1. Déborah Berebichez, Ph.D. February 2013
Current Global Equity Market Dynamics and the Use of Factor Portfolios for Hedging Effectiveness
Déborah Berebichez, Ph.D.
February 2013

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

3. I. Overview of our Global Equity Model

4. 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
Half Lives:
Long Term: Vol = 252 Days, Correl = 504 Days, Vol regime Adj = 168 Days
Short Term: Vol = 84 Days, Correl = 504 Days, Vol regime Adj = 42 Days
Regression Weighting Scheme: Square Root of USD Cap
Optimization Bias Adjustment
Traditional risk models tend to underpredict the risk of optimized portfolios
Sampling error causes eigenfactors to be systematically biased
Removing biases of eigenfactors improves forecasts for optimized portfolios
Volatility Regime Adjustment
Cross-sectional bias statistics provide an “instantaneous” measure of risk model bias
Cross-sectional observations can be used to calibrate volatilities to current market levels
New Specific Risk Model
GEM3 uses asset-level time-series estimates as the starting point
Bayesian adjustment technique is applied to remove biases at extremes
Applies Volatility Regime Adjustment to calibrate specific risk levels

5. GEM3 Regression Methodology
GEM3 treats country and industry factors symmetrically:
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
Confidential

6. Performance of Country Factors
USA has outperformed over sample period
Japan has underperformed, with higher volatility
Confidential

7. Performance of Industry Factors
Banking factor fared poorly during Internet Bubble and since 2007
Airlines performed poorly from

8. 11 Style Factors in GEM3 Beta Momentum Size Earnings Yield
Residual Volatility
Growth
Dividend Yield
Book to Price
Leverage
Liquidity
Non-linear Size

9. Descriptors of Residual Volatility Factor

10. Descriptor of Momentum Factor

11. January 2013 Global Equity Market Watch – Highlights
The World factor continued its positive performance with a 5% percent return in January This marks eight months of non-negative monthly performance for the World factor
The Value Factor posted a 1.1 percent return in January 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
Cross-sectional Volatility: instantaneous measure of the volatility in the market and it can be attributed among factor types. CSV also represents opportunities for active managers. The higher the CSV in the market, the better chance that a manger has to outperform his/her peers.
CSV is a point-in-time measure. Let’s assume MSCI World is our market, CSV is basically the standard deviation of the whole MSCI world portfolio, but at a specific point in time. So if say on 02/24/2013, the mean return of all the stocks in MSCI world was 2%, the CSV on that day should be the standard deviation calculated against this mean return. As you could see, the higher the CSV, the more each stock’s return deviates from the mean of the market. As a result, a skillful manager have a better chance of picking out those winner and avoiding the losers. If the CSV is low, which means skills basically don’t matter cuz an average manager can generate returns close to the mean. Therefore makes it difficult to differentiate a good stock picker from a bad one. This is why CSV represents opportunities for active managers.

12. Mean trailing 12-month realized volatilities of country, industry (cap-weighted) and style factors (equal-weighted)
Country factors dominated in late 1990s
Industries dominated during wake of Internet Bubble
Systemic Financial Crisis

13. II. Is Buying an Index Really a Country Bet?

14. 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

15. Malaysia Cumulative Returns 12 Months February 2013
MSCI Malaysia IMI Daily Cumulative Returns (blue) (-14%)
Pure Malaysia Market Returns (red) (0.27%)

16. III. Greece Case Study

17. Greece Cumulative Returns 12 Months February 2013
MSCI Greece IMI Cumulative Returns (blue) (8.5%)
Pure Greece Country Returns (red) (39%)

18. MSCI Greece IMI Return Attribution
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%
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
The discrepancy in Greece IMI Return Contribution of country Greece between this page (34.43%) and the previous page’s graph (39%) is that Greece Returns are calculated using the Local Currency (and in excess of the Greece Risk Free Rate) while this Attribution Chart is done using USD

19. MSCI Greece IMI Return Attribution

20. 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%)

21. MSCI Greece IMI Momentum Contribution
Exposure of the Index to Momentum
Cumulative Momentum Returns (blue)
Contribution of Momentum to the Index Returns (-10.22%)

22. IV. Hedging out Undesired Exposures with a Factor-Mimicking Portfolio

23. 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

24. 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

25. Characteristics of Residual Volatility Portfolio

26. Risk Style Exposures for Residual Volatility Portfolio
Insignificant Exposures to countries, sectors and the World Equity Factor

27. V. Rebalancing Frequency
Change in Quality of the Factor-Mimicking Portfolios

28. 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

29. 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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32. Appendix:
Technical Details

33. A Brief Digression: Risk Attribution
Return Attribution, Period t
Source Exposure;
Risk Attribution x-sigma-rho formula
Source Return
Identifies three drivers of time series volatility
Risk contributions are intuitive and fully additive
Aligns risk attribution model with investment process

34. Exact CSV Decomposition
Return Decomposition (factor vs specific)
Explained CS Volatility x-sigma-rho formula
Linear Factor Structure
Identifies three drivers of cross-sectional volatility
Volatility contributions are intuitive and fully additive
CSV can be attributed to individual factors!

35. Approximate CSV Decomposition
Collinearity among GEM2 factors is typically small
Reasonable and useful approximation:
Contribution to explained CSV is roughly proportional to the squared factor return and the variance of factor exposures
No-collinearity
Approximation

36. 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:
Factor Stability Coefficient
Collinearity Measure:
Variance Inflation Factor

37. Model Methodology
The Barra Global Equity Model (GEM2) decomposes the local excess stock returns into a systematic component (due to factors) and a stock-specific component . The factor returns are estimated each period by cross- sectional regression
(A1)
where is the exposure of stock n to factor k. The regression weights are proportional to the square root of market capitalization. The specific returns are assumed to be uncorrelated with one another as well as to the other factors
Factor returns can be estimated on a daily, weekly, or monthly basis. Daily factor returns are useful for performance attribution purposes. Weekly factor returns serve as inputs for estimating the factor covariance matrix. In this publication, we adopt monthly factor returns for the study of the global equity markets

38. Realized Volatilities
The trailing 12-month realized volatility of a factor is given by (A2)
where is the return to factor k for month t, and is the mean return to the factor over the past 12 months. The mean trailing 12-month realized volatility of a factor group is given by the weighted average
(A3)
For country and industry factors (Figure 1) we use end-of-period cap- weights, whereas for style factors we use equal weights. Currency and stock-specific volatility are reported on an end-of-period cap-weighted basis (Figure 2).

39. Standardized Returns (z-scores)
The standardized return (also known as a z-score) of a factor is given by the ratio of the realized return to the forecast volatility
(A4)
For perfect risk forecasts, the standard deviation of standardized returns is equal to 1. Ranking factors by z-score signals which factors saw the most extreme moves. For we use the GEM2S factor volatility forecasts. Table 3 reports the top and bottom factor returns over the previous month, ranked by z-score

40. 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

41. 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

42. 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

43. GEM3 Regression Methodology: Constraints
Cap-weighted country/industry factor returns sum to zero:
Constraints
Factor returns
gives the weight of stock n in pure factor portfolio k
Interpret fw as the cap-weighted return of the world portfolio
Confidential

44. 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:
Factor Stability Coefficient
Collinearity Measure:
Variance Inflation Factor

45. Korea Cumulative Returns 12 Months February 2013
MSCI Korea Daily Cumulative Returns (blue) (1.27%)
Pure Korea Market Returns (red) (-9%)

46. Optimization Bias Adjustment

47. 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
S-Model designed for most accurate forecasts at one-month horizon
L-Model designed for greater stability in risk forecasts (less responsive)

48. 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

49. Optimization Bias Adjustment Methodology
Assume that the sample FCM F0 denotes the “true” FCM
Simulate a set of factor returns fn from F0 (e.g., Cholesky approach)
Compute simulated FCM Fn using same estimator as used for F0
Diagonalize Fn to obtain simulated eigenfactor volatilities
Use F0 to compute the “true” volatilities of simulated eigenfactors
Compute the average bias of simulated eigenfactors by Monte Carlo simulation
Assume F0 suffers from the same biases as the simulated FCM and de- bias the eigenvariances
Transform adjusted FCM back to the original pure basis
Confidential

50. Volatility Regime Adjustment for Factors

51. 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
Cross-Sectional Bias Statistic (squared)
(EWMA)
Factor Volatility Multiplier
Volatility Regime Adjusted Factor Covariance Matrix
Confidential

52. Volatility Regime Adjustments for Factor Covariance Matrix
Industry and Style Factors
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”
(Factor CSV)
Confidential

53. Improvement with Volatility Regime Adjustment (Factors)
Plot mean bias statistics (rolling 12m) of all factors, with and without Volatility Regime Adjustment
Volatility Regime Adjustment (GEM3S)
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
Confidential