TY - JOUR
T1 - Inverse portfolio problem with mean-deviation model
AU - Grechuk, Bogdan
AU - Zabarankin, Michael
PY - 2014/4/16
Y1 - 2014/4/16
N2 - 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.
AB - 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.
KW - Conditional value-at-risk
KW - Deviation measure
KW - Portfolio optimization
KW - Risk preferences
UR - http://www.scopus.com/inward/record.url?scp=84890857961&partnerID=8YFLogxK
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U2 - 10.1016/j.ejor.2013.04.056
DO - 10.1016/j.ejor.2013.04.056
M3 - Article
AN - SCOPUS:84890857961
SN - 0377-2217
VL - 234
SP - 481
EP - 490
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 2
ER -