Current Global Equity Market Dynamics and the Use of Factor Portfolios for Hedging Effectiveness

Transcription

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

2 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 2

3 I. Overview of our Global Equity Model 3

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 Industry GICS-based and 11 Style Factors 4

5 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 5

6 Performance of Country Factors USA has outperformed over sample period Japan has underperformed, with higher volatility Cumulative Return (Percent) 40 USA Japan Year 6

7 Performance of Industry Factors Banking factor fared poorly during Internet Bubble and since 2007 Airlines performed poorly from Cumulative Return (Percent) Year Airlines Banks 7

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

9 Descriptors of Residual Volatility Factor Residual Volatility 9

10 Descriptor of Momentum Factor Momentum 10

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 11

12 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 Industries dominated during wake of Internet Bubble 20 Countries Industries Styles Systemic Financial Crisis Year 0 12

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

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 14

15 2012/02/ /02/ /03/ /03/ /03/ /04/ /04/ /04/ /05/ /05/ /05/ /06/ /06/ /06/ /07/ /07/ /07/ /08/ /08/ /08/ /08/ /09/ /09/ /10/ /10/ /10/ /10/ /11/ /11/ /11/ /12/ /12/ /12/ /01/ /01/ /01/ /02/ /02/14 Malaysia Cumulative Returns 12 Months February 2013 MSCI Malaysia IMI Daily Cumulative Returns (blue) (-14%) Pure Malaysia Market Returns (red) (0.27%) Pure Malaysia Mkt Factor MSCI Malaysia IMI Index

16 III. Greece Case Study 16

17 2012/02/ /02/ /03/ /03/ /03/ /04/ /04/ /04/ /05/ /05/ /05/ /06/ /06/ /06/ /07/ /07/ /07/ /08/ /08/ /08/ /09/ /09/ /09/ /10/ /10/ /10/ /10/ /11/ /11/ /11/ /12/ /12/ /12/ /01/ /01/ /01/ /02/ /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% % % % MSCI Greece IMI -Cumulative Returns Pure Greece -Cumulative Returns 17

18 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 % 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 % Non-Linear Size 0.21% Residual Volatility % Size 0.10% Specific % Currency 2.23% 18

19 MSCI Greece IMI Return Attribution 19

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%) 20

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%) 21

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

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 23

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 24

25 Characteristics of Residual Volatility Portfolio 25

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

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

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 28

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 29

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32 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 33

33 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! 34

34 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 35

35 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 36

36 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 (%) Year Momentum Beta 40

37 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 41

38 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 42

39 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 43

40 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 44

41 2012/02/ /03/ /03/ /03/ /04/ /04/ /04/ /05/ /05/ /05/ /06/ /06/ /07/ /07/ /07/ /08/ /08/ /08/ /09/ /09/ /09/ /10/ /10/ /11/ /11/ /11/ /12/ /12/ /12/ /01/ /01/ /01/ /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% % % % 45

42 Optimization Bias Adjustment 46

43 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 GEM3L S-Model designed for most accurate forecasts at one-month horizon L-Model designed for greater stability in risk forecasts (less responsive) 47

44 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

45 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 49

46 Volatility Regime Adjustment for Factors 50

47 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 51

48 Volatility Regime Adjustments for Factor Covariance Matrix Factor Volatility Multiplier Factor 0.2 CSV CSV F t Industry and Style Factors 1 K k f 2 kt Factor Volatility Multiplier Year (Factor CSV) 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 52

49 Improvement with Volatility Regime Adjustment (Factors) Plot mean bias statistics (rolling 12m) of all factors, with and without Volatility Regime Adjustment Mean Bias Statistic Volatility Regime Adjustment (GEM3S) With Volatility Regime Adjustment 0.7 Unadjusted Year 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 53