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Parameter uncertainty in estimation of portfolio efficiency: Evidence from an interval diversification-consistent DEA approach
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International audience. Traditional data envelopment analysis (DEA) and diversification-consistent DEA, as the data-driven relative performance evaluation approaches, are widely used in the estimation of portfolio efficiency. To some extent, diversification-consistent DEA is more favored by researchers compared with traditional DEA for it deals fully with portfolio diversification. However, the existing studies assume that decision-makers can accurately estimate the statistical characteristics of portfolio returns and ignore the impact of parameter uncertainty on the portfolio efficiency and its ranking. In this paper, we construct three diversification-consistent DEA models under the mean-variance framework. We treat the expectation and covariance of portfolio return as interval values to characterize the parameter uncertainly in the proposed DEA models. And the bi-level programming models and the corresponding equivalent models are also provided to obtain the lower and upper bounds of portfolio efficiency. We select 30 American industry portfolios and perform some empirical analyses under different datasets to find out which model has better robustness in dealing with the impact of parameter uncertainty on the portfolio efficiency and its ranking. Finally, we provide some robustness tests to further verify the consistency of our findings.
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