Source: Harvey & Siddique (2000) · The Journal of Finance · DOI: 10.1111/0022-1082.00247
TL;DR
Systematic (co)skewness is priced in the cross-section: stocks that make the market portfolio's return distribution more negatively skewed — i.e., that pay off poorly exactly when the market crashes — must offer higher expected returns. Adding conditional coskewness to the CAPM helps explain return patterns the market beta alone misses, including part of momentum.
What anomaly it documents
Predictor: coskewness — an asset's contribution to the skewness of the market portfolio (the covariance of the asset's return with the squared market return).
Direction: negative coskewness commands a positive premium. Assets with negative coskewness (low or negative returns when market volatility/declines are extreme) are undesirable and must pay more; assets with positive coskewness (lottery-like, good when the market is wild) are bid up and earn less.
Framework: a three-moment CAPM — investors care about mean, variance, and skewness. This generalizes the standard mean-variance model.
OSAP predictor: Coskewness.
How to construct it
Sorting variable: estimated coskewness, typically the standardized measure: the covariance of the stock's excess return with the squared market excess return, scaled (Harvey-Siddique's "direct" coskewness estimate), measured over a trailing window of daily/monthly returns.
Universe: US common stocks (sample ~1963–1993).
Portfolio formation: monthly; sort into coskewness portfolios.
Long / short: long low (negative) coskewness, short high (positive) coskewness — capturing the skewness risk premium.
Weighting: value-weighted in the headline tests.
Rebalancing: monthly.
Evidence and replication
Period
Notes
Source
IS (~1963–1993)
coskewness commands an economically significant premium (~ several % per year between extreme portfolios)
this paper
IS (explains other anomalies)
helps account for part of momentum and size
this paper
OOS (post-2000)
weaker, estimation-sensitive
post-publication
OSAP replication (Coskewness)
present but noisier
Chen & Zimmermann 2022
Harvey & Siddique show coskewness is priced even after controlling for the market factor and that it absorbs some of the explanatory power of momentum — momentum winners tend to have negative coskewness, so part of momentum's return is skewness-risk compensation.
The effect is real but estimation-sensitive: coskewness is a third moment and noisy to measure, so portfolio results vary with the estimation window and method.
Why it might work
Preference for skewness (risk-based): investors like positive skewness (lottery-type upside) and dislike negative coskewness (assets that crash with the market). This is a clean, preference-based extension of expected-utility theory beyond mean-variance — the premium is fair compensation for bearing crash-correlated risk.
Links to the low-vol/lottery family: positive-coskewness, lottery-like stocks being overpriced connects to the MAX effect (Bali-Cakici-Whitelaw) and the idiosyncratic-volatility puzzle (Ang et al. 2006).
Connection to downside risk: related in spirit to downside-beta pricing (Ang, Chen & Xing) — both formalize that "risk" is asymmetric and concentrated in bad states.
Limitations and risks
Noisy third moment: coskewness is hard to estimate precisely; results depend heavily on the window and estimator, and standard errors are wide.
Implementation: sorting on a noisy moment produces unstable portfolios and turnover.
Overlap: entangled with momentum, downside beta, and lottery/IVOL effects — limited standalone incremental value.
No free full text: paywalled; see DOI.
Key references
Harvey, C. & Siddique, A. (2000) — Conditional Skewness in Asset Pricing Tests — Journal of Finance — DOI: 10.1111/0022-1082.00247
Kraus, A. & Litzenberger, R. (1976) — Skewness Preference and the Valuation of Risk Assets — Journal of Finance
Ang, A., Chen, J. & Xing, Y. (2006) — Downside Risk — Review of Financial Studies
Bali, T., Cakici, N. & Whitelaw, R. (2011) — Maxing Out: Stocks as Lotteries… — Journal of Financial Economics
Chen, A. & Zimmermann, T. (2022) — Open Source Cross-Sectional Asset Pricing — Critical Finance Review
