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Making Leverage Aversion Great Again (#MLAGA)

Betting Against Correlation: Testing Theories for the Low-Risk Effect

Clifford S. Asness

Managing and Founding Principal

April 2017

For Institutional Investor Use Only

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

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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

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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The information contained herein is only as current as of the date indicated, and may be superseded by subsequent market events or for other reasons.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.

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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.

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Motivation

3

Based on “Betting Against Correlation: Testing Theories of the Low-Risk Effect,” a working paper by Clifford S. Asness, Andrea

Frazzini, Niels Gormsen, and Lasse H. Pedersen.

Not representative of any portfolio that AQR currently manages. For educational and illustrative purposes only. Hypothetical data has

inherent limitations, some of which are disclosed in the Appendix.

The low-risk effect: a major stylized fact in asset pricing

Disagreement about underlying economic theory and the best empirical measures:

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

Economic Theory Empirical Measure of Risk

A) Leverage constraints Beta ≈ volatility × correlation

B) Behavioral lottery demand Idiosyncratic volatiliy

MAX ≈ volatility × skew

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Defining the Duelists

4

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

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Main Results

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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)

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Main Results

6





Cumulative Alpha of U.S. BAB, BAC, and BAV Factors

January 1931–December 2015

-200%

0%

200%

400%

600%

800%

1000%

1931 1941 1951 1961 1971 1981 1991 2001 2011

BAB BAC BAV

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Overview of Talk

7

Theories

Testing the theory of leverage constraints: beta

Testing the theory of lottery demand: SMAX

Testing further economic predictions

Horserace

Theories

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Theory: Leverage Constraints

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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 𝛽𝑖 = 𝜌𝜎𝑖

𝜎𝑚𝑘𝑡

• 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


• 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)

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Theory: Lottery Demand and Sentiment

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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:

𝑆𝑀𝐴𝑋𝑖,𝑡 long stocks with low 𝑀𝐴𝑋𝑖,𝑡

𝜎𝑖,𝑡 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)

Testing the Theory of Leverage Constraints: Beta

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Decomposing Beta: Correlation vs. Volatility

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Recall that beta is 𝛽𝑖 = 𝜌𝜎𝑖

𝜎𝑚𝑘𝑡

Does sorting on volatility and correlation induce a beta spread in both?

• A simple 5x5 sort: ex post betas

US 1930-2015

CAPM beta

P1 P2 P3 P4 P5 LS

(low) (high)

0.5 0.6 0.7 0.8 0.9 0.4

(24.9)

0.7 0.9 1.0 1.1 1.2 0.5

(26.2)

0.7 1.0 1.2 1.3 1.4 0.7

(27.1)

0.8 1.0 1.2 1.3 1.6 0.8

(24.3)

0.8 1.0 1.1 1.3 1.6 0.8

(15.3)

LS 0.4 0.5 0.5 0.5 0.7

(8.3) (12.6) (15.3) (17.0) (21.1)

P4

P5 (high)

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𝜎𝑚𝑘𝑡

Is the low-risk effect due to volatility or correlation?

• A simple 5x5 sort: CAPM alphas

US 1930-2015

CAPM alpha

P1 P2 P3 P4 P5 LS

(low) (high)

0.4 0.3 0.2 0.1 0.1 -0.3

(5.6) (3.9) (3.2) (2.1) (2.3) (-3.6)

0.3 0.2 0.1 0.1 -0.1 -0.3

(3.3) (2.1) (1.6) (0.7) (-0.7) (-3.0)

0.4 0.3 0.1 0.0 -0.2 -0.6

(4.1) (2.8) (0.6) (-0.2) (-2.3) (-4.4)

0.4 0.3 0.0 -0.1 -0.3 -0.7

(3.3) (2.3) (0.3) (-1.0) (-2.2) (-4.2)

0.3 0.1 0.1 -0.3 -0.5 -0.8

(1.4) (0.2) (0.4) (-1.7) (-2.7) (-3.3)

LS -0.1 -0.2 -0.2 -0.4 -0.6

(-0.5) (-1.0) (-0.8) (-2.2) (-3.0)

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𝜎𝑚𝑘𝑡

Is the low-risk effect due to volatility or correlation?

• Alphas with respect to market, size, and value

US 1930-2015

Three-factor alpha

P1 P2 P3 P4 P5 LS

(low) (high)

0.4 0.2 0.2 0.1 0.1 -0.3

(5.2) (3.3) (2.6) (1.8) (2.9) (-3.3)

0.2 0.1 0.1 0.0 -0.1 -0.3

(2.6) (1.1) (0.8) (-0.6) (-1.6) (-3.0)

0.3 0.1 -0.1 -0.2 -0.4 -0.6

(3.4) (1.5) (-1.4) (-2.4) (-4.2) (-4.9)

0.3 0.1 -0.2 -0.3 -0.5 -0.8

(2.4) (1.1) (-1.5) (-2.9) (-4.4) (-4.5)

0.1 -0.2 -0.1 -0.5 -0.7 -0.8

(0.4) (-0.9) (-1.1) (-3.9) (-4.5) (-3.2)

LS -0.3 -0.4 -0.3 -0.6 -0.9

(-1.4) (-2.1) (-2.0) (-4.0) (-4.9)


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Decomposing BAB: BAC and BAV

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Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table III of the paper for more information.



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 = 𝒂𝟎 + 𝒂𝟏𝑩𝑨𝑪 + 𝒂𝟐𝑩𝑨𝑽 + 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 quintile, construct a rank-weighted betting-against-volatility factor, where both

the long and short sides are (de)leveraged to a beta of one

• The overall BAV factor is the average of these

Panel A: Long U.S. Sample (1930-2015) Panel B: Global sample (1990-2015)

BAB BAB

Intercept 0.00 Intercept 0.00

(-1.56) (-0.02)

BAC 0.71 BAC 0.84

(63.00) (66.77)

BAV 0.51 BAV 0.49

(60.33) (58.52)

R2 0.85 R2 0.96

Num 1020 306


BAB BAB


(-1.56) (-0.02)

BAC 0.71 BAC 0.84

(63.00) (66.77)

BAV 0.51 BAV 0.49

(60.33) (58.52)

R2 0.85 R2 0.96

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BAB BAB


(-1.56) (-0.02)

BAC 0.71 BAC 0.84

(63.00) (66.77)

BAV 0.51 BAV 0.49

(60.33) (58.52)

R2 0.85 R2 0.96

Num 1020 306


BAB BAB


(-1.56) (-0.02)

BAC 0.71 BAC 0.84

(63.00) (66.77)

BAV 0.51 BAV 0.49

(60.33) (58.52)

R2 0.85 R2 0.96

Num 1020 306

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U.S. Performance of Betting Against Correlation

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Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table IV of the paper for more information.



U.S. Sample

• From 1963 to 2015

Volatility quintile 1 2 3 4 5 BAC

Excess return 0.55 0.86 0.92 1.03 1.48 0.97

(4.32) (6.52) (6.31) (5.88) (5.78) (6.74)

Alpha 0.39 0.63 0.57 0.68 1.25 0.70

(3.56) (5.50) (4.26) (4.08) (4.96) (5.45)

MKT -0.14 -0.05 0.05 0.09 0.13 0.02

(-5.1) (-1.9) (1.5) (2.2) (2.14) (0.5)

SMB 0.62 0.61 0.58 0.58 0.61 0.60

(16.6) (15.7) (12.7) (10.1) (7.1) (13.6)

HML 0.12 0.17 0.26 0.31 0.23 0.22

(2.3) (3.2) (4.0) (3.9) (1.9) (3.5)

RMW 0.02 0.05 0.17 0.16 -0.28 0.02

(0.4) (0.9) (2.5) (1.9) (-2.2) (0.3)

CMA 0.08 0.08 0.18 0.04 0.01 0.08

(1.0) (0.9) (1.9) (0.4) (0.0) (0.8)

SR 0.60 0.90 0.87 0.81 0.80 0.93

IR 0.52 0.80 0.62 0.59 0.72 0.79

R2 0.34 0.31 0.25 0.18 0.13 0.27

# obs 630 630 630 630 630 630

Panel A: U.S. Sample (1963-2015)

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Global Performance of Betting Against Correlation

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Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table IV of the paper for more information.



Volatility quintile 1 2 3 4 5 BAC

Excess return 0.27 0.64 0.64 0.70 1.15 0.68

(2.08) (4.57) (3.98) (3.95) (4.55) (4.48)

Alpha 0.11 0.41 0.27 0.24 0.81 0.37

(0.99) (3.19) (1.84) (1.48) (3.39) (2.77)

MKT 0.01 0.07 0.15 0.18 0.21 0.12

(0.4) (2.0) (3.7) (4.1) (3.27) (3.5)

SMB 0.65 0.71 0.75 0.85 1.11 0.81

(11.9) (11.5) (10.6) (10.8) (9.6) (12.6)

HML 0.10 0.14 0.26 0.23 0.05 0.16

(1.4) (1.9) (2.9) (2.4) (0.4) (1.9)

RMW 0.18 0.31 0.49 0.71 0.41 0.42

(2.2) (3.3) (4.6) (6.0) (2.3) (4.3)

CMA 0.10 0.09 0.08 0.11 0.15 0.10

(1.2) (0.9) (0.7) (0.8) (0.8) (1.0)

SR 0.41 0.90 0.79 0.78 0.90 0.89

IR 0.21 0.69 0.40 0.32 0.73 0.60

R2 0.33 0.31 0.29 0.30 0.23 0.35

# obs 306 306 306 306 306 306

Panel B: Global Sample (1990-2015)

Broad global sample

• 24 countries (the U.S. and 23 others) from 1990 to 2015

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The Low-Risk Effect: Not All About Volatility

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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)

Testing the Theory of Lottery Demand: SMAX

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Decomposing MAX: Volatility and SMAX

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Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table V of the paper for more information.



Recall that MAX is driven by volatility and SMAX:

𝑆𝑀𝐴𝑋𝑖,𝑡 =𝑀𝐴𝑋𝑖,𝑡

𝜎𝑖,𝑡 or 𝑀𝐴𝑋𝑖,𝑡 = 𝑆𝑀𝐴𝑋𝑖,𝑡 ∗ 𝜎𝑖,𝑡

Which captures the shape of the return distribution?

• CAPM alphas

US 1930-2015

CAPM alpha

P1 P2 P3 P4 P5 LS

(low) (high)

0.3 0.2 0.1 0.1 0.1 -0.3

(5.4) (3.2) (1.4) (2.0) (1.1) (-3.4)

0.3 0.2 0.1 0.0 -0.2 -0.5

(3.8) (2.5) (1.6) (0.1) (-2.7) (-5.0)

0.3 0.2 -0.1 -0.1 -0.4 -0.7

(3.6) (1.7) (-1.3) (-1.3) (-3.8) (-5.5)

0.4 0.1 -0.1 -0.3 -0.5 -0.9

(3.5) (1.1) (-0.9) (-2.1) (-3.7) (-6.2)

0.4 0.0 -0.2 -0.5 -0.8 -1.2

(2.0) (-0.0) (-0.8) (-2.6) (-3.8) (-5.5)

LS 0.0 -0.2 -0.2 -0.7 -0.9

(0.2) (-1.0) (-1.0) (-2.8) (-3.7)

Conditional sort on SMAX

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Decomposing MAX: Volatility and SMAX

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Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table V of the paper for more information.



Recall that MAX is driven by volatility and SMAX:

𝑆𝑀𝐴𝑋𝑖,𝑡 =𝑀𝐴𝑋𝑖,𝑡

𝜎𝑖,𝑡 or 𝑀𝐴𝑋𝑖,𝑡 = 𝑆𝑀𝐴𝑋𝑖,𝑡 ∗ 𝜎𝑖,𝑡

Which captures the shape of the return distribution?

• Alphas with respect to market, size, and value

US 1930-2015

Three-factor alpha

P1 P2 P3 P4 P5 LS

(low) (high)

0.3 0.2 0.1 0.1 0.1 -0.3

(5.4) (3.3) (1.1) (1.9) (1.0) (-3.4)

0.2 0.1 0.1 -0.1 -0.3 -0.5

(3.1) (1.8) (0.9) (-0.9) (-3.9) (-5.1)

0.2 0.0 -0.3 -0.2 -0.5 -0.7

(2.8) (0.3) (-3.1) (-2.9) (-5.4) (-5.7)

0.3 0.0 -0.2 -0.4 -0.6 -0.9

(3.0) (-0.3) (-2.4) (-3.9) (-5.6) (-6.3)

0.4 -0.2 -0.3 -0.8 -1.0 -1.3

(2.3) (-0.9) (-1.9) (-4.3) (-5.2) (-6.2)

LS 0.0 -0.4 -0.4 -0.9 -1.0

(0.3) (-2.0) (-2.0) (-4.4) (-5.1)

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U.S. Performance of SMAX

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Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table VII of the paper for more information.



Positive returns of SMAX

• Consistent with theory of lottery demand

• Appears as strong as LMAX and IVOL

SMAX SMAX SMAX LMAX LMAX LMAX IVOL IVOL

Alpha 0.44 0.38 0.25 0.58 0.31 0.24 0.53 0.22

(5.60) (4.78) (3.69) (5.81) (3.34) (2.64) (5.27) (2.46)

MKT -0.04 -0.02 -0.09 -0.42 -0.35 -0.39 -0.44 -0.35

(-2.0) (-1.2) (-5.4) (-17.8) (-15.8) (-17.40) (-18.2) (-16.2)

SMB -0.02 0.01 -0.03 -0.48 -0.35 -0.37 -0.65 -0.50

(-0.7) (0.3) (-1.1) (-14.3) (-11.2) (-12.0) (-19.7) (-16.8)

HML 0.08 0.04 -0.03 0.45 0.24 0.20 0.41 0.18

(2.8) (1.1) (-0.9) (12.6) (5.5) (4.8) (11.4) (4.4)

RMW 0.12 0.12 0.57 0.57 0.68

(3.0) (3.6) (12.3) (12.7) (15.5)

CMA 0.08 0.16 0.46 0.50 0.49

(1.4) (3.4) (6.9) (7.8) (7.8)

REV 0.36 0.19 -0.01

(16.9) (6.6) (-0.5)

SR 0.78 0.78 0.78 0.34 0.34 0.34 0.22 0.22

IR 0.79 0.70 0.54 0.82 0.49 0.39 0.74 0.36

R2 0.03 0.04 0.34 0.64 0.71 0.73 0.69 0.78

# obs 630 630 630 630 630 630 630 630

Panel A: U.S. Sample (1963-2015)

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SMAX SMAX SMAX LMAX LMAX LMAX IVOL IVOL

Alpha 0.19 0.10 0.05 0.45 0.02 -0.01 0.46 -0.01

(1.97) (1.01) (0.63) (3.71) (0.16) (-0.12) (3.76) (-0.09)

MKT -0.07 -0.03 -0.10 -0.56 -0.35 -0.39 -0.51 -0.30

(-3.1) (-1.1) (-4.5) (-20.2) (-11.9) (-13.60) (-18.4) (-10.3)

SMB -0.02 0.02 0.04 -0.49 -0.26 -0.25 -0.68 -0.43

(-0.5) (0.5) (1.0) (-8.4) (-5.0) (-5.1) (-11.6) (-8.5)

HML 0.18 0.14 0.06 0.57 0.18 0.14 0.56 0.11

(4.2) (2.2) (1.2) (10.7) (2.8) (2.3) (10.5) (1.7)

RMW 0.19 0.22 0.83 0.85 0.86

(2.5) (3.9) (10.4) (11.2) (11.2)

CMA 0.05 0.14 0.61 0.66 0.72

(0.7) (2.3) (7.2) (8.2) (8.7)

REV 0.39 0.21 0.07

(14.6) (6.0) (2.0)

SR 0.43 0.43 0.43 0.34 0.34 0.34 0.35 0.35

IR 0.40 0.22 0.14 0.75 0.03 -0.03 0.76 -0.02

R2 0.09 0.10 0.48 0.69 0.78 0.81 0.68 0.80

# obs 306 306 306 306 306 306 306 306

Panel B: Global Sample (1990-2015)

Global Performance of SMAX

23


Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table VII of the paper for more information.



Testing Further Economic Predictions

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Further Economic Predictions

25





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

MD=amount of margin debt for NYSE stocks held at broker dealers

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

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Controlling for the five factor model:

Further Economic Predictions

26


Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table VIII of the paper for more information.



BABt;t+1 BABt;t+1 BACt;t+1 BACt;t+1 LMAXt;t+1 LMAXt;t+1 SMAXt;t+1 SMAXt;t+1 IVOLt;t+1 IVOLt;t+1

MDt -0.31 -0.60 -0.36 -0.76 0.18 -0.03 0.14

(-1.69) (-2.78) (-1.87) (-3.30) (1.14) (-0.22) (0.91)

MDt+1-MDt 6.18 5.74 10.45 9.30 -2.03 0.88 -1.96

(3.55) (3.17) (5.63) (4.83) (-1.51) (0.86) (-1.49)

SENT t 0.13 -0.06 0.21 0.17 0.09 0.07 0.24 0.24

(1.09) (-0.46) (2.35) (1.85) (1.35) (1.03) (2.79) (2.69)

SENT t+1-SENTt 1.07 1.24 0.55 0.69 1.03 1.03 0.00 0.11

(1.33) (1.44) (0.91) (1.14) (2.27) (2.24) (0.01) (0.19)

Higher MD = lower leverage constraints

Horserace

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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

Horserace

28





BAC SMAX

BAB

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Turnover

29


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.



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

HML BAB BAB BAB BAC BAV LMAX SMAX IVOL LMAX(1Y) SMAX(1Y)

MethodFF: june

update

FF: june

update

FF:

monthly

Rank

weights

Rank

weights

Rank

weights

FF:

monthly

FF:

monthly

FF:

monthly

FF:

monthly

FF:

monthly

Turnover 0.24 0.21 0.41 0.34 0.35 0.36 2.06 2.77 1.76 0.46 1.14

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 yearPeriod over which

the characteristics

are calculated

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SMAX at Conventional Turnover

30


Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table XI of the paper for more information.



Yearly MAX is the average of the 20 highest daily returns over the previous year

LMAX(1Y) LMAX(1Y) LMAX(1Y) SMAX(1Y) SMAX(1Y) SMAX(1Y)

Alpha 0.40 0.09 -0.11 -0.13 -0.25 -0.23

(3.73) (0.89) (-1.26) (-1.67) (-3.57) (-3.25)

MKT -0.50 -0.43 -0.47 0.00 -0.05 -0.04

(-19.6) (-17.5) (-21.9) (0.0) (-2.6) (-2.4)

SMB -0.67 -0.54 -0.59 -0.23 -0.21 -0.21

(-18.8) (-16.0) (-19.9) (-9.1) (-8.8) (-8.6)

HML 0.36 0.11 0.00 0.16 0.17 0.18

(9.2) (2.3) (-0.1) (5.8) (4.8) (5.1)

RMW 0.61 0.42 0.17 0.19

(12.3) (9.4) (4.8) (5.2)

CMA 0.52 0.37 -0.07 -0.05

(7.4) (5.9) (-1.3) (-1.0)

REV 0.04 0.06 0.25 0.25

(1.2) (2.3) (10.9) (10.8)

BAB 0.41 -0.04

(14.5) (-1.8)

SR 0.07 0.07 0.07 -0.22 -0.22 -0.22

IR 0.53 0.13 -0.19 -0.24 -0.52 -0.48

R2 0.68 0.75 0.81 0.18 0.34 0.34

# obs 630 630 630 630 630 630

Panel A: U.S. Sample (1963 - 2015)

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Consistent Factor Methodology: Rank Weights

31





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

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Consistent Factor Methodology: Rank Weights

32


Frazzini, Niels Gormsen, and Lasse H. Pedersen. Please see Table XIII of the paper for more information.



BAB BAB BAC BAC BAV BAV LMAX LMAX SMAX SMAX IVOL IVOL

Alpha 0.32 0.24 0.27 0.24 0.02 -0.10 0.14 -0.10 0.22 0.14 0.14 -0.05

(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 0.02 0.06 -0.01 0.01 -0.05 0.01 -0.08 -0.09 -0.04 -0.05 -0.06 -0.07

(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 0.14 0.15 0.36 0.37 -0.17 -0.16 -0.02 -0.12 0.09 0.06 -0.15 -0.24

(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 0.33 0.31 0.20 0.19 0.24 0.22 0.03 -0.21 -0.12 -0.20 0.17 -0.03

(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 0.49 -0.12 0.12 -0.12 1.05 0.16 1.12 0.75 0.43 0.31 0.96 0.67

(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 0.02 -0.18 -0.10 -0.18 0.34 0.05 0.36 0.35 0.11 0.10 0.31 0.30

(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 -0.01 -0.15 -0.05 -0.10 0.05 -0.15 0.25 0.27 0.37 0.37 -0.02 -0.01

(-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 0.75 0.24 0.59

(22.7) (8.7) (23.8)

LMAX 0.54 0.22 0.79

(22.7) (9.3) (57.4)

SR 0.83 0.83 0.78 0.78 0.33 0.33 0.68 0.68 1.17 1.17 0.36 0.36

IR 0.48 0.48 0.52 0.48 0.02 -0.33 0.18 -0.16 0.41 0.28 0.23 -0.12

R2 0.44 0.67 0.51 0.56 0.79 0.96 0.65 0.79 0.45 0.50 0.79 0.88

# obs 762 762 762 762 762 762 762 762 762 762 761 761

Panel A: U.S. Sample (1952 - 2015)

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Conclusion

33





BAC is

• New

• Unique

• Consistent only with leverage aversion

• Holds up quite strongly

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.

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