Portfolio management with higher moments: the cardinality impact

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.