A similarity measure for the cardinality constrained frontier in the mean–variance optimization model

Abstract

This paper proposes a new measure to find the cardinality constrained frontier in the mean–variance portfolio optimization problem. In previous research, assets belonging to the cardinality constrained portfolio change according to the desired level of expected return, so that the cardinality constraint can actually be violated if the fund manager wants to satisfy clients with different return requirements. We introduce a perceptual approach in the mean–variance cardinality constrained portfolio optimization problem by considering a novel similarity measure, which compares the cardinality constrained frontier with the unconstrained mean–variance frontier. We assume that the closer the cardinality constrained frontier to the mean–variance frontier, the more appealing it is for the decision maker. This makes the assets included in the portfolio invariant to any specific level of return, through focusing not on the optimal portfolio but on the optimal frontier.