Portfolio management with higher moments: the cardinality impact

Abstract

This paper extends the study of the cardinality impact on portfolio performance, from the traditional mean-variance framework to more general frameworks that include higher moments. For each framework, we propose a biobjective model that allows the investor to explicitly analyze the efficient trade-off between expected utility and cardinality. We applied the proposed methodology to data from the Portuguese Stock Index (PSI20 index). The empirical results show that, in-sample, the certainty equivalent and the Sharpe ratio increase with the cardinality level in all frameworks. The results also suggest that there are no performance gains, in-sample, in terms of certainty equivalent, when higher moments are considered. Out of sample, the turnover increases up to a certain cardinality level, then decreases. For certain cardinality levels, there are gains in terms of out-of-sample certainty equivalent and Sharpe ratio, when skewness and kurtosis are considered. Finally, we check the robustness of these results in a large dataset from the EUROSTOXX50 index.