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Statistical properties of the sample semi-variance

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  • Shaun Bond
  • Stephen Satchell

Abstract

In finance theory the standard deviation of asset returns is almost universally recognized as a measure of risk. This universality continues to exist even in the presence of known limitations of using the standard deviation and also an extensive and growing literature on alternative risk measures. One possible reason for this persistence is that the sample properties of alternative risk measures are not well understood. This paper attempts to compare the sample distribution of the semi-variance with that of the variance. In particular, the belief that, while there are convincing theoretical reasons to use the semi-variance the volatility of the sample measure is so high as to make the measure impractical in applied work, is investigated. In addition arguments based on stochastic dominance are also used to compare the distribution of the two statistics. Conditions are developed to identify situations in which the semi-variance may be preferred to the variance. An empirical example using equity data from emerging markets demonstrates this approach.

Suggested Citation

  • Shaun Bond & Stephen Satchell, 2002. "Statistical properties of the sample semi-variance," Applied Mathematical Finance, Taylor & Francis Journals, vol. 9(4), pages 219-239.
    • Handle: RePEc:taf:apmtfi:v:9:y:2002:i:4:p:219-239
    DOI: 10.1080/1350486022000015850
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    References listed on IDEAS

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    1. Stephen Satchell, 1996. "Lower Partial Capital Asset Pricing Models: A Re-examination," Archive Working Papers 020, Birkbeck, Department of Economics, Mathematics & Statistics.
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    Cited by:

    1. Alexandrino Tavares Barreto, 2018. "The Contribution of African Capital Markets in the Diversification of European Investment Portfolios," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 10(3), pages 1-29, March.
    2. Sager, Michael & Taylor, Mark P., 2014. "Generating currency trading rules from the term structure of forward foreign exchange premia," Journal of International Money and Finance, Elsevier, vol. 44(C), pages 230-250.
    3. Cumova, Denisa & Nawrocki, David, 2014. "Portfolio optimization in an upside potential and downside risk framework," Journal of Economics and Business, Elsevier, vol. 71(C), pages 68-89.
    4. Enrique Ballestero, 2005. "Mean-Semivariance Efficient Frontier: A Downside Risk Model for Portfolio Selection," Applied Mathematical Finance, Taylor & Francis Journals, vol. 12(1), pages 1-15.
    5. Ravi Kashyap, 2024. "The Blockchain Risk Parity Line: Moving From The Efficient Frontier To The Final Frontier Of Investments," Papers 2407.09536, arXiv.org.
    6. Beach, Steven L., 2011. "Semivariance decomposition of country-level returns," International Review of Economics & Finance, Elsevier, vol. 20(4), pages 607-623, October.
    7. Stephen E. Satchell & Shaun A. Bond, 2004. "Asymmetry, Loss Aversion and Forecasting," Econometric Society 2004 Australasian Meetings 160, Econometric Society.

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