Diversification-consistent data envelopment analysis based on directional-distance measures |
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Institution: | 1. Buckingham Business School, University of Buckingham, Buckingham MK18 1EG, United Kingdom;2. Center of Operations Research (CIO), University Miguel Hernandez of Elche, Elche (Alicante), Spain;3. Foisie Business School, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA, USA;1. School of Business Administration, Hunan University, Changsha 410082, China;2. Business School, Hunan Normal University, Changsha 410081, China;3. Kent Business School, University of Kent, Canterbury CT2 7PE, UK |
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Abstract: | We propose new diversification-consistent DEA models suitable for assessing efficiency of investment opportunities available on financial markets. The formulations based on directional distance measures enable to use several risk measures as inputs and return measures as outputs, which can take both positive and negative values. We show that various models with different strength can be obtained and strongly, semi-strongly or weakly Pareto–Koopmans efficient investment opportunities can be identified. Moreover, the optimal solutions correspond to efficient investment opportunities and can be used by investors to revise the inefficient ones. If we consider discretely distributed returns, we can prove that under proper choice of the inputs (CVaRs) and outputs (expected return), the strongest model is able to identify efficient investment opportunities with respect to the second-order stochastic dominance. Moreover, the model can be formulated as a linear programming problem. In the numerical study, the proposed DEA models are applied to 48 representative industry portfolios from US stock markets. |
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Keywords: | Data envelopment analysis Financial efficiency Diversification Directional-distance measure Second-order stochastic dominance |
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