Skewness and Risk: When Risk Doesn't Lead To Return
From ETF.com:
Among the more notable anomalies in modern finance is the finding
that the lowest-beta stocks have produced higher returns than the
highest-beta stocks. Another anomaly is that idiosyncratic
(diversifiable) volatility negatively predicts equity returns. In other
words, stocks with the lowest idiosyncratic volatility outperform stocks
with the highest idiosyncratic volatility.
These findings have spurred a large body of literature on what
are referred to as “low-risk anomalies.” Such results are considered
puzzling because higher risk should be rewarded with higher returns, but
here we see just the opposite.
Paul Schneider, Christian Wagner and Josef Zechner—authors of the April 2015 paper “Low Risk Anomalies?”—add
to our understanding of these anomalies by investigating the link
between them and a higher moment of the return distribution, the
skewness of returns. This is a link that standard measures of market
risk and volatility ignore. We’ll begin with a definition.
Defining Skewness
Skewness measures the asymmetry of a distribution. In terms of the
market, the historical pattern of returns does not resemble a normal
distribution (also known as the familiar “bell curve”) and so
demonstrates skewness. Negative skewness occurs when the values to the
left of (less than) the mean are fewer but farther from it than values
to the right of (greater than) the mean.
For example, the return series of -30%, 5%, 10% and 15% has a
mean of 0%. There is only one return less than zero, and three that are
higher. The single negative return is much farther from zero than the
positive ones, so the return series has negative skewness. Positive
skewness, on the other hand, occurs when values to the right of (greater
than) the mean are fewer but farther from it than values to the left of
(less than) the mean.
The question Schneider, Wagner and Zechner sought to answer is:
Is there a link between skewness and returns? Said another way, do
stocks with more negative skewness produce higher returns? Their theory
is that investors require comparably lower (higher) expected equity
returns for firms that are less (more) coskewed with the market.
Coskewness is a measure of the symmetry of a variable’s
probability distribution in relation to the symmetry of another
variable’s probability distribution. It’s calculated using a security’s
historic price data as the first variable, and the market’s historic
price data as the second. This provides an estimate of the security’s
risk in relation to market risk.
All else equal, a positive coskewness means that the first
variable’s probability distribution is skewed to the right of the second
variable’s distribution. Investors prefer positive coskewness because
this represents a higher probability for extreme positive returns in the
security over market returns.
The Study And Its Results
The study’s database included about 5,000 U.S. firms for the period
January 1996 to August 2014 and covered all CRSP firms for which data on
common stocks and equity options was available.
Employing the options data, the authors computed ex-ante skewness
from an options portfolio that took long positions in out-of-the-money
(OTM) call options and short positions in OTM puts. This measure becomes
more negative the more expensive put options become relative to call
options (investors are willing to pay high premiums for protection
against downside risk). Equity options are more expensive for firms with
high compared with low credit risk. Thus, credit risk acts as a natural
source of skewness.
Following is a summary of their findings:
- Corporate credit risk generates
time-varying skewness in a firm’s equity returns, which in turn impacts
the pricing of its stock. And credit risk matters for the shape of a
firm’s equity return distribution—equity is an option on the underlying
assets and, hence, its value can drop to zero....
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