Inverse portfolio problem with mean-deviation model |
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Authors: | Bogdan Grechuk Michael Zabarankin |
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Institution: | 1. Department of Mathematics, University of Leicester, Leicester LE1 7RH, UK;2. Department of Mathematical Sciences, Stevens Institute of Technology, Hoboken, NJ, USA |
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Abstract: | A Markowitz-type portfolio selection problem is to minimize a deviation measure of portfolio rate of return subject to constraints on portfolio budget and on desired expected return. In this context, the inverse portfolio problem is finding a deviation measure by observing the optimal mean-deviation portfolio that an investor holds. Necessary and sufficient conditions for the existence of such a deviation measure are established. It is shown that if the deviation measure exists, it can be chosen in the form of a mixed CVaR-deviation, and in the case of n risky assets available for investment (to form a portfolio), it is determined by a combination of (n + 1) CVaR-deviations. In the later case, an algorithm for constructing the deviation measure is presented, and if the number of CVaR-deviations is constrained, an approximate mixed CVaR-deviation is offered as well. The solution of the inverse portfolio problem may not be unique, and the investor can opt for the most conservative one, which has a simple closed-form representation. |
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Keywords: | Risk preferences Portfolio optimization Deviation measure Conditional value-at-risk |
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