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Classical mean-variance model revisited: pseudo efficiency

Author

Listed:
  • 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)

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.

Suggested Citation

  • Xiangyu Cui & Li Duan & Jiaan Yan, 2015. "Classical mean-variance model revisited: pseudo efficiency," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(10), pages 1646-1655, October.
    • Handle: RePEc:pal:jorsoc:v:66:y:2015:i:10:p:1646-1655
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    Cited by:

    1. Xiao, Helu & Zhou, Zhongbao & Ren, Teng & Liu, Wenbin, 2022. "Estimation of portfolio efficiency in nonconvex settings: A free disposal hull estimator with non-increasing returns to scale," Omega, Elsevier, vol. 111(C).
    2. De Gennaro Aquino, Luca & Sornette, Didier & Strub, Moris S., 2023. "Portfolio selection with exploration of new investment assets," European Journal of Operational Research, Elsevier, vol. 310(2), pages 773-792.

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