Downside beta and the cross section of equity returns: A decade later

• Published date: 01 March 2020
• Author: A. Doruk Gunaydin,Yigit Atilgan,K. Ozgur Demirtas
• Date: 01 March 2020
• DOI: http://doi.org/10.1111/eufm.12258

Eur Financ Manag. 2020;26:316–347.wileyonlinelibrary.com/journal/eufm316

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© 2020 John Wiley & Sons Ltd.

DOI: 10.1111/eufm.12258

ORIGINAL ARTICLE

Downside beta and the cross section of equity

returns: A decade later

Yigit Atilgan

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K. Ozgur Demirtas

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A. Doruk Gunaydin

School of Management, Sabanci

University, Istanbul, Turkey

Correspondence

K. Ozgur Demirtas, School of

Management, Sabanci University,

Orhanli, 34956 Tuzla/Istanbul, Turkey.

Email: ozgurdemirtas@sabanciuniv.edu

Abstract

This study reexamines the relation between downside

beta and equity returns in the United States. First, we

replicate the 2006 work of Ang, Chen, and Xing who

find a positive relation between downside beta and

future equity returns for equal‐weighted portfolios of

NYSE stocks. We show that this relation doesn't hold

after using value‐weighted returns or controlling for

various return determinants. We also extend the original

sample, add AMEX/NASDAQ stocks or utilize alter-

native downside beta measures and still find no down-

side risk premium. We focus on factor analysis results,

persistence of downside beta, and various subsamples to

understand the economic reasons behind the findings.

KEYWORDS

asset pricing, downside beta, downside risk, equity returns, tail risk

JEL CLASSIFICATION

G10; G11; G12

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INTRODUCTION

Studies that focus on the relation between asset returns and downside risk have a long history in

asset pricing. Almost 70 years ago, Roy (1952) introduced the concept of safety‐first investors who

are concerned about minimizing the probability of a loss event and Markowitz (1959) suggested the

use of semi‐variance rather than variance as a risk metric.HoganandWarren(1974),Krausand

Litzenberger (1976), Arzac and Bawa (1977), Bawa and Lindenberg (1977), and Harlow and Rao

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The authors acknowledge the helpful comments and suggestions by John Doukas (the Editor), two anonymous referees,

and the participants of the 2017 European Financial Management Association annual meeting and 24th Annual

Conference of the Multinational Finance Society.

(1989) went beyond the original capital asset pricing model framework and introduced models that

incorporate lower partial moments in an equilibrium context. Kahneman and Tversky (1979) also

contributedtothefieldwithprospecttheoryin which investors make decisions based on the

potential value of losses and gains rather than expected outcomes and their asymmetric value

functions are steeper for losses than gains which implies loss aversion.

In recent years, the literature that empirically tests the relation between downside risk and

equity returns has blossomed. Bali, Cakici, and Whitelaw (2014) document a positive and

significant relation between expected stock returns and hybrid tail covariance risk based on the

colower partial moment between daily equity and market returns. Kelly and Jiang (2014)

construct an aggregate measure of tail risk by exploiting monthly firm‐level crashes and show

that equities with higher sensitivities towards aggregate tail risk earn higher returns. Using

investable option trading strategies, Cremers, Halling, and Weinbaum (2015) construct

mimicking portfolios for aggregate volatility and jump risk factors and find that equities that

load more on these two factors have lower expected returns. Lu and Murray (2019) also rely on

S&P 500 options to construct an Arrow–Debreu security that pays off in bear market states. The

authors use the returns on this security as a measure of bear market risk and find that equities

with higher exposure to this risk have lower future returns. Chabi‐Yo, Ruenzi, and Weigert

(2018) focus on the concept of crash sensitivity and use a copula‐based approach to calculate the

lower‐tail dependence of each stock with the market. Their results suggest that stocks with

stronger lower‐tail dependence earn higher future returns. Finally, Atilgan, Bali, Demirtas, and

Gunaydin (2019) measure downside risk using value‐at‐risk and expected a shortfall and

uncover a negative relation between these metrics and future equity returns.

A key study that evoked this recent interest on downside risk has been authored by Ang,

Chen, and Xing (ACX, 2006). ACX are driven by the idea that assets that are more sensitive to

market downturns than uptrends are undesirable for loss‐averse investors since such assets

provide their investors with low payoffs precisely when the wealth of investors is decreasing.

The authors motivate the role for downside beta in asset pricing as a risk attribute by relying on

the disappointment utility function of Gul (1991) in a rational representative‐agent framework.

They investigate the significance of a relation between downside beta and the cross section of

returns of US equities. Their main results are two‐fold. First, for equities trading in NYSE

between 1962 and 2001, individual stocks with higher downside betas have higher average

contemporaneous returns as equities that have high covariation with the market when the

market declines display high average returns over the same period. Second, high past downside

beta predicts higher equity returns over the next month except the portion of the cross section

which includes stocks with excess volatility.

Harvey, Liu, and Zhu (2016) call for the reexamination of past research on the cross section

of equity returns and argue that ‘many of the historically discovered factors would be deemed

significant by chance.’In this paper, we revisit the evidence for the existence of a significant

downside risk premium by investigating the relation between downside beta and future equity

returns. We focus on future returns rather than contemporaneous returns since there is a long

tradition in finance starting with Fama and MacBeth (1973) who calculate predictive betas

based on conditional information and examine one‐period‐ahead returns. Moreover, a return

determinant must successfully predict future returns to present a trading strategy. We measure

downside beta in the exact manner as ACX (2006) as the sensitivity of excess stock returns to

excess market returns during market downturns. A market downturn is defined as periods

during which the excess market return has been lower than its mean value during the past year.

First, we replicate the results of ACX (2006) and find a significant downside risk premium when

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equities with the highest volatilities are excluded from the sample each month. Second, we

observe that this premium vanishes when standard asset pricing factors are controlled for and/

or value‐weighted portfolio returns are used. The significantly positive relation between

downside beta and future equity returns also ceases to exist in a cross‐sectional regression

framework that controls for a multitude of firm‐specific attributes. Adding non‐NYSE stocks to

the original sample and/or extending the sample period until 2014 also erases any significant

trade‐off between downside risk and future equity returns.

Next, we investigate some potential economic mechanisms behind why changing the sample

period or methodology causes the downside risk premium to vanish. First, we focus on the

results from the factor regressions and find that the market factor is the main driver behind the

significantly positive relation between downside beta and future stock returns documented in

ACX (2006). Moreover, the factor model used in our study is able to better explain equal‐

weighted portfolio returns due to the lower exposure of value‐weighted portfolio returns

towards the market, size, and value factors. Second, we investigate whether the lack of a

downside premium is due to lower post‐ranking downside betas associated with a zero‐cost

strategy that buys (sells) equities in the highest (lowest) downside beta quintile every month

when alternative samples and methodologies are utilized. Our results provide no evidence for

this hypothesis. Third, we investigate the performance of the zero‐cost strategy for different

subsample periods. We find that the zero‐cost strategy performed better during periods of high

market volatility, displayed very low returns during the post‐2001 period, and experienced

sharp drops and jumps around the 2008 financial crisis.

Finally, we focus on an extended sample that includes all NYSE, AMEX, and NASDAQ

stocks between 1962 and 2014 to check the robustness of our results. For this sample, we show

that altering the proxy for the market portfolio does not affect the main results. Moreover,

bivariate portfolio analyses and firm‐level cross‐sectional regressions show that the relation

between downside beta and 1‐month‐ahead stock returns is insignificant. Furthermore, we

show that the particular definition of downside beta that we use in our tests is not the driver of

the flat relation between downside beta and equity returns by utilizing alternative downside

beta metrics based on new cut‐off points and time windows.

The remainder of the paper is organized as follows. Section 2 describes the data and

variables. Section 3 presents the empirical results. Section 4 provides additional tests and

robustness checks. Section 5 concludes.

2

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DATA AND VARIABLES

2.1

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Data

The data for equity returns, shares outstanding, and volume of shares traded comes from Center

for Research in Security prices (CRSP). The book value of equity for each firm is necessary to

calculate book‐to‐market ratios and this data is obtained from Compustat. The risk‐free rate

used to calculate excess returns is the interest rate on 1‐month US T‐bills obtained from the

Federal Reserve database. We winsorize all independent variables at the 1% and 99% level

within each month to avoid putting too much weight on extreme observations following ACX

(2006). Our study aims to investigate the robustness of the positive relation between downside

beta and future equity returns in different sample settings. In the tests that examine the relation

between downside betas and future returns, ACX (2006) focus only on NYSE stocks between

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