Coskewness

Variance measures the spread of returns, while skewness describes asymmetry, so a negatively skewed series may have many small gains and occasional unusually large losses. Covariance asks whether two variables move together on average, whereas coskewness asks a third-order question about how one series interacts with unusually large moves or squared deviations of another.

In portfolio analysis, the important question can be whether a security suffers when the broad portfolio has unusually bad outcomes. A security that looks uncorrelated in ordinary months may still add downside risk, and correlation near zero does not eliminate coskewness because a position may move little with the market in most observations yet react strongly to a very large market move.

Harvey and Siddique's 2023 research revisits evidence on systematic skewness and its potential risk premium, explaining coskewness as an asset's contribution to skewness of a diversified portfolio. A higher expected return might compensate investors for exposure to undesirable negative-tail outcomes, but that is a theoretical and empirical relationship, not a promise that one specific asset will earn a premium.

Different statistical definitions can place the squared term on different variables, so always state the formula before comparing coefficients from separate reports. Positive coskewness under one convention can signal more favourable co-movement during extremes, but a sign label alone is ambiguous, so confirm whether the model measures the market squared term, downside states or another normalisation.

Rare events create estimation problems, because a short return history may contain too few extreme observations to produce a stable third-moment estimate. Outliers and data errors are especially influential because deviations are multiplied, so verify prices, splits, stale quotes and matching timestamps before calculating, and remember that short rolling windows react faster but give noisier coefficients.

Liquidity matters during tail events, since an asset that appears to hedge on a chart may be hard to sell at the recorded price when markets are stressed. Managers should pair coskewness with stress tests, drawdown scenarios and conventional volatility measures, and a fund report should describe the benchmark, return frequency, sample period and estimation formula so the coefficient can be reproduced.

The goal is to understand which holdings deepen or soften portfolio losses during unusual markets, which is different from forecasting the exact day or size of the next shock.