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An Analytical Comparison of Variance and Semivariance Capital Market Theories

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  • Nantell, Timothy J.
  • Price, Barbara

Abstract

Most research in modern portfolio theory and capital market theory is based on investor selection of portfolios that are efficient in the sense that they are not dominated by other portfolios in terms of their risk-expected return characteristics. The most widely used measure of portfolio risk is the variance about the mean of the exante distribution of portfolio returns. The theoretical framework from which this measure of risk is usually derived was initially suggested by Markowitz [12], and is by now well known. Although variance has the attention of most researchers, another measure, semivariance, had some early support from Markowitz himself, and from Quirk and Saposnik [17], Mao [10], and others. Semivariance as a measure of risk can be derived from the same theoretical framework as is variance; it requires only a slightly different utility function. The semivariance of returns of portfolio p below some point h is defined aswhere fp (R) represents the probability density function of returns for portfolio p. Semivariance portfolio theory is enjoying something of a revival in the works of Porter [15, 16], Hogan and Warren [6] and Klemkosky [8], and semivariance capital market models have been developed by Hogan and Warren [7] and Greene [5].

Suggested Citation

  • Nantell, Timothy J. & Price, Barbara, 1979. "An Analytical Comparison of Variance and Semivariance Capital Market Theories," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 14(2), pages 221-242, June.
  • Handle: RePEc:cup:jfinqa:v:14:y:1979:i:02:p:221-242_00
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    Cited by:

    1. Galagedera, Don U.A., 2007. "An alternative perspective on the relationship between downside beta and CAPM beta," Emerging Markets Review, Elsevier, vol. 8(1), pages 4-19, March.
    2. Jose Fernandes & Augusto Hasman & Juan Ignacio Pena, 2007. "Risk premium: insights over the threshold," Applied Financial Economics, Taylor & Francis Journals, vol. 18(1), pages 41-59.
    3. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    4. Zengjing Chen & Larry G. Epstein & Guodong Zhang, 2022. "Approximate optimality and the risk/reward tradeoff in a class of bandit problems," Papers 2210.08077, arXiv.org, revised Dec 2023.
    5. Courtney Droms Hatch & Kurt Carlson & William G. Droms, 2018. "Effects of market returns and market volatility on investor risk tolerance," Journal of Financial Services Marketing, Palgrave Macmillan, vol. 23(2), pages 77-90, June.
    6. Asgar Ali & K. N. Badhani, 2023. "Downside risk matters once the lottery effect is controlled: explaining risk–return relationship in the Indian equity market," Journal of Asset Management, Palgrave Macmillan, vol. 24(1), pages 27-43, February.
    7. Ravi Kashyap, 2024. "The Blockchain Risk Parity Line: Moving From The Efficient Frontier To The Final Frontier Of Investments," Papers 2407.09536, arXiv.org.
    8. 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.
    9. Sana Hussain, 2020. "Good volatility vs. bad volatility: The asymmetric impact of financial depth on macroeconomic volatility," Manchester School, University of Manchester, vol. 88(3), pages 405-438, June.
    10. Ping Cheng, 2004. "Asymmetric Risk Measures and Real Estate Returns," The Journal of Real Estate Finance and Economics, Springer, vol. 30(1), pages 89-102, October.
    11. Galagedera, Don U.A. & Brooks, Robert D., 2007. "Is co-skewness a better measure of risk in the downside than downside beta?: Evidence in emerging market data," Journal of Multinational Financial Management, Elsevier, vol. 17(3), pages 214-230, July.

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