Directional distance based cross-efficiency evaluation and decomposition for parallel two-stage systems: An application to equity funds

Abstract

As an effective approach in ranking decision making units (DMUs), cross-efficiency evaluation is only extended to two basic network systems: series and parallel, which is not applicable to the common complex network system in reality. By using the directional distance function (DDF), this paper extends the cross-efficiency evaluation to a complex system called the parallel two-stage system, which consists of several independent parallel processes and each of them is a sub-system with a general two-stage series structure. The proposed method is able to decompose the cross-efficiency measure of the system into the weighted average of those of processes, stages and overall stages, respectively, and as a result, successfully achieves the layer-by-layer decomposition of cross-efficiency measures under complex nested networks. An empirical study on 40 open-ended equity funds in China from 2018 to 2020 verifies that the newly proposed method not only has a stronger performance discrimination power than self-evaluation, but also can identify the relationships among efficiencies of the system, processes and stages, and meanwhile it can reflect the effects of processes and stages on the system. More importantly, our method has a better practical value for actual fund investment selection.