# Definition of asymmetry

## What is coskewness?

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

Key points to remember

- Coskewness is used to measure the risk of securities against market risk.
- A positive coskewness measure means that there is a higher probability that two assets in a portfolio will have positive returns above market returns.
- A negative coskewess means that there is a higher probability that two assets in a portfolio will simultaneously have returns below market returns.
- A positive cosymmetry reduces the risk of the portfolio but reduces the expected return.

## Understanding coskewness

Coskewness is a measure of a security’s risk relative to market risk. It was first used to analyze risk in stock 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 skewness by compared to the normal distribution.

Coskweness is very similar to covariance, which is used in the fixed asset valuation model as a measure of the volatility, or systematic risk, of a security relative to the market as a whole, that is, beta. Thus, assets with a higher covariance contribute more to the variance of a well-diversified market portfolio and should require a higher risk premium.

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

All other things being equal, an asset with a higher coskewness should be more attractive because it increases the systematic asymmetry of an investor’s portfolio. Assets with greater 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 different asset classes tend to increase 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 could reduce portfolio variance, as it is more “skewed to the right”.