A Comparison of Risk Measures When Used in a Simple Portfolio Selection Heuristic

Abstract

Assuming that a portfolio manager selects a portfolio by maximizing the returnto‐risk ratios of the securities that constitute the portfolio, the performance of this “heuristic” is sensitive to the choice of risk measure in the return‐to‐risk ratio. Using sixty month holding periods and second degree stochastic dominance to evaluate the performance of the portfolio selection heuristic; the mean absolute deviation, beta and target semivariance were found to be superior to the variance and the mean semivariance. In addition, the heuristic with the superior risk measures provided performance comparable to the optimal single index model.

Mean-Semivariance Optimization: A Heuristic Approach

“…Ang (1975) proposes to linearize the semivariance so that the optimization problem can be solved using linear (instead of quadratic) programming. Nawrocki (1983) proposes a further simplification of the heuristic proposed by Elton, Gruber, and Padberg (1976). The latter focus on the mean-variance problem and impose the simplifying assumption that all pairwise correlations are the same; the former further imposes a value of zero for all of these correlations and extends the analysis to other measures of risk, including the semivariance.…”

“…Nawrocki and Staples (1989) expand the scope of Nawrocki (1983) by considering the lower partial moment (LPM) as a risk measure.…”

A symmetric LPM model for heuristic mean–semivariance analysis

“…Ang (1975) suggests a linear programming approach while Nawrocki (1983) proposes using the semivariance in a further simplification of the Elton, Gruber, and Padberg (1976) constant correlation heuristic. Markowitz et al (1993) transform the mean-semivariance problem into a quadratic problem by adding fictitious securities and then solving the problem with the critical line algorithm developed by Markowitz (1959).…”

“…Research for a closed form solution has centered on heuristic algorithms that (1) ignore the intercorrelations between securities (Ang, 1975;Markowitz, Peter, Ganlin, & Yuji, 1993;Nawrocki, 1983) or (2) convert the asymmetric cosemivariance matrix to a symmetric cosemivariance matrix that is positive semi-definite (Estrada, 2008;Huang, Srivastava, & Raatz, 2001;Nawrocki, 1991). 2 The research reported here takes the latter approach by providing a proof that the asymmetric cosemivariance matrix may be converted to a symmetric cosemivariance matrix without ignoring the intercorrelations.…”

A Customized LPM Risk Measure for Portfolio Analysis

“…He suggests that a generalized n-degree lower partial moment model (nz0) is superior to the target semi-variance (n=2) and the expected opportunity loss, (n=l), because the n-degree LPM can be closely tailored to the individual's risk preference.Laughhunn, Payne and Crum[2] developed an interactive computer program in IBM PC BASIC for measuring Fishburn's a (LPM's n) for individual investors. Once the degree of the LPM is established, the LPM is integrated into return-torisk ratio portfolio allocation heuristic developed by Nawrocki [3].This simple heuristic is flexible enough to work with any risk measure. We are interested in the performance of the heuristic using the lower partial moment for various degrees of n. Portfolios are generated for portfolio sizes of 5, 10, 15, 20, 25 and 30 securities.…”