A Parsimonious Approach for Higher-Order Moments in Portfolio Selection
44 Pages Posted: 13 Feb 2020 Last revised: 13 Apr 2020
Date Written: April 10, 2020
This paper investigates the economic value of higher moments in portfolio selection under estimation risk. It deploys a non-elliptical distribution for the asset returns. Such distribution decomposes the asset returns into two independent stochastic components: a Gaussian and a Bernoulli jump process. Given the adverse effects of estimation risk on portfolio selection, the distribution imposes a parsimonious structure to identify the higher-order moments. The moments can be easily calibrated using the expected maximization algorithm for maximum likelihood estimation. We find that the corresponding portfolio outperforms the conventional mean-variance portfolio as well as the equally weighted (naive) portfolio. Nonetheless, the evidence is more statistically significant when one considers a larger number of assets and a higher level of risk aversion. While this outperformance comes at the cost of a larger turnover, we show that the performance prevails after taking into consideration a transaction cost of 5% per traded dollar.
Keywords: Downside Risk, Statistical Learning, Non-Elliptical Distributions, Multivariate Analysis
JEL Classification: C13, C44, C46, G11
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