Performance Evaluation of Portfolios with Margin Requirements

In financial markets, short sellers will be required to post margin to cover possible losses in case the prices of the risky assets go up. Only a few studies focus on the optimization and performance evaluation of portfolios in the presence of margin requirements. In this paper, we investigate the theoretical foundation of DEA (data envelopment analysis) approach to evaluate the performance of portfolios with margin requirements from a different perspective. Under the mean-variance framework, we construct the optimization model and portfolio possibility set on considering margin requirements. The convexity of the portfolio possibility set is proved and the concept of efficiency in classical economics is extended to the portfolio case. The DEA models are then developed to evaluate the performance of portfolios with margin requirements. Through the simulations carried out in the end, we show that, with adequate portfolios, DEA can be used as an effective tool in computing the efficiencies of portfolios with margin requirements for the performance evaluation purpose. This study can be viewed as a justification of DEA into performance evaluation of portfolios with margin requirements.