Estimation of cardinality constrained portfolio efficiency via segmented DEA

The cardinality constrained portfolio selection problem arises due to the empirical findings that investors tend to hold a limited number of assets. Yet the lack of fast computational methods for frontier of cardinality constrained portfolio investments makes the performance evaluation of this problem a long-standing challenge. Classic Data Envelopment Analysis (DEA) models have been justified valid in evaluating and ranking portfolio performance. Unfortunately, when it comes to the cardinality constrained portfolio selection problem, the DEA models fail to approximate the portfolio efficiency (PE) since the real frontier is discontinuous and not concave. To solve this problem, we propose a segmented DEA approach based on data segment points. A searching algorithm is introduced to approach the real segment points and proved to be valid. In each segment, the frontier is continuous and concave; hence, classic DEA models can be applied to evaluate the PE. The simulation results further indicate that the segmented DEA approach proposed in this paper is effective and practical in evaluating the cardinality constrained portfolio performance.