Smart Alpha: A Post Factor Investing Paradigm

Transcription

1 Smart Alpha: A Post Factor Investing Paradigm This presentation reflects only its authors opinions and does not necessarily reflect those of their employers.

2 Smart Alpha: A Post Factor Investing Paradigm Christophe Boucher ABN AMRO Investment Solutions U. Paris Nanterre christophe.boucher@abnamro.com Alexandre Jasinski ABN AMRO Investment Solutions Patrick Kouontchou ABN AMRO Investment Solutions U. Lorraine Sessi Tokpavi ABN AMRO Investment Solutions U. Orléans 10 th FINANCIAL RISKS INTERNATIONAL FORUM - Paris, 27 & 28 March This presentation reflects only its authors opinions and does not necessarily reflect those of their employers.

3 In a Nutschell A new paradigm/methodology for portfolio construction: Portfolio of 100% Equities; Active (concentrated 50 to 100 stocks); Pure stock picking (no regional or sectoral constraint); Simple and transparent (no derivatives, long-only); «Natural» diversification (no factor dependent); Decorrelated portfolio. Max Alpha Min Systematic Risks Identify significant multi-factors Systematic analysis of the universe Post factor investing approach: Anti-smart beta / anti-factor investing; maximization of the expected return uncorrelated to various systematic sources of risk (alpha); while minimizing the exposures to these risk factors (systematic risk). Select high Robust Alphas Minimizing Systematic Risks Smart Stock selection Portfolio construction All road long-only 100% equity portfolio 3

4 Motivations & Objectives

5 Motivations: the rise of factor investing The efficiency of Markowitz (1952) MV optimized portfolios and Capital Asset Pricing Model of Sharpe (1964) challenged: Mean-variance optimized portfolios and market-capitalization weighting portfolios perform relatively poorly out-of-sample; Existence beyond the market of some common risk factors in the returns of stocks (Fama and French, 1992; Jegadeesh and Titman, 1993); With many factors that are suspected to explain the cross-sectional variations of stock returns, alpha appears as beta in disguise (shadowed betas). Alternative heuristic approaches have been proposed and rapidly attracted, under the smart beta or factor investing labels: Change of paradigm: move from active alpha seeking strategies to exposures to risk factors; Capture risk factors and thus risk premia, such as low volatility, momentum, quality, value and size; Assets under management have grown by 500 percent since 2008 to 616bn at the end of 2015 (Morningstar). 5

6 Motivations: but too much factors In the academic literature, factors are becoming so numerous and exotic that John Cochrane referred as a zoo : Only few of the 314 factors in the zoo are statistically significant (Harvey et al., 2014); Large part of impossible replication and anomalies that disappear few months later publication: data mining (600 factors in Levy and Welch, 2014; McLean and Pontif, 2013). William Sharpe at the CFA Institute Annual conference in Seattle on May, : 6

7 Motivations: while offering poor diversification in practice Correlations of the weekly returns of factor investing/smart beta European Equity Indexes, : Source: Bloomberg, Datastream, weekly data in EUR from January 5, 2001 to May 13, Computations by the authors. The European equity indices are the MSCI Europe Total Return Index, MSCI Europe Small Capitalization Total Return Index, MSCI Europe Large Capitalization Total Return Index, MSCI Europe Value Total Return Index, MSCI Europe Growth Total Return Index, MSCI Europe Quality Total Return Index, MSCI Europe Momentum Total Return Index and the MSCI Europe Minimum Volatility Total Return Index. Traditional systematic factors are characterized by a high degree of correlation that persists even if one removes the common market component. 7

8 Motivations: many challenges in factor investing Factor investing is conceptually elegant: The asset management industry has tended to neglect the importance of betas due to an exclusive focus on alpha; The increasing attention to the variety of betas is thus a worthy development. But hard to implement: Model risk Implementation Specification risk: A «bazar of factors»: the need to properly identify significant factors; Estimation risk: How to build and measure each factor (various and not coherent fundamental/risk metrics)? Factor timing? Factors in the literature as long-short portfolios difficult to implement. 8

9 Objectives: and so what? A new step after the Factor Investing / Smart Beta revolution. Main working hypothesis: Only few factors are priced, difficult to identify with some unstability; Don t play with factors, instead looking for performance non related to systematic risks; Alphas as temporary anomalies (industry is focusing on pseudo-factors). Myth of Plato's cave. Need for a systematic/heuristic process Identifying alpha is complex (number of factors, shadow betas, unstable betas, timevarying factors); Requires «cold blood» and reactivity (temporary alpha opportunities); While managing risks of alpha chasing (unstable betas); Avoid human biases: preferred stock, false fallacy, etc. Robust alpha: controlling all significant betas and factors. 9

10 Objectives: Smart Alpha? Smart Alpha Portfolio Security Market Line Min Var Portfolio Market Portfolio Source: Figure based on simulations for illustrative purpose, past performance does not guarantee future returns. 10

11 Objectives: Smart Alpha New methodology that consists in a maximization of the expected return uncorrelated to various systematic sources of risk (alpha), while minimizing the exposures to these risk factors (systematic risks): Using hidden factors instead of traditional empirical factors; Using stock s smart alpha extracted through a latent factor model with a consistent timing of the exact number of optimal factors. Empirical results on the STOXX 600 universe confirm the value of our integrated framework for Smart Alpha: High and significant alpha in all market states (bull, bear or crisis); Limited exposition to traditional factors (at least the Market Cap); High expected return/risk profile compared to the market cap-weighted index and popular smart-beta investment strategies. 11

12 Smart Alpha Strategy - Latent Factors and Smart Alpha - Smart Alpha Optimization Program

13 Latent Factors and Smart Alpha (1/3) We consider a factor representation of the observed data: where is the return on stock i at time t, is a vector of length m with components the m latent factors that drive the returns on stocks, the vector of length m of factor loadings for stock i, and is the idiosyncratic or residual return at time t. Bai and Ng (2002) propose to estimate the correct number of latent factor (m) by using information-criteria statistics: balance between residual variance that mechanically diminishes with the number of factors and the complexity of the model increasing in the number of factors: where is the principal components estimates of latent factors,, and is the average residual variance across stocks and time when the number of factor is set to k and defined by: with the estimated residual return on stock i. 13

14 Latent Factors and Smart Alpha (2/3) The estimated value of the number of latent factor m corresponds to the value of k that minimizes the information criterion: with the maximum number of factors we set to 50. Bai and Ng (2002) show that: Finally, the principal component estimate of alpha (smart alpha) for stock i equal to where is the empirical mean of stock returns over the sample of size T, the vector of the empirical means of the optimal factors and the corresponding estimated factor loadings vector for stock i. 14

15 Latent Factors and Smart Alpha (3/3) Illustration: Timing of the number of factors for the STOXX 600 universe Source: Bloomberg, daily data from January 3, 2000 to May 17, Computations by the authors. Substantial variation over time, with a clear-cut shape corresponding to a significant increase in the beginning of crisis periods (maximum of 18), and a decrease at the exit (minimum of 3). 15

16 Latent and a-priori factor matching Latent and a-priori factor matching (absolute value of the correlation coefficients) Source: Bloomberg, daily data from January, 01, 2000 to May 17, Computations by the authors. Rm: MSCI Europe; China: MSCI China; EONIA: Eonia rate; GOLD: Gold Bullion LBM U$/Troy Ounce; GROWTH: MSCI Europe Growth; LARGE: MSCI Europe Large; MinVol: MSCI Europe Minimum Volatility; MOM: MSCI Europe Momentum; OIL : Crude Oil WTI Cushing U$/BBL; Sect Auto: DS Equity Auto & Parts; Sect Basic: DS Equity Basic Resources; Sect Bks: DS Equity Banks; Sect Chemistry: DS Equity Chemistry; Sect Constr: DS Equity Construction; Sect Food: DS Equity Food & Beverage; Sect Oil: DS Equity Oil & Gas; Sect Pers: DS Equity Personal and Household Goods; Sect RealEstate: DS Equity Real Estate; Sect Telecom: DS Equity Telecom; Sect Travel: DS Equity Travel & Leisures; Sect Utilities: DS Equity Utilities; SMALL: MSCI Europe Small; TERM: US term spread (10year - 3months rates); US: MSCI US; VALUE: MSCi Europe Value. Notes: Higher absolute value of correlations coefficients for each latent factor and the corresponding a-priori factor. 16

17 Smart Alpha Optimization Program Let w be a vector of length N with elements the weights of a given portfolio. Based on the two objectives underlying the smart alpha investment paradigm, the optimization program can be written as follows: with the estimates of smart alphas, the systematic covariance matrix given by: where is the (N,m) matrix of stock s exposures, is the (m,m) matrix corresponding to the covariance matrix of factors, is the required portfolio alpha (grid search), the upper-bound on portfolio weights for diversification purpose, and e the unit vector of length N. A constraint to manage turnover level is considered. 17

18 Empirical Results - Data and Evaluation Methodology - Performance, Risk Analyses and Economic Value - Sensitivity Analysis

19 Data and Evaluation Methodology Database comes from Bloomberg and Datastream, and includes daily returns of all constituents of the STOXX 600 index from January 4, 1999 to May 17, 2016: N = 1211 stocks (all stocks in the composition of the STOXX 600 index since January 4, 1999) and T = 4532 daily observations; No survivorship bias: the database is not limited to only those stocks in the capitalization universe at the end of the sample. Rolling one-month optimization with n = 260 days: By restricting the investment universe to only the 600 stocks in the capitalization universe at the optimization date; By using a delay of one day for investment, and a proportional transaction cost of 25 basis point. The smart alpha portfolio strategy is compared to: The minimum systematic risk strategy (same program as for Smart alpha but without alpha constraint); and some common smart beta alternatives, including the minimum volatility, the risk parity and the equally-weighted. 19

20 Performance Analyses of Smart Alpha Strategy Performance measures for Smart Alpha (SA) portfolio and alternatives portfolios Source: Bloomberg, daily data from January 3, 2000 to May 17, Computations by the authors. SA refers to Smart Alpha portfolio strategy, MSR to Minimum Systematic Risk portfolio strategy, MV to Minimum Volatility portfolio strategy, RP to Risk Parity portfolio strategy, EW to Equally-Weighted portfolio strategy, and Benchmark is here the STOXX 600 index. Statistics are computed in four periods: Full Sample (January 3, 2000 to May 17, 2016), Pre-crisis (January 3, 2000 to December 29, 2006), Crisis (December 29, 2006 to March 31, 2009) and Post-crisis (March 31, 2009 to May 17, 2016). With respect to the other portfolios the Smart Alpha portfolio has the best performance over all three periods. 20

21 Performance Analyses of Smart Alpha Strategy Net Asset Value of Smart Alpha (SA) and alternatives portfolios Source: Bloomberg, daily data from January 3, 2000 to May 17, Computations by the authors. SA refers to Smart Alpha strategy portfolio, MSR to Minimum Systematic Risk strategy portfolio, MV to Minimum Volatility strategy portfolio, RP to Risk Parity strategy portfolio, EW to Equally-Weighted strategy portfolio and Benchmark is here the STOXX 600 Index. The smart alpha portfolio has the highest net asset value at the end of the period equal to 641 for an initial investment of

22 Risk Analyses of Smart Alpha Strategy Ex-post Risk statistics for the Smart Alpha and Alternative Strategies Source: Bloomberg, daily data from January 3, 2000 to May 17, Computations by the authors. SA refers to Smart Alpha portfolio strategy, MSR to Minimum Systematic Risk portfolio strategy, MV to Minimum Volatility portfolio strategy, RP to Risk Parity portfolio strategy, EW to Equally-Weighted portfolio strategy, and Benchmark is here the STOXX 600 index. Statistics are computed in four periods: Full Sample (January 3, 2000 to May 17, 2016), Pre-crisis (January 3, 2000 to December 29, 2006), Crisis (December 29, 2006 to March 31, 2009) and Post-crisis (March 31, 2009 to May 17, 2016). Volatility and CVaR of the smart alpha portfolio are higher than those of the minimum systematic risk and the minimum volatility portfolios (due to the alpha constraint). However, the maximum drawdown of the smart alpha portfolio is better compared to both portfolios. 22

23 Economic Value of Smart Alpha Strategy In order to measure the economic value of switching from trading strategy 2 to strategy 1, we equate their average realized quadratic utilities with constant relative risk aversion ( ) as in Fleming et al. (2001 and 2002): where and are the returns for the two strategies, and represents the cost that the investor could give up (i.e, a performance fees) to have the same expected utility as under strategy 1. Willingness-to-Pay ( ) to switch from Smart Alpha (SA) strategy to others strategies (in annual %): all values are positive Source: Bloomberg, daily data from January 3, 2000 to May 17, Computations by the authors. SA refers to Smart Alpha portfolio strategy, MSR to Minimum Systematic Risk portfolio strategy, MV to Minimum Volatility portfolio strategy, RP to Risk Parity portfolio strategy, EW to Equally-Weighted portfolio strategy, and Benchmark is here the STOXX 600 index. Statistics are computed in four periods: Full Sample (January 3, 2000 to May 17, 2016), Pre-crisis (January 3, 2000 to December 29, 2006), Crisis (December 29, 2006 to March 31, 2009) and Post-crisis (March 31, 2009 to May 17, 2016). 23

24 Sensitivity Analysis for Smart Alpha Strategy Weekly OLS regressions of the Smart Alpha Strategy on the five Fama-French European factors: Whole sample ( ): Source: Bloomberg, Fama-French European five-factor model, weekly data from January 14, 2000 to May 13, Computations by the authors. The estimated alpha (Intercept) is positive and significant for all of the univariate and multivariate models. Low marginal contribution of Fama-French factors to adjusted R-squared. 24

25 Sensitivity Analysis for Smart Alpha Strategy Evolution of t-statistics from multivariate OLS regressions of the Smart Alpha Strategy on the 5 Fama-French European Factors (52-weeks rolling windows): Source: Bloomberg, Fama-French European five-factor model, weekly data from January 14, 2000 to May 13, The Newey-West corrected T- Statistic of each parameter is represented. The dashed lines represent the critical level of the Student-t distribution at the 1% risk level (2.58). An intercept is included in each regression. Computations by the authors. Market factor beta is always significant at the one percent critical level, while the other factor betas are overall insignificant. 25

26 Conclusion The Smart Alpha investment paradigm shows valuable results on the STOXX 600 universe: Significant outperformance over traditional smart beta strategies; With limited level of risk. Consistent timing of the exact number of factors thus has an economic value. These results mitigate the current folklore in the asset management industry about the death of alpha and the predominance of Factor Investing. Further extensions: Our methodology is general and can be applied to other regions (World, EM and SRI), asset classes as well as portfolio managers selection; Identification of latent factors from empirical factors or stock characteristics (only the Market Cap confirmed). 26

27 Smart Alpha: A Post Factor Investing Paradigm Thanks for your attention 10 TH FINANCIAL RISKS INTERNATIONAL FORUM - Paris, 27 & 28 March This presentation reflects only its authors opinions and does not necessarily reflect those of their employers.

28 Appendix

29 Sensitivity Analysis for Smart Alpha Strategy Evolution of estimated betas from multivariate OLS regressions of the Smart Alpha Strategy on the five Fama-French European Factors (52-weeks rolling windows) Source: Bloomberg, Fama-French European five-factor model, weekly data from January 14, 2000 to May 13, An intercept is included in each regression. Computations by the authors. Stability of Market factor beta around 0.6 but high volatility of Fama-French factors. 29

30 Correlations of the factor investing European Equity Indexes Correlations of the weekly returns of factor investing/smart beta European Equity Indexes (adjusted for the market beta), : Source: Bloomberg, Datastream, weekly data in EUR from January 5, 2001 to May 13, Computations by the authors. The European equity indices are the MSCI Europe Total Return Index, MSCI Europe Small Capitalization Total Return Index, MSCI Europe Large Capitalization Total Return Index, MSCI Europe Value Total Return Index, MSCI Europe Growth Total Return Index, MSCI Europe Quality Total Return Index, MSCI Europe Momentum Total Return Index and the MSCI Europe Minimum Volatility Total Return Index. The Small Capitalization, Large Capitalization, Value, Growth, Momentum, Quality and Minimum Volatility factor returns are the excess returns vs the market index (adjusted for the beta). 30

31 Correlations of the Five Fama-French European Factors Correlations of weekly returns of the Five Fama-French European Factors, : Source: Fama-French European five-factor model, weekly data from January 14, 2000 to May 13, Computations by the authors. 31

32 Real track-record AA European Equities Source: Morningstar, daily data from 31/12/2016 to 23/03/2017. Source: Bloomberg, daily data from 31/12/2016 to 24/03/

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