Portfolio management with higher moments: the cardinality impact

In this paper we extend the study of the cardinality impact from the standard mean-variance scenario to higher moments, considering a utility maximization framework. For each scenario, we propose a bi-objective model that allows the investor to directly analyse the efficient trade-off between expected utility and cardinality. We study not only the effect of cardinality in each scenario but also the real gain of considering higher moments in portfolio management. This analysis is performed assuming that the investor has constant relative risk aversion (CRRA) preferences. For the data collected on the PSI20 index, the empirical results showed that there are no performance gains, in-sample, from the efficient mean-variance expected utility/cardinality portfolios to the efficient expected utility/cardinality portfolios when higher moments are considered. However, the out-of-sample performance of the efficient mean-variance-skewness expected utility/cardinality portfolios and of the efficient mean-variance-skewness-kurtosis expected utility/cardinality portfolios suggest the existence of real gains, especially when transaction costs are considered.

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