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An approximate solution for the power utility optimization under predictable returns

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  • Dmytro Ivasiuk

Abstract

This work derives an approximate analytical single period solution of the portfolio choice problem for the power utility function. It is possible to do so if we consider that the asset returns follow a multivariate normal distribution. It is shown in the literature that the log-normal distribution seems to be a good proxy of the normal distribution in case if the standard deviation of the last one is way smaller than its mean. So we can use this property because this happens to be true for gross portfolio returns. In addition, we present a different solution method that relies on the machine learning algorithm called Gradient Descent. It is a powerful tool to solve a wide range of problems, and it was possible to implement this approach to portfolio selection. Besides, the paper provides a simulation study, where we compare the derived results with the well-known solution, which uses a Taylor series expansion of the utility function.

Suggested Citation

  • Dmytro Ivasiuk, 2019. "An approximate solution for the power utility optimization under predictable returns," Papers 1911.06552, arXiv.org, revised Oct 2021.
    • Handle: RePEc:arx:papers:1911.06552
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    References listed on IDEAS

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    1. Michael W. Brandt & Pedro Santa‐Clara, 2006. "Dynamic Portfolio Selection by Augmenting the Asset Space," Journal of Finance, American Finance Association, vol. 61(5), pages 2187-2217, October.
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    3. 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.
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    5. Bodnar, Taras & Parolya, Nestor & Schmid, Wolfgang, 2015. "On the exact solution of the multi-period portfolio choice problem for an exponential utility under return predictability," European Journal of Operational Research, Elsevier, vol. 246(2), pages 528-542.
    6. Campbell, John Y. & Viceira, Luis M., 2002. "Strategic Asset Allocation: Portfolio Choice for Long-Term Investors," OUP Catalogue, Oxford University Press, number 9780198296942.
    7. Mark Broadie & Weiwei Shen, 2017. "Numerical solutions to dynamic portfolio problems with upper bounds," Computational Management Science, Springer, vol. 14(2), pages 215-227, April.
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    9. Nicholas Barberis, 2000. "Investing for the Long Run when Returns Are Predictable," Journal of Finance, American Finance Association, vol. 55(1), pages 225-264, February.
    10. Taras Bodnar & Dmytro Ivasiuk & Nestor Parolya & Wofgang Schmid, 2018. "Mean-Variance Efficiency of Optimal Power and Logarithmic Utility Portfolios," Papers 1806.08005, arXiv.org, revised May 2019.
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