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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
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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
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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 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
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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
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Performance of Country Factors
USA has outperformed over sample period Japan has underperformed, with higher volatility Confidential
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Performance of Industry Factors
Banking factor fared poorly during Internet Bubble and since 2007 Airlines performed poorly from
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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
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Descriptor of Momentum Factor
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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 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.
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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 Industries dominated during wake of Internet Bubble Systemic Financial Crisis
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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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Malaysia Cumulative Returns 12 Months February 2013
MSCI Malaysia IMI Daily Cumulative Returns (blue) (-14%) Pure Malaysia Market Returns (red) (0.27%)
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III. Greece Case Study
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Greece Cumulative Returns 12 Months February 2013
MSCI Greece IMI Cumulative Returns (blue) (8.5%) Pure Greece Country Returns (red) (39%)
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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
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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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Appendix: Technical Details
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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
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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!
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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
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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: Factor Stability Coefficient Collinearity Measure: Variance Inflation Factor
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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
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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).
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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
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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
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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
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
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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: Factor Stability Coefficient Collinearity Measure: Variance Inflation Factor
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Korea Cumulative Returns 12 Months February 2013
MSCI Korea Daily Cumulative Returns (blue) (1.27%) Pure Korea Market Returns (red) (-9%)
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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 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 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
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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 Cross-Sectional Bias Statistic (squared) (EWMA) Factor Volatility Multiplier Volatility Regime Adjusted Factor Covariance Matrix Confidential
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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
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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 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
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