A Tale of Two Anomalies: Higher Returns of Low‐Risk Stocks and Return Seasonality

Date01 May 2015
Published date01 May 2015
The Financial Review 50 (2015) 257–273
A Tale of Two Anomalies: Higher Returns
of Low-Risk Stocks and Return Seasonality
Christopher Fioreand Atanu Saha
Compass Lexecon
Prior studies have shown that low beta and low volatility stocks earn higher average
returns than high beta and high volatility stocks, contradicting the prediction of the capital
asset pricing model and the fundamental relationship between risk and return. In this paper, we
demonstrate that this phenomenon is driven by the seasonality of stock returns. We show that
the risk-return tradeoff does hold in the nonsummer months, and that switching to a portfolio
of low-risk stocks in summer outperforms—both in terms of absolute and in risk-adjusted
returns—buy and hold strategies as well as the Sell in May strategy of switching to treasury
bills in summer.
Keywords: low-risk anomaly, beta, idiosyncratic volatility, Halloween effect, sell in May,
return seasonality
JEL Classifications: G11, G12, G14
1. Introduction
The fundamental concept of asset pricing is that investors are rewarded with
higher returns in compensation for greater exposure to risk. There is a tradeoff
Corresponding author: Compass Lexecon, 156 West 56th Street, 19th Floor, New York, NY 10019;
Phone: (212) 782-3508; E-mail: cfiore@compasslexecon.com.
We are immensely grateful to Mary Shen for her research assistance.
C2015 The Eastern Finance Association 257
258 C. Fiore and A. Saha/The Financial Review 50 (2015) 257–273
between risk and return: if one invests in a portfolio with greater risk, then one can
earn higher returns on average; and, if one invests in safe assets, one must expect to
earn lower average returns.
The capital asset pricing model (CAPM), originally put forth by Sharpe (1964)
and Lintner (1965), postulates that an asset’s exposure to overall market movements
is the relevant risk measure. In other words, the risk of an asset should be measured by
the extent to which it contributes to the volatility of a well-diversifiedportfolio. These
authors have pointed to beta, the measure of an asset’s covariance with the market,
as the relevant risk measure. Thus, according to CAPM, higher beta assets should
command a higher average return to compensate investors for bearing higher risk.
The CAPM theory also predicts that any risk that is idiosyncratic can be diversified
away and will not command a risk premium: it will instead yield the same expected
return as a risk-free asset.
Evidence has shown, however, that, at best, the market factor does not entirely
explain how assets are priced, and, at worst, it is not a relevant factor. According
to Black (1972), Black, Jensen and Scholes (1975), and Haugen and Heins (1975),
the relationship between beta and return is much flatter than predicted by CAPM.
Fama and French (1992) also find that the relationship between beta and returns is
flat when controlling for size.
Baker, Bradley and Wurgler (2011), analyzing a period of 50 years from 1968
through 2008, find that high beta and high volatility stocks have consistently un-
derperformed low beta and low volatility stocks. This finding not only contradicts
CAPM, but it seemingly violates the very principle behind risk and return: low-risk
portfolios seem to have yielded greater reward than high-risk portfolios. The finding
begs the question: why are low beta and low volatility stocks priced as if they were
less risky than high beta and high volatility stocks?
Ang, Hodrick, Xing and Zhang (2006, 2009) find that across a variety of coun-
tries, stocks with low idiosyncratic volatility (based on the Fama-French three-factor
model) outperform stocks with high idiosyncratic volatility. That is, stocks appear
to earn a negative risk premium when risk is measured in idiosyncratic volatility.
This finding is interesting for two reasons. First, as noted earlier, CAPM suggests
that idiosyncratic volatility should not be priced. Second, theories suggest that id-
iosyncratic volatility, if anything, should earn a positive risk premium. For example,
Malkiel and Xu (2002) and Ewens, Jones and Rhodes-Kropf (2013) argue that id-
iosyncratic volatility is to be priced if investors are not fully able to diversify this
Several explanations have been put forth in the literature for the observed “in-
verted” risk-reward relationship. Baker, Bradley and Wurgler (2011), for example,
suggest benchmarking as an explanation; they argue that because mutual fund returns
are typically compared to a benchmark, such as the Standard & Poor’s 500, fund
managers underweight low-risk investments that do not track the benchmark as well.
Asness, Frazzini and Pedersen (2012) suggest that investors are averse to leverage;
as a result, they prefer to invest in higher-risk stocks rather than leveraging low-risk

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