# Coskewness

## What Is Coskewness?

Coskewness, in statistics, measures how much two random variables change together, and is used in finance to analyze security and portfolio risk. If they exhibit positive coskewness, they will tend to undergo positive deviations at the same time. But if they exhibit negative coskewness, they will tend to undergo negative deviations at the same time.

### Key Takeaways

• Coskewness is used to measure securities' risk with regard to market risk.
• Positive coskewness measure means there is a higher probability that two assets in a portfolio will have positive returns in excess of market returns.
• Negative coskewess means there is a higher probability that two assets in a portfolio will simultaneously have lower returns than market returns.
• Positive coskewness reduces portfolio risk but lowers expected return.

## Understanding Coskewness

Coskewness is a measure of a security's risk in relation to market risk. It was first used to analyze risk in stock market investments by Krauss and Litzenberger in 1976, and then by Harvey and Siddique in 2000. Skewness measures the frequency of excess returns in a particular direction, which describes an asymmetry from the normal distribution.

Coskweness is much like covariance, which is used in the capital asset pricing model as a measure of the volatility, or systematic risk, of a security in relation to the market as a whole—which is otherwise known as beta. Thus, assets with higher covariance contribute more to the variance of a well-diversified market portfolio—and should command a larger risk premium.

Investors prefer positive coskewness, because this represents a higher probability that two assets in a portfolio will show extreme positive returns in excess of market returns at the same time. If the return distributions of these two assets tended to exhibit negative coskewness, it would mean that both assets have a higher probability of underperforming the market at the same time.

Everything else being equal, an asset with higher coskewness should be more attractive as it increases the systematic skewness of an investor's portfolio. Assets with higher coskewness should provide a hedge against periods when the benefits of portfolio diversification deteriorate; such as during periods of high market volatility when correlations between various asset classes tend to rise sharply.

In theory, positive coskewness reduces the risk of a portfolio and lowers the expected return or risk premium. Emerging markets, for example, is an asset class that might reduce portfolio variance, because it is more “right-skewed."

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