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A moment matching approach to log-normal portfolio optimization

Author

Listed:
  • Elçin Çetinkaya

    (Amazon.com)

  • Aurélie Thiele

    (Lehigh University)

Abstract

We consider the problem where a manager aims to minimize the probability of his portfolio return falling below a threshold while keeping the expected return no worse than a target, under the assumption that stock returns are Log-Normally distributed. This assumption, common in the finance literature for daily and weekly returns, creates computational difficulties because the distribution of the portfolio return is difficult to estimate precisely. We approximate it with a single Log-Normal random variable using the Fenton–Wilkinson method and investigate an iterative, data-driven approximation to the problem. We propose a two-stage solution approach, where the first stage requires solving a classic mean-variance optimization model and the second step involves solving an unconstrained nonlinear problem with a smooth objective function. We suggest an iterative calibration method to improve the accuracy of the method and test its performance against a Generalized Pareto Distribution approximation. We also extend our results to the design of basket options.

Suggested Citation

  • Elçin Çetinkaya & Aurélie Thiele, 2016. "A moment matching approach to log-normal portfolio optimization," Computational Management Science, Springer, vol. 13(4), pages 501-520, October.
    • Handle: RePEc:spr:comgts:v:13:y:2016:i:4:d:10.1007_s10287-016-0255-4
    DOI: 10.1007/s10287-016-0255-4
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    References listed on IDEAS

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    Cited by:

    1. Dmytro Ivasiuk, 2019. "An approximate solution for the power utility optimization under predictable returns," Papers 1911.06552, arXiv.org, revised Oct 2021.

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