A data envelopment analysis approach to evaluate the performance of mutual funds

The data envelopment analysis (DEA) is an optimization based technique that has been proposed by Charnes, Cooper and Rhodes (1978) to measure the relative efficiency of public sector activities and no profit organizations, such as for example educational institutions and health services. The DEA efficiency measure is computed by solving a fractional linear programming model that can be converted into an equivalent linear programming problem which can be easily solved. Afterwards, the same methodology has been applied to many profit oriented companies, too. For a review of various applications, see for example Seiford (1996). The main purpose of this contribution is to use the DEA methodology in order to compute a mutual fund performance index that can take into account many conflicting objectives together with the costs required by the investment. In particular, the traditional performance indexes proposed in the literature do not allow to consider investment costs such as the subscription and redemption costs, while the DEA approach can naturally include many costs among the inputs of the model. It will be seen that the DEA performance index for mutual funds can be considered as a generalization of many traditional ratios such as Sharpe, Treynor, and reward to half-variance ratios. Moreover, the results of the DEA technique can be used in order to identify, for each inefficient decision making unit, a corresponding efficient set (called peer group) which represents a “virtual” composite portfolio. This composite portfolio can be seen as a personalized benchmark and characterizes the portfolio style.