Mean-Semivariance Efficient Frontier: A Downside Risk Model for Portfolio Selection
An ongoing stream in financial analysis proposes mean-semivariance in place of mean-variance as an alternative approach to portfolio selection, since segments of investors are more averse to returns below the mean value than to deviations above and below the mean value. Accordingly, this paper searches for a stochastic programming model in which the portfolio semivariance is the objective function to be minimized subject to standard parametric constraints, which leads to the mean-semivariance efficient frontier. The proposed model relies on an empirically tested basis, say, portfolio diversification and the empirical validity of Sharpe's beta regression equation relating each asset return to the market. From this basis, the portfolio semivariance matrix form is strictly mathematically derived, thus an operational quadratic objective function is obtained without resorting to heuristics. Ease of computation is highlighted by a numerical example, which allows one to compare the results from the proposed mean-semivariance approach with those derived from the traditional mean-variance model.
Volume (Year): 12 (2005)
Issue (Month): 1 ()
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- Dybvig, Philip H, 1984. " Short Sales Restrictions and Kinks on the Mean Variance Frontier," Journal of Finance, American Finance Association, vol. 39(1), pages 239-44, March.
- J. G. Kallberg & W. T. Ziemba, 1983. "Comparison of Alternative Utility Functions in Portfolio Selection Problems," Management Science, INFORMS, vol. 29(11), pages 1257-1276, November.
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