Semivolatility of Returns as a Measure of Downside Risk

Abstract

Within statistics, semistandard deviation is a well-known measure used to analyze the dispersion of probability distributions. In finance, semistandard deviation of returns is sometimes defined consistently with its statistical definition, but it is sometimes defined differently. The ambiguity emanates from whether the number of observations in its calculation is specified as T, the total number of observations in a sample, or T*, the number of negative deviations. The authors show that the use of T is consistent with the statistical definition but generates a measure that cannot be directly compared to standard deviation. Practitioners should be aware of the implications of using either T or T* both as a stand-alone risk measure and as the denominator of the Sortino ratio. The authors derive an alternative measure of downside risk based on T* that provides several advantages over semistandard deviation. They term that measure semivolatility and demonstrate its usefulness.