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The Journal of Alternative Investments

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Semivolatility of Returns as a Measure of Downside Risk

Donald R. Chambers and Qin Lu
The Journal of Alternative Investments Winter 2017, 19 (3) 68-74; DOI: https://doi.org/10.3905/jai.2017.19.3.068
Donald R. Chambers
is a professor of finance in the Department of Economics at Lafayette College in Easton, PA.
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  • For correspondence: chambers@lafayette.edu
Qin Lu
is an associate professor of mathematics in the Department of Mathematics at Lafayette College in Easton, PA.
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  • For correspondence: luq@lafayette.edu
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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.

TOPICS: Statistical methods, VAR and use of alternative risk measures of trading risk, performance measurement

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The Journal of Alternative Investments: 19 (3)
The Journal of Alternative Investments
Vol. 19, Issue 3
Winter 2017
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Semivolatility of Returns as a Measure of Downside Risk
Donald R. Chambers, Qin Lu
The Journal of Alternative Investments Dec 2016, 19 (3) 68-74; DOI: 10.3905/jai.2017.19.3.068

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Semivolatility of Returns as a Measure of Downside Risk
Donald R. Chambers, Qin Lu
The Journal of Alternative Investments Dec 2016, 19 (3) 68-74; DOI: 10.3905/jai.2017.19.3.068
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  • Article
    • Abstract
    • DERIVATION OF SEMIVOLATILITY
    • ANALYTICAL ANALYSIS
    • DOWNSIDE RISK AND THE SORTINO RATIO
    • STATISTICAL TESTING
    • EMPIRICAL ANALYSIS
    • SUMMARY AND CONCLUSION
    • REFERENCE
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