Conditional Skewness in Asset Pricing Tests
CAMPBELL R. HARVEY and AKHTAR SIDDIQUE
Title, authors, journals
Title: Conditional Skewness in Asset Pricing Tests
Authors: CAMPBELL R. HARVEY and AKHTAR SIDDIQUE
Journal: THE JOURNAL OF FINANCE
ABSTRACT
- If asset returns have systematic skewness, expected returns should include rewards for
accepting this risk.
- We formalize this intuition with an asset pricing model that incorporates conditional
skewness.
- Our results show that conditional skewness helps explain the cross-sectional variation of
expected returns across assets and is significant even when factors based on size and book-
to-market are included.
- Systematic skewness is economically important and commands a risk premium, on average,
of 3.60 percent per year.
- Our results suggest that the momentum effect is related to systematic skewness.
- The low expected return momentum portfolios have higher skewness than high expected
return portfolios.
Research Question + underlying intuition
Research Question: Everything else being equal, do investors prefer portfolios that are right-skewed
to portfolios that are left-skewed?
Underlying intuition: In his 2000 paper in the Journal of Finance with Siddique, Harvey presents a
two-part argument in favour of incorporating skewness. First, asset returns are not normally
distributed. Second, investors like positive skew (big profits) and dislike negative skew (big losses);
Harvey argues these preferences need to be taken into account in both portfolio management and
risk management. Harvey also asserts estimates are imprecise and this uncertainty needs to be taken
into account when making investment decisions.
The results show that conditional skewness helps explain the cross-sectional variation of expected
returns across assets and is significant even when factors based on size and book-to-market are
included.
,The results suggest that the momentum effect is related to systematic skewness.
The low expected return momentum portfolios have higher skewness than high expected return
portfolios.
In probability theory and statistics, skewness is a measure of the asymmetry of the probability
distribution of a real-valued random variable about its mean. The skewness value can be positive or
negative, or undefined. The qualitative interpretation of the skew is complicated and unintuitive
One clue that pushed us in the direction of skewness is the fact that some of the empirical
shortcomings of the standard CAPM stem from failures in explaining the returns of specific securities
or groups of securities such as the smallest market-capitalized deciles and returns from specific
strategies such as ones based on momentum.
A positively skewed investment return means there were frequent small losses and a few
large gains.
Negatively skewed means there were frequent small gains and a few large losses.
- Managers may prefer portfolios with high positive skewness.
In probability theory and statistics, skewness is a measure of the asymmetry of the
probability distribution of a real-valued random variable about its mean. The skewness value
can be positive or negative, or undefined. The qualitative interpretation of the skew is
complicated and unintuitive
- THE SINGLE FACTOR CAPITAL ASSET PRICING MODEL (CAPM) of Sharpe (1964) and Lintner
(1965) has come under recent scrutiny. Tests indicate that the crossasset variation in
expected returns cannot be explained by the market beta alone.
o SMB ((the difference between the return on a portfolio of small size stocks and the
return on a portfolio of large size stocks)
o HML ((the difference between the return on a portfolio of high book-to-market value
stocks and the return on a portfolio of low book-to-market value stocks)
- The goal of this paper is to examine the linkage between the empirical evidence on these
additional factors and systematic coskewness.
, Hypothesis: Everything else being equal, investors should prefer portfolios that are right-skewed to
portfolios that are left-skewed.
- Hence, assets that decrease a portfolio's skewness (i.e., that make the portfolio returns more
leftskewed) are less desirable and should command higher expected returns. Similarly, assets
that increase a portfolio's skewness should have lower expected returns.
One clue that pushed us in the direction of skewness is the fact that some of the empirical
shortcomings of the standard CAPM stem from failures in explaining the returns of specific securities
or groups of securities such as the smallest market-capitalized deciles and returns from specific
strategies such as ones based on momentum.
A positively skewed investment return means there were frequent small losses and a few
large gains.
Negatively skewed means there were frequent small gains and a few large losses.
- Managers may prefer portfolios with high positive skewness.
CAMPBELL R. HARVEY and AKHTAR SIDDIQUE
Title, authors, journals
Title: Conditional Skewness in Asset Pricing Tests
Authors: CAMPBELL R. HARVEY and AKHTAR SIDDIQUE
Journal: THE JOURNAL OF FINANCE
ABSTRACT
- If asset returns have systematic skewness, expected returns should include rewards for
accepting this risk.
- We formalize this intuition with an asset pricing model that incorporates conditional
skewness.
- Our results show that conditional skewness helps explain the cross-sectional variation of
expected returns across assets and is significant even when factors based on size and book-
to-market are included.
- Systematic skewness is economically important and commands a risk premium, on average,
of 3.60 percent per year.
- Our results suggest that the momentum effect is related to systematic skewness.
- The low expected return momentum portfolios have higher skewness than high expected
return portfolios.
Research Question + underlying intuition
Research Question: Everything else being equal, do investors prefer portfolios that are right-skewed
to portfolios that are left-skewed?
Underlying intuition: In his 2000 paper in the Journal of Finance with Siddique, Harvey presents a
two-part argument in favour of incorporating skewness. First, asset returns are not normally
distributed. Second, investors like positive skew (big profits) and dislike negative skew (big losses);
Harvey argues these preferences need to be taken into account in both portfolio management and
risk management. Harvey also asserts estimates are imprecise and this uncertainty needs to be taken
into account when making investment decisions.
The results show that conditional skewness helps explain the cross-sectional variation of expected
returns across assets and is significant even when factors based on size and book-to-market are
included.
,The results suggest that the momentum effect is related to systematic skewness.
The low expected return momentum portfolios have higher skewness than high expected return
portfolios.
In probability theory and statistics, skewness is a measure of the asymmetry of the probability
distribution of a real-valued random variable about its mean. The skewness value can be positive or
negative, or undefined. The qualitative interpretation of the skew is complicated and unintuitive
One clue that pushed us in the direction of skewness is the fact that some of the empirical
shortcomings of the standard CAPM stem from failures in explaining the returns of specific securities
or groups of securities such as the smallest market-capitalized deciles and returns from specific
strategies such as ones based on momentum.
A positively skewed investment return means there were frequent small losses and a few
large gains.
Negatively skewed means there were frequent small gains and a few large losses.
- Managers may prefer portfolios with high positive skewness.
In probability theory and statistics, skewness is a measure of the asymmetry of the
probability distribution of a real-valued random variable about its mean. The skewness value
can be positive or negative, or undefined. The qualitative interpretation of the skew is
complicated and unintuitive
- THE SINGLE FACTOR CAPITAL ASSET PRICING MODEL (CAPM) of Sharpe (1964) and Lintner
(1965) has come under recent scrutiny. Tests indicate that the crossasset variation in
expected returns cannot be explained by the market beta alone.
o SMB ((the difference between the return on a portfolio of small size stocks and the
return on a portfolio of large size stocks)
o HML ((the difference between the return on a portfolio of high book-to-market value
stocks and the return on a portfolio of low book-to-market value stocks)
- The goal of this paper is to examine the linkage between the empirical evidence on these
additional factors and systematic coskewness.
, Hypothesis: Everything else being equal, investors should prefer portfolios that are right-skewed to
portfolios that are left-skewed.
- Hence, assets that decrease a portfolio's skewness (i.e., that make the portfolio returns more
leftskewed) are less desirable and should command higher expected returns. Similarly, assets
that increase a portfolio's skewness should have lower expected returns.
One clue that pushed us in the direction of skewness is the fact that some of the empirical
shortcomings of the standard CAPM stem from failures in explaining the returns of specific securities
or groups of securities such as the smallest market-capitalized deciles and returns from specific
strategies such as ones based on momentum.
A positively skewed investment return means there were frequent small losses and a few
large gains.
Negatively skewed means there were frequent small gains and a few large losses.
- Managers may prefer portfolios with high positive skewness.
