Betting Against Correlation:

Transcription

1 Betting Against Correlation: Testing Making Theories Leverage for Aversion the Low-Risk Great Again Effect (#MLAGA) Clifford S. Asness Managing and Founding Principal For Institutional Investor Use Only April 2017 AQR Capital Management, LLC Two Greenwich Plaza Greenwich, CT p: w: aqr.com The views and opinions expressed herein are those of the author and do not necessarily reflect the views of AQR Capital Management, LLC, its affiliates or its employees

2 Disclosures The information set forth herein has been obtained or derived from sources believed by AQR Capital Management, LLC ( AQR ) to be reliable. However, AQR does not make any representation or warranty, express or implied, as to the information s accuracy or completeness, nor does AQR recommend that the attached information serve as the basis of any investment decision. This document has been provided to you solely for information purposes and does not constitute an offer or solicitation of an offer, or any advice or recommendation, to purchase any securities or other financial instruments, and may not be construed as such. This document is intended exclusively for the use of the person to whom it has been delivered by AQR and it is not to be reproduced or redistributed to any other person. Please refer to the Appendix for more information on risks and fees. Past performance is not a guarantee of future performance. This presentation is not research and should not be treated as research. This presentation does not represent valuation judgments with respect to any financial instrument, issuer, security or sector that may be described or referenced herein and does not represent a formal or official view of AQR. The views expressed reflect the current views as of the date hereof and neither the speaker nor AQR undertakes to advise you of any changes in the views expressed herein. It should not be assumed that the speaker or AQR will make investment recommendations in the future that are consistent with the views expressed herein, or use any or all of the techniques or methods of analysis described herein in managing client accounts. AQR and its affiliates may have positions (long or short) or engage in securities transactions that are not consistent with the information and views expressed in this presentation. The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons. Charts and graphs provided herein are for illustrative purposes only. The information in this presentation has been developed internally and/or obtained from sources believed to be reliable; however, neither AQR nor the speaker guarantees the accuracy, adequacy or completeness of such information. Nothing contained herein constitutes investment, legal, tax or other advice nor is it to be relied on in making an investment or other decision. There can be no assurance that an investment strategy will be successful. Historic market trends are not reliable indicators of actual future market behavior or future performance of any particular investment which may differ materially, and should not be relied upon as such. Target allocations contained herein are subject to change. There is no assurance that the target allocations will be achieved, and actual allocations may be significantly different than that shown here. This presentation should not be viewed as a current or past recommendation or a solicitation of an offer to buy or sell any securities or to adopt any investment strategy. The information in this presentation may contain projections or other forward looking statements regarding future events, targets, forecasts or expectations regarding the strategies described herein, and is only current as of the date indicated. There is no assurance that such events or targets will be achieved, and may be significantly different from that shown here. The information in this presentation, including statements concerning financial market trends, is based on current market conditions, which will fluctuate and may be superseded by subsequent market events or for other reasons. Performance of all cited indices is calculated on a total return basis with dividends reinvested. The investment strategy and themes discussed herein may be unsuitable for investors depending on their specific investment objectives and financial situation. Please note that changes in the rate of exchange of a currency may affect the value, price or income of an investment adversely. Neither AQR nor the speaker assumes any duty to, nor undertakes to update forward looking statements. No representation or warranty, express or implied, is made or given by or on behalf of AQR, the speaker or any other person as to the accuracy and completeness or fairness of the information contained in this presentation, and no responsibility or liability is accepted for any such information. By accepting this presentation in its entirety, the recipient acknowledges its understanding and acceptance of the foregoing statement.

3 Motivation The low-risk effect: a major stylized fact in asset pricing Disagreement about underlying economic theory and the best empirical measures: Economic Theory Empirical Measure of Risk A) Leverage constraints Beta volatility correlation B) Behavioral lottery demand Idiosyncratic volatiliy MAX volatility skew Problem: most risk measures are hard to distinguish from one another Our solution: Introduce new factors that are more unique to each theory Perform a range of empirical tests based on 23 countries Test underlying economic drivers Frazzini, Niels Gormsen, and Lasse H. Pedersen. 3

4 Defining the Duelists Factor duel: which theory has the best factor We sign all factors such that they should have a positive return A) Theory of leverage aversion: Traditional factor used in the literature (Frazzini and Pedersen 2014): Betting against beta (BAB): long low-beta stocks, short high-beta stocks New factor Betting against correlation (BAC): long low-correlation stocks, short high-correlation ones Recall: beta increases with volatility and correlation B) Behavioral theories of lottery demand: Traditional factor used in the literature (Bali, Cakici, and Whitelaw, 2011): LMAX: long stocks with low MAX and short those with high MAX, where MAX = average of the 5 highest daily returns over the last month Literature uses FMAX which is just LMAX (we want signs to be positive) New factor: Scaled MAX (SMAX): long stocks with low MAX/volatility Another traditional factor: IVOL: long stocks with low idiosyncratic volatility, short high ones 4

5 Main Results Testing specific predictions of theories: strong returns to our new factors Betting against correlation (BAC): SR of 0.93, t-stat of five-factor alpha of 5.45 Scaled MAX (SMAX): SR of 0.78, t-stat of five-factor alpha of 4.78 Consistent with both leverage constraints and behavioral effects playing largely separate roles Testing specific predictions of theories: economic drivers BAB and BAC: Alphas predicted by amount of margin debt at broker dealers, not by sentiment LMAX (i.e., low MAX) and low IVOL factors: Alphas predicted by sentiment, not by margin Horse race BAB and BAC appear robust LMAX and SMAX also work in many specifications, but not robust to yearly formation periods We note that theories Do predict alpha w.r.t. CAPM Do not predict alpha w.r.t. factors that could capture part of the same effect (e.g., could just be value as ultimately it s about whether people pay too little/much for some stocks) Frazzini, Niels Gormsen, and Lasse H. Pedersen. 5

6 Main Results Cumulative Alpha of U.S. BAB, BAC, and BAV Factors January 1931 December % 800% 600% 400% 200% 0% -200% BAB BAC BAV Frazzini, Niels Gormsen, and Lasse H. Pedersen. 6

7 Overview of Talk Theories Testing the theory of leverage constraints: beta Testing the theory of lottery demand: SMAX Testing further economic predictions Horserace 7

8 Theories

9 Theory: Leverage Constraints Predictions and Literature Leverage constraints Push certain investors to demand assets with high systemic risk Lower the expected return of high-beta assets Theory: Black (1972), Frazzini and Pedersen (2014) Evidence: Black, Scholes, Jensen (1972), Frazzini and Pedersen (2014) Additional return predictions: Beta is defined as β i = ρ σ i σ mkt Both higher correlation and higher volatility should give lower alpha Volatility is closely related to IVOL and to MAX Correlation more distinct from alternative measures that is why we introduce BAC Testing further economic predictions Shadow cost of capital should predict excess return to BAB (Frazzini and Pedersen, 2014) We confirm this proposition using margin debt of broker-dealers Previous evidence on impact of shadow cost of capital: Adrian, Etula, and Muir (2014), Boguth and Simutin (2014), Jylhä (2015), Malkhozov, Mueller, Vedolin, and Venter (2016) Frazzini, Niels Gormsen, and Lasse H. Pedersen. 9

10 Theory: Lottery Demand and Sentiment Lottery demand and sentiment Prospect theory can cause investors to demand lottery stocks with a chance of a high return (Barberis and Huang, 2008; Brunnermeier, Gollier, and Parker, 2007) Lowers the return on lottery-like stocks Evidence MAX (Bali, Cakici, and Whitelaw, 2011) and expected idiosyncratic skewness (Boyer, Mitton, and Vorkink, 2010) Additional return predictions: MAX is the average of the five highest daily returns over the last month MAX is closely related to total volatility and beta We introduce SMAX which captures idiosyncratic skewness more cleanly: SMAX i,t long stocks with low MAX i,t σ i,t Testing further economic predictions short the opposite ones Behavioral finance also looks at IVOL (Ang, Hodrick, Xing, and Zhang, 2006) Liu, Stambaugh, and Yuan (2016): sentiment should predict returns low risk (IVOL and MAX) We confirm that sentiment predicts the five-factor alpha of LMAX and IVOL (though not SMAX) Frazzini, Niels Gormsen, and Lasse H. Pedersen. 10

11 Testing the Theory of Leverage Constraints: Beta

12 Decomposing Beta: Correlation vs. Volatility Recall that beta is β i = ρ σ i σ mkt Does sorting on volatility and correlation induce a beta spread in both? A simple 5x5 sort: ex post betas US CAPM beta Sort on volatility P1 (low) P2 P3 P4 P5 (high) (low) Conditional sort on correlation P1 P2 P3 P4 P5 LS (high) (24.9) (26.2) (27.1) (24.3) (15.3) LS (8.3) (12.6) (15.3) (17.0) (21.1) Frazzini, Niels Gormsen, and Lasse H. Pedersen. 12

13 Decomposing Beta: Correlation vs. Volatility Recall that beta is β i = ρ σ i σ mkt Is the low-risk effect due to volatility or correlation? A simple 5x5 sort: CAPM alphas US CAPM alpha Conditional sort on correlation P1 P2 P3 P4 P5 LS (low) (high) Sort on volatility P1 (low) P2 P3 P4 P5 (high) (5.6) (3.9) (3.2) (2.1) (2.3) (-3.6) (3.3) (2.1) (1.6) (0.7) (-0.7) (-3.0) (4.1) (2.8) (0.6) (-0.2) (-2.3) (-4.4) (3.3) (2.3) (0.3) (-1.0) (-2.2) (-4.2) (1.4) (0.2) (0.4) (-1.7) (-2.7) (-3.3) LS (-0.5) (-1.0) (-0.8) (-2.2) (-3.0) Frazzini, Niels Gormsen, and Lasse H. Pedersen. 13

14 Decomposing Beta: Correlation vs. Volatility Recall that beta is β i = ρ σ i σ mkt Is the low-risk effect due to volatility or correlation? Alphas with respect to market, size, and value US Three-factor alpha Conditional sort on correlation P1 P2 P3 P4 P5 LS (low) (high) Sort on volatility P1 (low) P2 P3 P4 P5 (high) (5.2) (3.3) (2.6) (1.8) (2.9) (-3.3) (2.6) (1.1) (0.8) (-0.6) (-1.6) (-3.0) (3.4) (1.5) (-1.4) (-2.4) (-4.2) (-4.9) (2.4) (1.1) (-1.5) (-2.9) (-4.4) (-4.5) (0.4) (-0.9) (-1.1) (-3.9) (-4.5) (-3.2) LS (-1.4) (-2.1) (-2.0) (-4.0) (-4.9) Frazzini, Niels Gormsen, and Lasse H. Pedersen. 14

15 Decomposing BAB: BAC and BAV Betting against beta, BAB A rank-weighted factor where both the long and short sides are (de)leveraged to a beta of one The BAB factor can be decomopsed as: BAB = a 0 + a 1 BAC + a 2 BAV + ε Betting against correlation, BAC, construction In each volatility quintile, construct a rank-weighted betting-against-correlation factor, where both the long and short sides are (de)leveraged to a beta of one Rolling estimation of volatilities (1yr window of 1-day returns) and correlations (5yr window of 3-day returns) The overall BAC factor is the average of these Betting against volatility, BAV: constructed analogously to BAC In each correlation Panel A: Long quintile, U.S. Sample ( ) construct a rank-weighted Panel betting-against-volatility B: Global sample ( ) factor, where both the long and Panel short A: Long sides U.S. Sample are ( ) (de)leveraged to a beta of Panel one B: Global sample ( ) BAB BAB Intercept Panel A: Long U.S. Sample ( ) 0.00 Panel Intercept B: Global sample ( ) BAB 0.00 Intercept Panel A: Long U.S. Sample ( ) (-1.56) 0.00 Intercept Panel B: Global sample ( ) (-0.02) 0.00 BAC (-1.56) 0.71 BAB BAC (-0.02) 0.84 BAB BAC (63.00) 0.71 BAC 0.84 Intercept 0.00 BAB (66.77) Intercept 0.00 BAB BAV (63.00) 0.51 BAV (66.77) 0.49 Intercept (-1.56) (-0.02) BAV (60.33) Intercept BAV (58.52) BAC 0.71 BAC 0.84 (60.33) (-1.56) (58.52) (-0.02) BAC (63.00) 0.71 BAC (66.77) 0.84 BAV (63.00) 0.51 BAV (66.77) 0.49 BAV R2 (60.33) BAV R2 (58.52) R2 Num (60.33) R2 (58.52) Num The overall BAV factor is the average of these BAB R2 Based on Betting Against Correlation: Testing Theories 0.85 of the Low-Risk Effect, R2 a working paper by Clifford S. Asness, Andrea 0.96 Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table III of the paper for more information. R2 Num 1020 Not representative of any portfolio that AQR currently manages For educational R2 and illustrative purposes only. Hypothetical data has Num inherent limitations, some of which are disclosed in the 1020 Appendix

16 U.S. Performance of Betting Against Correlation U.S. Sample From 1963 to 2015 Panel A: U.S. Sample ( ) Volatility quintile BAC Excess return (4.32) (6.52) (6.31) (5.88) (5.78) (6.74) Alpha (3.56) (5.50) (4.26) (4.08) (4.96) (5.45) MKT (-5.1) (-1.9) (1.5) (2.2) (2.14) (0.5) SMB (16.6) (15.7) (12.7) (10.1) (7.1) (13.6) HML (2.3) (3.2) (4.0) (3.9) (1.9) (3.5) RMW (0.4) (0.9) (2.5) (1.9) (-2.2) (0.3) CMA (1.0) (0.9) (1.9) (0.4) (0.0) (0.8) SR IR R # obs Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table IV of the paper for more information. 16

17 Global Performance of Betting Against Correlation Broad global sample 24 countries (the U.S. and 23 others) from 1990 to 2015 Panel B: Global Sample ( ) Volatility quintile BAC Excess return (2.08) (4.57) (3.98) (3.95) (4.55) (4.48) Alpha (0.99) (3.19) (1.84) (1.48) (3.39) (2.77) MKT (0.4) (2.0) (3.7) (4.1) (3.27) (3.5) SMB (11.9) (11.5) (10.6) (10.8) (9.6) (12.6) HML (1.4) (1.9) (2.9) (2.4) (0.4) (1.9) RMW (2.2) (3.3) (4.6) (6.0) (2.3) (4.3) CMA (1.2) (0.9) (0.7) (0.8) (0.8) (1.0) SR IR R # obs Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table IV of the paper for more information. 17

18 The Low-Risk Effect: Not All About Volatility Low risk effect not simply about low volatility BAB driven by BAV: the much talked about volatility BAC: at least as importantly, correlation, a new factor BAC evidence Consistent with theory of leverage constraints Different from behavioral theories of idiosyncratic lottery demand (not implied by such theories) Frazzini, Niels Gormsen, and Lasse H. Pedersen. 18

19 Testing the Theory of Lottery Demand: SMAX

20 Decomposing MAX: Volatility and SMAX Recall that MAX is driven by volatility and SMAX: SMAX i,t = MAX i,t σ i,t or MAX i,t = SMAX i,t σ i,t Which captures the shape of the return distribution? CAPM alphas US CAPM alpha Conditional sort on SMAX P1 P2 P3 P4 P5 LS (low) (high) Sort on volatility P1 (low) P2 P3 P4 P5 (high) (5.4) (3.2) (1.4) (2.0) (1.1) (-3.4) (3.8) (2.5) (1.6) (0.1) (-2.7) (-5.0) (3.6) (1.7) (-1.3) (-1.3) (-3.8) (-5.5) (3.5) (1.1) (-0.9) (-2.1) (-3.7) (-6.2) (2.0) (-0.0) (-0.8) (-2.6) (-3.8) (-5.5) LS (0.2) (-1.0) (-1.0) (-2.8) (-3.7) Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table V of the paper for more information. 20

21 Decomposing MAX: Volatility and SMAX Recall that MAX is driven by volatility and SMAX: SMAX i,t = MAX i,t σ i,t or MAX i,t = SMAX i,t σ i,t Which captures the shape of the return distribution? Alphas with respect to market, size, and value US Three-factor alpha Conditional sort on SMAX P1 P2 P3 P4 P5 LS (low) (high) Sort on volatility P1 (low) P2 P3 P4 P5 (high) (5.4) (3.3) (1.1) (1.9) (1.0) (-3.4) (3.1) (1.8) (0.9) (-0.9) (-3.9) (-5.1) (2.8) (0.3) (-3.1) (-2.9) (-5.4) (-5.7) (3.0) (-0.3) (-2.4) (-3.9) (-5.6) (-6.3) (2.3) (-0.9) (-1.9) (-4.3) (-5.2) (-6.2) LS (0.3) (-2.0) (-2.0) (-4.4) (-5.1) Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table V of the paper for more information. 21

22 U.S. Performance of SMAX Positive returns of SMAX Consistent with theory of lottery demand Appears as strong as LMAX and IVOL Panel A: U.S. Sample ( ) SM AX SM AX SM AX LM AX LM AX LM AX IVOL IVOL Alpha (5.60) (4.78) (3.69) (5.81) (3.34) (2.64) (5.27) (2.46) M KT (-2.0) (-1.2) (-5.4) (-17.8) (-15.8) (-17.40) (-18.2) (-16.2) SM B (-0.7) (0.3) (-1.1) (-14.3) (-11.2) (-12.0) (-19.7) (-16.8) HM L (2.8) (1.1) (-0.9) (12.6) (5.5) (4.8) (11.4) (4.4) RM W (3.0) (3.6) (12.3) (12.7) (15.5) CM A (1.4) (3.4) (6.9) (7.8) (7.8) REV (16.9) (6.6) (-0.5) SR IR R # obs Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table VII of the paper for more information. 22

23 Global Performance of SMAX Panel B: Global Sample ( ) SM AX SM AX SM AX LM AX LM AX LM AX IVOL IVOL Alpha (1.97) (1.01) (0.63) (3.71) (0.16) (-0.12) (3.76) (-0.09) M KT (-3.1) (-1.1) (-4.5) (-20.2) (-11.9) (-13.60) (-18.4) (-10.3) SM B (-0.5) (0.5) (1.0) (-8.4) (-5.0) (-5.1) (-11.6) (-8.5) HM L (4.2) (2.2) (1.2) (10.7) (2.8) (2.3) (10.5) (1.7) RM W (2.5) (3.9) (10.4) (11.2) (11.2) CM A (0.7) (2.3) (7.2) (8.2) (8.7) REV (14.6) (6.0) (2.0) SR IR R # obs Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table VII of the paper for more information. 23

24 Testing Further Economic Predictions

25 Further Economic Predictions As another test of the theories, we study how factor returns depend on MD: margin debt SENT: sentiment MD: testing the theory of leverage constraints amount of margin debt for NYSE stocks held at broker dealers MD= market cap of NYSE stocks Data from NYSE SENT: Using sentiment to test behavioral theories The Baker and Wurgler (2006) Sentiment index consisting of Equity share in new issues, closed end fund discount, market turnover, #IPOs, dividend premium Controls: FF factors Frazzini, Niels Gormsen, and Lasse H. Pedersen. 25

26 Further Economic Predictions Controlling for the five factor model: Higher MD = lower leverage constraints BAB t;t+1 BAB t;t+1 BAC t;t+1 BAC t;t+1 LMAX t;t+1 LMAX t;t+1 SMAX t;t+1 SMAX t;t+1 IVOL t;t+1 IVOL t;t+1 MD t (-1.69) (-2.78) (-1.87) (-3.30) (1.14) (-0.22) (0.91) MD t+1 -MD t (3.55) (3.17) (5.63) (4.83) (-1.51) (0.86) (-1.49) SENT t (1.09) (-0.46) (2.35) (1.85) (1.35) (1.03) (2.79) (2.69) SENT t+1 -SENT t (1.33) (1.44) (0.91) (1.14) (2.27) (2.24) (0.01) (0.19) Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table VIII of the paper for more information. 26

27 Horserace

28 Horserace Leaving theory for a horserace Theory predicts a positive 1-factor alpha; 5-factor alpha should be interpreted carefully Challenges: Fama and French (2015): low-beta effect is subsumed by profitability (RMW) and investment (CMA) Bali, Brown, Murray, and Tang (2016): the low-beta effect is subsumed by LMAX Liu, Stambaugh, and Yuan (2016): the low-beta effect is subsumed by IVOL Apples-to-apples, must address differences in: Factor construction Turnover Sensitivity to microstructure and lags Sample periods SMAX BAB BAC Frazzini, Niels Gormsen, and Lasse H. Pedersen. 28

29 Turnover BAB, BAC, BAV Turnover comparable to traditional factors LMAX, SMAX, IVOL Turnover much larger, implying hard to implement in practice We add examination of lottery-based factors using a more conventional look-back period Still relatively high turnover Portfolio HML BAB BAB BAB BAC BAV LMAX SMAX IVOL LMAX(1Y) SMAX(1Y) Method FF: june update FF: june update FF: monthly Rank weights Rank weights Rank weights FF: monthly FF: monthly FF: monthly FF: monthly FF: monthly Turnover Period over which the characteristics are calculated NA 1 to 5 years 1 to 5 years 1 to 5 years 1 to 5 years 1 to 5 years 1 month 1 to 12 months 1 month 1 year 1 year Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table X of the paper for more information. Turnover is measured as the amount of dollars that has to be traded in each trading strategy on a monthly basis. 29

30 SMAX at Conventional Turnover Yearly MAX is the average of the 20 highest daily returns over the previous year Panel A: U.S. Sample ( ) LMAX(1Y) LMAX(1Y) LMAX(1Y) SMAX(1Y) SMAX(1Y) SMAX(1Y) Alpha (3.73) (0.89) (-1.26) (-1.67) (-3.57) (-3.25) MKT (-19.6) (-17.5) (-21.9) (0.0) (-2.6) (-2.4) SMB (-18.8) (-16.0) (-19.9) (-9.1) (-8.8) (-8.6) HML (9.2) (2.3) (-0.1) (5.8) (4.8) (5.1) RMW (12.3) (9.4) (4.8) (5.2) CMA (7.4) (5.9) (-1.3) (-1.0) REV (1.2) (2.3) (10.9) (10.8) BAB (14.5) (-1.8) SR IR R # obs Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table XI of the paper for more information. 30

31 Consistent Factor Methodology: Rank Weights We construct rank-weighted editions of all factors for apples-to-apples Following Asness, Moskowitz, and Pedersen (2013), Frazzini and Pedersen (2014) Methodology: Sort stocks into two groups based on market capitalization in June (median NYSE breakpoint) Within each size group, we construct a rank-weighted portfolio (hedged to beta zero) The final factor is the average of the factors in the large and small universes All factors using exactly the same method (e.g., BAB, BAC, BAV are redone this way and all LHS factors, e.g., HML, save SMB are done this way SMB naturally must be simply a rank-weighted factor) Benefits of rank-weighting Includes all stocks Gives more weight to stocks with more pronounced characteristics Not relying on ad-hoc cut-offs Using ranks rather than raw values limits the effects of outliers or data errors in the characteristics Limits the exposure to the largest stocks Generally looks more like what a real life implementer might do Frazzini, Niels Gormsen, and Lasse H. Pedersen. 31

32 Consistent Factor Methodology: Rank Weights Panel A: U.S. Sample ( ) BAB BAB BAC BAC BAV BAV LMAX LMAX SMAX SMAX IVOL IVOL Alpha (3.34) (3.29) (3.56) (3.33) (0.16) (-2.25) (1.26) (-1.12) (2.84) (1.90) (1.56) (-0.80) MKT (1.0) (3.7) (-0.4) (0.6) (-2.1) (1.1) (-2.8) (-4.5) (-2.4) (-2.8) (-2.8) (-4.6) SMB (8.1) (11.2) (25.8) (27.4) (-9.5) (-20.3) (-0.8) (-7.4) (6.4) (4.0) (-9.5) (-18.7) HML (7.7) (9.4) (5.8) (5.9) (5.6) (11.4) (0.7) (-5.2) (-3.6) (-5.9) (4.3) (-0.8) RMW (14.7) (-3.1) (4.7) (-3.3) (30.5) (7.7) (28.5) (21.9) (16.3) (11.0) (31.1) (25.2) CMA (0.2) (-2.9) (-1.6) (-3.0) (4.1) (1.4) (3.9) (4.9) (1.7) (1.7) (4.3) (5.4) REV (-0.6) (-7.7) (-2.5) (-5.3) (2.2) (-12.8) (8.9) (12.0) (18.9) (20.0) (-0.7) (-0.4) BAB (22.7) (8.7) (23.8) LMAX (22.7) (9.3) (57.4) SR IR R # obs Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table XIII of the paper for more information. 32

33 Conclusion BAC is New Unique Consistent only with leverage aversion Holds up quite strongly Frazzini, Niels Gormsen, and Lasse H. Pedersen. 33

34 Disclosures This document has been provided to you solely for information purposes and does not constitute an offer or solicitation of an offer or any advice or recommendation to purchase any securities or other financial instruments and may not be construed as such. The factual information set forth herein has been obtained or derived from sources believed to be reliable but it is not necessarily all-inclusive and is not guaranteed as to its accuracy and is not to be regarded as a representation or warranty, express or implied, as to the information s accuracy or completeness, nor should the attached information serve as the basis of any investment decision. This document is intended exclusively for the use of the person to whom it has been delivered and it is not to be reproduced or redistributed to any other person. There is no guarantee, express or implied, that long-term return and/or volatility targets will be achieved. Hypothetical performance results (e.g., quantitative backtests) have many inherent limitations, some of which, but not all, are described herein. No representation is being made that any fund or account will or is likely to achieve profits or losses similar to those shown herein. In fact, there are frequently sharp differences between hypothetical performance results and the actual results subsequently realized by any particular trading program. One of the limitations of hypothetical performance results is that they are generally prepared with the benefit of hindsight. In addition, hypothetical trading does not involve financial risk, and no hypothetical trading record can completely account for the impact of financial risk in actual trading. For example, the ability to withstand losses or adhere to a particular trading program in spite of trading losses are material points which can adversely affect actual trading results. The hypothetical performance results contained herein represent the application of the quantitative models as currently in effect on the date first written above and there can be no assurance that the models will remain the same in the future or that an application of the current models in the future will produce similar results because the relevant market and economic conditions that prevailed during the hypothetical performance period will not necessarily recur. There are numerous other factors related to the markets in general or to the implementation of any specific trading program which cannot be fully accounted for in the preparation of hypothetical performance results, all of which can adversely affect actual trading results. Discounting factors may be applied to reduce suspected anomalies. This backtest s return, for this period, may vary depending on the date it is run. Hypothetical performance results are presented for illustrative purposes only. In addition, our transaction cost assumptions utilized in backtests, where noted, are based on AQR's historical realized transaction costs and market data. Certain of the assumptions have been made for modeling purposes and are unlikely to be realized. No representation or warranty is made as to the reasonableness of the assumptions made or that all assumptions used in achieving the returns have been stated or fully considered. Changes in the assumptions may have a material impact on the hypothetical returns presented. Hypothetical performance is gross of advisory fees, net of transaction costs, and includes the reinvestment of dividends. If the expenses were reflected, the performance shown would be lower.