Skewness
Understanding Tail Risk: Skewness & Kurtosis
Over the last decade or more there has been an increased awareness of “tail risk”- those extreme events in the market that have an outsized impact upon an investment. By definition, tail events are supposed to be infrequent, but these shocks are happening much more frequently and are more extreme than a lot of investors anticipated. The LTCM crisis, and Asian meltdown, the dot-com bust, the credit crisis, and most recently the debt ceiling showdown have whipsawed investors.
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Skewness and Kurtosis by Marc Odo, CFA, CAIA, CFP
Recent market events like the dot-com bust the credit crunch have increased the awareness of “tail events”, i.e. rare, but extreme and traumatic market environments. Skewness and kurtosis are the traditional ways one would measure the impact of extreme market conditions upon a distribution of returns. Although well-established in statistical theory, skewness and kurtosis are often ignored or misunderstood in performance analysis. This paper seeks to give the reader useful definitions and a working knowledge of skewness and kurtosis.
Skewness
Skewness characterizes the degree of asymmetry of a distribution around its mean. Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values. Negative skewness indicates a distribution with an asymmetric tail extending toward more negative values.
Skewness (r1, ..., rn) = 
where r1, ..., rn is a return series, i.e., a sequence of returns for n time periods.