Higher-moment portfolios with practical constraints based on Polynomial goal programming

Abstract

This thesis contributes to the field of portfolio selection by constructing and analyzing the impact of incorporating higher-moments by Polynomial goal programming. We construct the mean-variance-skewness and the mean-variance-skewness-kurtosis portfolio over a 20-year horizon using 29 stocks from the S&P Global 1200-index. We examine the performance of higher-moment portfolios in terms of return, risk and allocation, compared to two benchmark portfolios; the traditional Markowitz portfolio and the global minimum variance portfolio. Our findings suggest that an investor obtains a higher return and risk-adjusted return by incorporating skewness into the mean-variance allocation framework. The mean-varianceskewness portfolio can further be improved by a diversification constraint as a result of the portfolio’s occasional concentrated allocations, while limiting turnover turns out to be relatively detrimental for its performance. The results are less clear when both skewness and kurtosis are incorporated into the asset allocation framework, as the mean-variance-skewness-kurtosis portfolio is outperformed by the benchmark portfolios unless a turnover or a strong diversification constraint is imposed. In general we find that higher-moment portfolios obtain more optimal out-of-sample higher-moments at the cost of higher out-of-sample variance. The differences between the out-of-sample moments are augmented by rebalancing the portfolios or by imposing the strong diversification constraint.