Nonparametric portfolio efficiency measurement with higher moments

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.

Automated summary

The paper explores a nonparametric approach for determining portfolio efficiency by using specific directions towards the portfolio frontier function, allowing for incorporation of higher moments of the returns distribution beyond mean and variance. The extension of the nonparametric approach involves computing optimal directions by maximizing the distance towards the portfolio frontier, with skewness playing a key role in determining the optimal direction.