Coskewness and Cokurtosis

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Coskewness and Cokurtosis

Postby edupristine » Thu Jul 24, 2014 10:08 am

Cross moments are multi-variate higher moments important in asset allocation process and portfolio management.

The second cross moment i.e. covariance of a random variable with itself is variance of the variable. The third cross moment i.e. coskewness of a random variable with itself is skewness of the variable itself. Similarly, the fourth cross moment of a random variable with itself is kurtosis of the variable.

To summarize, examples of cross moments could be:
• co-variance (second cross moment)
• co-skewness (third cross moment)
• co-kurtosis (fourth cross moment)

Interpretation of negative co-skewness:

If the returns distributions of two assets in a portfolio tend to exhibit negative coskewness, it means both the assets will have extreme negative returns at about the same point of time which is not at all desirable.

Hence positive coskewness (i.e both the assets showing extreme positive returns at about same time) is preferable to negative co skewness.

I hope you have now understood how to interpret cross moments like co skewness. The same interpretation goes for other cross moments like covariance, co kurtosis etc.

Now lets understand the meaning of "non trivial":

As the no of variables increase, the number of non trivial coskewness, covariance and cokurtosis statistics increase manifold and for calculation of these statistics, the data is generally not available. This is one of the drawbacks of higher order cross moments.

Here non trivial means observable values. These are significant to such an extent that they cant be ignored.

Here the word ”non trivial” does not have a financial connotation but rather used to specify that the cross moment values are too significant to be ignored.

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