
2012/04/18
2012/04/27
2012/05/08
2012/05/17
2012/05/28
2012/06/06
2012/06/15
2012/06/26
2012/07/05
2012/07/16
2012/07/25
2012/08/03
2012/08/14
2012/08/23
2012/09/03
2012/09/12
2012/09/21
2012/10/02
2012/10/11
2012/10/22
2012/10/31
2012/11/09
2012/11/20
2012/11/29
2012/12/10
2012/12/19
2012/12/28
2013/01/08
2013/01/17
2013/01/28
2013/02/06
2013/02/15
Greece Cumulative Returns 12 Months February 2013
• MSCI Greece IMI Cumulative Returns (blue) (8.5%)
• Pure Greece Country Returns (red) (39%)
60.00%
40.00%
20.00%
0.00%
-20.00%
-40.00%
-60.00%
MSCI Greece IMI -Cumulative Returns
Pure Greece -Cumulative Returns
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MSCI Greece IMI Return Attribution
• Country is a large positive driver
of returns (34.43%)
• Risk Styles are a large detractor
from returns (-23.88%)
• The most negative influence
comes from the Residual
Volatility factor (-16.39%)
• Followed by the Momentum
factor (-10.22%)
• Large negative specific return
(-16.62%) not typical of an Index
Source of Return
Contribution to Return
Total Managed 8.48%
Residual 6.16%
Common Factor 22.78%
World 11.88%
Industry 0.35%
Country 34.43%
Risk Indices -23.88%
Beta 2.56%
Book-to-Price 0.04%
Dividend Yield 0.01%
Earnings Yield -0.17%
Growth -0.09%
Leverage 0.13%
Liquidity -0.08%
Momentum -10.22%
Non-Linear Size 0.21%
Residual Volatility -16.39%
Size 0.10%
Specific -16.62%
Currency 2.23%
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MSCI Greece IMI Return Attribution
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MSCI Greece IMI Residual Volatility Contribution to return
• Exposure of the Index to Residual Volatility
• Cumulative Residual Volatility Returns (blue)
• Contribution of Residual Volatility to the Index Returns (-16.39%)
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MSCI Greece IMI Momentum Contribution
• Exposure of the Index to Momentum
• Cumulative Momentum Returns (blue)
• Contribution of Momentum to the Index Returns (-10.22%)
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IV. Hedging out
Undesired
Exposures with a
Factor-Mimicking
Portfolio
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Characteristics of Factor Mimicking Portfolios
• A pure factor portfolio exactly replicates the payoffs to the factor
• A factor-mimicking portfolio strikes a balance between factor tracking and
index investability and replicability
• Achieves a high level of exposure to a particular factor (the “Target Factor”) and very low
exposure to all other styles, industries, countries and the world factor, while minimizing
specific risk
• Constraints can be number of constituents, monthly turnover, trade limit, shorting cost,
etc
• Applications:
• PASSIVE: To capture alpha as the basis for ETFs for style investing such as value, growth,
large-cap, etc
• ACTIVE: To hedge out undesired risk
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Constructing a Factor-Mimicking Portfolio
• Barra Aegis Optimizer Settings
• Benchmark: Pure Factor Asset
• Universe: MSCI ACWI IMI
• Trading Constraint: Maintain Exposures Close to the Benchmark
• Style Constraints:
• Risk Style Exposures = All Zero except for a Target Exposure of 1 to the desired Style
• Country Equity Exposures = All Zero Country Equity Exposures
• Industries Exposures = All Zero Industry Exposures
• World Equity Exposure = Zero World Equity Exposure
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Characteristics of Residual Volatility Portfolio
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Risk Style Exposures for Residual Volatility Portfolio
• Insignificant Exposures to countries, sectors and the World Equity Factor
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V. Rebalancing
Frequency
Change in Quality of the
Factor-Mimicking Portfolios
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Exposure of Initial Portfolio to Residual Volatility Over Time
• One Year Degradation (no rebalancing)
• With monthly rebalancing
Factor mimicking portfolios get degraded over time. This determines the frequency of
rebalancing
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Exposure of Initial Portfolio to Momentum Over Time
• One Year Degradation (no rebalancing)
• With monthly rebalancing
Factor mimicking portfolios get degraded over time. This determines the frequency of
rebalancing
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Americas
Europe, Middle East & Africa
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• This document and all of the information contained in it, including without limitation all text, data, graphs, charts (collectively, the “Information”) is the property of MSCl Inc. or its
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“Information Providers”) and is provided for informational purposes only. The Information may not be reproduced or redisseminated in whole or in part without prior written
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• The Information may not be used to create derivative works or to verify or correct other data or information. For example (but without limitation), the Information may not be used
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& Poor’s.
© 2012 MSCI Inc. All rights reserved. RV Jan 2012
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A Brief Digression: Risk Attribution
R
x g
t m mt
m
Return Attribution, Period t
xm
Source Exposure;
gmt
Source Return
R x ,
m gm gm R
m
Risk Attribution
x-sigma-rho formula
• Identifies three drivers of time series volatility
• Risk contributions are intuitive and fully additive
• Aligns risk attribution model with investment process
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Exact CSV Decomposition
r
u
Return Decomposition (factor vs specific)
n n n
f
n k nk
k
X
Linear Factor Structure
( ) f ,
k
X
k
X
k
k
Explained CS Volatility
x-sigma-rho formula
• Identifies three drivers of cross-sectional volatility
• Volatility contributions are intuitive and fully additive
• CSV can be attributed to individual factors!
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Approximate CSV Decomposition
• Collinearity among GEM2 factors is typically small
• Reasonable and useful approximation:
( )
k
f
2
k
2
X
k
No-collinearity
Approximation
• Contribution to explained CSV is roughly proportional to the squared
factor return and the variance of factor exposures
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Style Factor Selection
• Good style factors should:
• Significantly increase explanatory power of model
• Have high statistical significance
• Be stable across time
• Not be excessively collinear with other factors
• Be intuitive and consistent with investors’ views
• Stability Measure:
corr X , X
t t t 1
k k k
Factor Stability
Coefficient
• Collinearity Measure:
1
X
nk
X
nlbl + nk VIFk
1 R
lk
2
k
Variance Inflation
Factor
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Contribution of Style Factors to Cross-Sectional Volatility
• Beta dominated in the aftermath of the Internet bubble
• Momentum dominated in late 1990s and in 2009
Monthly RMS Contribution (%)
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1997 1999 2001 2003 2005 2007 2009 2011
Year
Momentum
Beta
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Outline
• Model Highlights and Overview
• Methodology Details
• Factor Structure
• Explanatory Power
• Optimization Bias Adjustment
• Volatility Regime Adjustment
• New Specific Risk Model
• Additional Empirical Results
• Summary
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Model Highlights
• Full daily updates of all components of the model
• Extended coverage to 22 frontier markets
• Enhanced style factors
• Methodology Advances:
• An innovative Optimization Bias Adjustment methodology designed to provide improved
risk forecasts for optimized portfolios by reducing the effects of sampling error
• Volatility Regime Adjustment designed to calibrate volatility forecasts to current levels
• A new specific risk model based on daily asset-level specific returns with Bayesian
adjustment designed to reduce biases due to sampling error
• Improved risk forecasts
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GEM3 Regression Methodology: Constraints
GEM3 Regression:
r
n
f
w
c
X
nc
f
c
i
X
ni
f
i
s
X
ns
f
s
u
n
Cap-weighted country/industry factor returns sum to zero:
c
w f ; w f 0
c
c
0 Constraints
i
i
i
f k
r
n
kn
n
Factor returns
kn
gives the weight of stock n in pure factor portfolio k
Interpret f w as the cap-weighted return of the world portfolio
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Style Factor Selection
• Good style factors should:
• Significantly increase explanatory power of model
• Have high statistical significance
• Be stable across time
• Not be excessively collinear with other factors
• Be intuitive and consistent with investors’ views
• Stability Measure:
corr X , X
t t t 1
k k k
Factor Stability
Coefficient
• Collinearity Measure:
1
X
nk
X
nlbl + nk VIFk
1 R
lk
2
k
Variance Inflation
Factor
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2012/02/20
2012/03/01
2012/03/13
2012/03/23
2012/04/04
2012/04/16
2012/04/26
2012/05/08
2012/05/18
2012/05/30
2012/06/11
2012/06/21
2012/07/02
2012/07/12
2012/07/24
2012/08/03
2012/08/15
2012/08/27
2012/09/06
2012/09/18
2012/09/28
2012/10/10
2012/10/22
2012/11/01
2012/11/13
2012/11/23
2012/12/05
2012/12/17
2012/12/27
2013/01/08
2013/01/18
2013/01/30
2013/02/11
Korea Cumulative Returns 12 Months February 2013
• MSCI Korea Daily Cumulative Returns (blue) (1.27%)
• Pure Korea Market Returns (red) (-9%)
10.00%
5.00%
MSCI Korea Daily Returns
0.00%
Korea Mkt Factor
-5.00%
-10.00%
-15.00%
-20.00%
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Optimization Bias
Adjustment
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Initial Factor Covariance Matrix
• Use daily factor returns to estimate factor covariance matrix (FCM)
• Use shorter half-life to estimate volatilities (responsiveness)
• Use longer half-life for correlations (conditioning)
• Account for serial correlations and asynchronicity using the Newey-West
method
Factor Newey-West Factor Newey-West Factor
Volatility Volatility Correlation Correlation CSV
Model Half-Life Lags Half-Life Lags Half-Life
GEM3S 84 10 504 3 42
GEM3L 252 10 504 3 168
• S-Model designed for most accurate forecasts at one-month horizon
• L-Model designed for greater stability in risk forecasts (less responsive)
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Eigenfactors and Optimization Bias
• Traditional risk models tend to underpredict the risk of optimized
portfolios
• This bias is related to estimation error in the covariance matrix
• Eigenfactors represent uncorrelated linear combinations of pure factors
• Eigenfactors solve certain classes of minimum variance optimizations
• Eigenfactors reliably capture systematic biases in the sample factor
covariance matrix (FCM)
• The biases can be demonstrated and estimated by simulation
• Removing the biases of the eigenfactors is effective at removing the biases
of optimized portfolios
Jose Menchero, DJ Orr, and Jun Wang. “Eigen-Adjusted Covariance Matrices,”
MSCI Research Insight, May 2011
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Optimization Bias Adjustment Methodology
• Assume that the sample FCM F 0 denotes the “true” FCM
• Simulate a set of factor returns f n from F 0 (e.g., Cholesky approach)
• Compute simulated FCM F n using same estimator as used for F 0
• Diagonalize F n to obtain simulated eigenfactor volatilities
• Use F 0 to compute the “true” volatilities of simulated eigenfactors
• Compute the average bias of simulated eigenfactors by Monte Carlo
simulation
• Assume F 0 suffers from the same biases as the simulated FCM and debias
the eigenvariances
• Transform adjusted FCM back to the original pure basis
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Volatility Regime Adjustment
for Factors
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Volatility Regime Adjustment for Factor Covariance Matrix
• Construct factor covariance matrix F using “standard” time-series
techniques (e.g., EWMA with serial correlation adjustments)
• Use cross-sectional observations (bias statistics) to calibrate factor
volatilities to current levels
k
B
f
2 1
kt
t
K k
kt
2
Cross-Sectional Bias
Statistic (squared)
B
2 2
F t t
t
(EWMA)
F
Factor Volatility Multiplier
F
F
2
k F k F
Volatility Regime Adjusted
Factor Covariance Matrix
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Volatility Regime Adjustments for Factor Covariance Matrix
Factor Volatility Multiplier
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
Factor
0.2
CSV
1995 1997 1999 2001 2003 2005 2007 2009 2011
CSV
F
t
Industry and Style Factors
1
K
k
f
2
kt
Factor
Volatility
Multiplier
Year
(Factor CSV)
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
Factor CSV (percent daily)
• Cross-sectional
observations provide
an “instantaneous”
measure of factor
volatility levels
• During stable periods,
Volatility Regime
Adjustment tends to
be very small
• Adjustments are rapid
and intuitive following
market shocks
• Volatility Regime
Adjustment helps
“when needed most”
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Improvement with Volatility Regime Adjustment (Factors)
• Plot mean bias statistics (rolling 12m) of all factors, with and without
Volatility Regime Adjustment
Mean Bias Statistic
1.4
1.3
1.2
1.1
1.0
0.9
0.8
Volatility Regime Adjustment (GEM3S)
With Volatility
Regime Adjustment
0.7
Unadjusted
0.7
0.6
0.6
1998 2000 2002 2004 2006 2008 2010 2012
Year
1.4
1.3
1.2
1.1
1.0
0.9
0.8
• With Volatility Regime
Adjustment, most
months the mean bias
statistics are closer to
the ideal value of 1
• Volatility Regime
Adjustment reduces the
underforecasting bias
during crises and the
overforecasting bias
following crises
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