Abstract
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.
Highlights
In financial markets, the potential losses on short sales can be huge when the prices of the risky assets go up; in practice, the short sellers will be required to post margin or collateral to cover possible losses
A few studies focus on the optimization and performance evaluation of portfolios in the presence of margin requirements
Since we have proved that the portfolio possibility set in (6) is convex, we can conclude that the frontiers derived by DEA models will approximate the exact frontier for portfolios with margin requirements due to the convergence theory in Banker et al [31]
Summary
The potential losses on short sales can be huge when the prices of the risky assets go up; in practice, the short sellers will be required to post margin or collateral to cover possible losses. We can construct the following optimization model under the mean-variance framework proposed by Markowitz [10], which minimizes the variance of the portfolio subject to the constraints that the expected value is no less than the given level and the margin requirements are satisfied. We can develop the following optimization model, which maximize the expected value subject to the constraints that the variance of the portfolio is no greater than the given level and the margin requirements are satisfied. For the purpose of using DEA to evaluate the performance of portfolios with margin requirements, we must construct the theoretical foundation, that is, the convexity of the following portfolio possibility set with the strongly free disposability principle proposed by Liu et al [30], in the presence of margin requirements. It is obvious that the frontiers are not straight lines, which indicate that variable return to scale (VRS) should be adopted in the following DEA models; see detailed discussion in Banker et al [31]
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