Abstract
The paper considers a nonparametric approach to determine portfolio efficiency using specific directions toward the portfolio frontier function. This approach allows for a straightforward incorporation of higher moments of the returns distribution beyond mean and variance. The nonparametric approach is extended by the computation of optimal directions endogenously by maximizing the distance toward the portfolio frontier as a novel methodological feature. An empirical application to Fama–French portfolios demonstrates the applicability of the nonparametric approach. The results show that the optimal directions to the frontier depend on the portfolio considered as well as on the period for which the moments are estimated. Skewness in particular plays a role in determining the optimal direction, whereas kurtosis seems to be less crucial.
Highlights
Portfolio selection in the legacy of Markowitz (1952, 1959) is traditionally concerned with finding a compromise between a high return and low risk
Their quadratic optimization programs are specified either to maximize mean return for the actual variance of an asset or to minimize the variance for a given return. This mean–variance (MV) analysis has been extended to a simultaneous enhancement of mean return and reduction in variance by Briec et al (2004). They use the device of the Luenberger (1992, 1995) shortage function, used as directional distance function (DDF) by Chambers et al (1996) for the formulation of the respective optimization problems
The cornerstone of the nonparametric approach to portfolio efficiency measurement is the so-called shortage function introduced by Luenberger (1992, 1995) in a production context
Summary
Portfolio selection in the legacy of Markowitz (1952, 1959) is traditionally concerned with finding a compromise between a high return and low risk This setting can be criticized, and in particular, it neglects the influence of higher moments of the returns distribution beyond mean and variance on the utility of an investor.. The Briec–Kerstens approach allows for a straightforward extension to incorporate higher moments (skewness, kurtosis) in addition to mean and variance into the nonparametric approach. This is developed by Briec et al (2004) for the mean–variance analysis and extended by Briec et al (2004) to a mean–variance– skewness analysis. The results are summarized, and conclusions are drawn in the final Sect. 6
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