Does It Pay to Bet Against Beta? On the Conditional Performance of the Beta Anomaly

• Date: 01 April 2016
• DOI: http://doi.org/10.1111/jofi.12383
• Published date: 01 April 2016

THE JOURNAL OF FINANCE •VOL. LXXI, NO. 2 •APRIL 2016

Does It Pay to Bet Against Beta? On the

Conditional Performance of the Beta Anomaly

SCOTT CEDERBURG and MICHAEL S. O’DOHERTY∗

ABSTRACT

Prior studies find that a strategy that buys high-beta stocks and sells low-beta stocks

has a significantly negative unconditional capital asset pricing model (CAPM) alpha,

such that it appears to pay to “bet against beta.” We show, however, that the condi-

tional beta for the high-minus-low beta portfolio covaries negatively with the equity

premium and positively with market volatility. As a result, the unconditional alpha

is a downward-biased estimate of the true alpha. We model the conditional market

risk for beta-sorted portfolios using instrumental variables methods and find that the

conditional CAPM resolves the beta anomaly.

THE SHARPE-LINTNER CAPITAL asset pricing model (CAPM) implies that expo-

sure to market risk, as measured by beta, should be compensated by the mar-

ket risk premium. Based on the performance of portfolios formed on lagged

firm-level beta, however, a number of empirical studies find that the risk-

reward relation is too flat. For example, Friend and Blume (1970) and Black,

Jensen, and Scholes (1972) demonstrate that portfolios of high-beta stocks earn

lower returns than implied by the CAPM and therefore have negative alphas,

whereas portfolios of low-beta stocks earn positive alphas. Fama and French

(1992,2006) extend these results by showing that the beta-return relation be-

comes even flatter after controlling for size and book-to-market characteristics.

Finally, Frazzini and Pedersen (2014) confirm the underperformance of high-

beta stocks over a long sample period extending from 1926 to 2012 and develop

a “betting-against-beta” strategy, which has drawn substantial interest from

academics and practitioners alike.1

∗Scott Cederburg is with the Eller College of Management, University of Arizona. Michael

O’Doherty is with the Trulaske College of Business, University of Missouri. Weare grateful to Phil

Davies and Rick Sias for their detailed suggestions on the paper. We also thank Oliver Boguth,

Wayne Ferson, Iva Kalcheva, Eric Kelley, Kenneth Singleton (the Editor), an Associate Editor,

two anonymous referees, and seminar participants at Arizona State University, the University of

Arizona, the University of Kansas, the University of Missouri, and the 2013 Northern Finance

Association for helpful comments. We have read the Journal of Finance’s disclosure policy and

have no conflicts of interest to disclose.

1For example, Asness, Frazzini, and Pedersen (2014), Bali et al. (2014), Huang, Lou, and Polk

(2014), Novy-Marx (2014), Boguth and Simutin (2015), and Malkhozov et al. (2015) examine aspects

of the betting-against-beta strategy.Dozens of funds have also been set up to take advantage of the

low-beta and closely related low-volatility anomalies (see, for example, “Beat the Market—With

DOI: 10.1111/jofi.12383

737

738 The Journal of Finance R

Figure 1. Cross-sectional distribution of firm betas, July 1927 to December 2012. The

figure displays statistics for the cross-sectional distribution of firm betas. The dashed line is the

median and the solid lines show the 5th and 95th percentiles of firm betas. Firm betas are estimated

at the beginning of each month using daily returns over the previous 12 months.

In this paper, we reconsider the evidence on the abnormal performance of

beta-sorted portfolios. Prior work focuses on the unconditional CAPM alphas of

these strategies and finds a significantly negative alpha on a high-minus-low

beta-spread portfolio. It is well known, however, that unconditional alphas are

biased estimates of the true portfolio alphas if portfolio betas vary systemat-

ically with the market risk premium or market volatility (see Grant (1977),

Jagannathan and Wang (1996), Lewellen and Nagel (2006), and Boguth et al.

(2011)).2For the beta anomaly to be explained by a bias in unconditional alpha,

the conditional beta for the high-minus-low strategy must display meaningful

time-series variation. Consistent with this argument, we find that the betas

of portfolios sorted on past firm beta vary substantially over time, largely as

a result of the shifting cross-sectional variation in firm betas. For instance,

Figure 1reveals that the 90% interval of the cross section of firm betas exhibits

pronounced changes over the sample period. We observe a relatively tight dis-

tribution of betas early in the postwar period, with a beta difference between

the 95th and 5th percentiles of about 1.5, whereas this difference approximately

doubles to a beta spread of around 3.0 in the 1990s and early 2000s. The be-

tas of portfolios sorted on past firm beta inherit these time-series patterns,

displaying large swings over the sample period.

Less Risk,” The Wall Street Journal, October 1, 2011, and “High Hopes for ‘Low Volatility’Funds,”

The Wall Street Journal, April 6, 2014).

2Given that unconditional and conditional CAPM inferences may differ, a recent literature

reevaluates several other cross-sectional anomalies while allowing for time variation in betas. See,

for example, Lettau and Ludvigson (2001), Avramov and Chordia (2006), Fama and French (2006),

Lewellen and Nagel (2006), Ang and Chen (2007), Boguth et al. (2011), and O’Doherty (2012).

Does It Pay to Bet against Beta? 739

Panel A: Market Timing Panel B: Volatility Timing

Figure 2. Systematic trends in portfolio betas, July 1930 to December 2012. Panel A

(Panel B) shows the instrumental variables (IV) beta for the high-minus-low beta portfolio and

the aggregate log dividend yield (volatility of the CRSP value-weighted portfolio). The conditional

beta estimate corresponds to case 7 in Table 2, and the IV approach is outlined in Section I.A. The

log dividend yield is the log of the sum of dividends accruing to the CRSP value-weighted portfolio

over the previous 12 months scaled by the lagged level of this portfolio. Market volatility is the

realized volatility using daily excess market returns over the previous 12 months.

As noted above, previous work establishes a formal link between time vari-

ation in market exposure for a given strategy and the bias in its unconditional

CAPM alpha. Specifically,Lewellen and Nagel (2006), Boguth et al. (2011), and

others show that, if the conditional CAPM holds, the unconditional alpha for a

particular asset can be approximated by

αU

i≈Cov(βi,t,Et−1(Rm,t)) −E(Rm,t)

σ2

m

Cov βi,t,σ2

m,t,(1)

where βi,tis the asset’s conditional beta, E(Rm,t)andEt−1(Rm,t) are the uncondi-

tional and conditional market expected excess returns, and σ2

mand σ2

m,tare the

unconditional and conditional market volatilities. A negative bias in uncondi-

tional alpha arises when beta is negatively related to the expected excess return

on the market (“market timing”) and/or positively related to market volatility

(“volatility timing”). In empirical applications, biases in unconditional alphas

can be substantial, with the volatility timing channel having a particularly

large potential effect (Boguth et al. (2011)).

Our tests focus on contrasting the unconditional and conditional performance

of decile portfolios sorted on prior market beta. Figure 2provides a preliminary

indication that a negative unconditional CAPM alpha for a high-minus-low beta

portfolio is plausibly attributable to market timing and volatility timing effects

in the data.3Panel A shows that this strategy’s beta is inversely related to

the log dividend yield for the market portfolio, which is a positive predictor

of the equity premium (e.g., Fama and French (1988) and Cochrane (2008)).

3We introduce our method for estimating conditional portfolio betas in Section I.A and detail

the construction of the beta-sorted test assets in Section I.B.