What is Cokurtosis

Cokurtosis is a statistical measure which is used in asset management to measure the extent to which a security and a portfolio will undergo extreme positive and negative deviations from the market portfolio at the same time. It can be thought of as how an asset is “correlated” with the kurtosis of another reference asset or portfolio, or the marginal contribution of an asset to a portfolio’s risk.


Cokurtosis is used in fund management to evaluate the potential an asset has to diversify a portfolio, not only in terms of normal risk or volatility, but also in terms of the risk of extreme events – which is known as kurtosis. It measures a security’s risk in relation to the market as a whole – or beta – by using a security's historic price data as the first variable, and historical market data as the second. A risk-adverse investor would prefer lower cokurtosis, as the security's returns would not be much different from the market's returns. While a risk investor would prefer high cokurtosis with the potential for extreme positive returns.

Cokurtosis is a similar measure to coskewness, which estimates a security’s skewness related to the skewness of the market portfolio. It enables portfolio managers to manage risk by ensuring that the securities in a portfolio do not exhibit pronounced negative coskewness. For example, adding an asset to a portfolio that has significant coskewness – such as a hedge fund – will increase or decrease the asymmetry, or skewness, of its returns.

Cokurtosis and coskewness are also known as co-moments, and are used as inputs for portfolio optimization in addition to covariance, which is used to measure the extent to which the returns on two assets move together.