Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

Hanen Ben Salah (), Jan G. Gooijer, Ali Gannoun () and Mathieu Ribatet ()
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Hanen Ben Salah: BESTMOD Laboratory, ISG 41 Rue de la Liberté
Ali Gannoun: IMAG
Mathieu Ribatet: IMAG

Financial Markets and Portfolio Management, 2018, vol. 32, issue 4, No 4, 419-436

Abstract: Abstract While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.

Keywords: Downside risk; Forecasting; Multivariate kernel-based mean estimation; Multivariate kernel-based median estimation; Semivariance (search for similar items in EconPapers)
JEL-codes: C14 C30 G11 G17 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11408-018-0317-4

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