Classical mean-variance model revisited: pseudo efficiency

Xiangyu Cui, Li Duan and Jiaan Yan
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Xiangyu Cui: Shanghai University of Finance and Economics, Shanghai, China
Li Duan: The Chinese University of Hong Kong, Shatin, Hong Kong
Jiaan Yan: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Journal of the Operational Research Society, 2015, vol. 66, issue 10, 1646-1655

Abstract: Investigating the inverse problem of the classical Markowitz mean-variance formulation: Given a mean-variance pair, find initial investment levels and their corresponding portfolio policies such that the given mean-variance pair can be realized, we reveal that any mean-variance pair inside the reachable region can be achieved by multiple portfolio policies associated with different initial investment levels. Therefore, in the mean-variance world for a market of all risky assets, the common belief of monotonicity: ‘The larger you invest, the larger expected future wealth you can expect for a given risk (variance) level’ does not hold, which stimulates us to extend the classical two-objective mean-variance framework to an expanded three-objective framework: to maximize the mean and minimize the variance of the final wealth as well as to minimize the initial investment level. As a result, we eliminate from the policy candidate list the set of pseudo efficient policies that are efficient in the original mean-variance space, but inefficient in this newly introduced three-dimensional objective space.

Date: 2015
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