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Optimal portfolio allocation with uncertain covariance matrix

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  • Maxime Markov
  • Vladimir Markov

Abstract

In this paper, we explore the portfolio allocation problem involving an uncertain covariance matrix. We calculate the expected value of the Constant Absolute Risk Aversion (CARA) utility function, marginalized over a distribution of covariance matrices. We show that marginalization introduces a logarithmic dependence on risk, as opposed to the linear dependence assumed in the mean-variance approach. Additionally, it leads to a decrease in the allocation level for higher uncertainties. Our proposed method extends the mean-variance approach by considering the uncertainty associated with future covariance matrices and expected returns, which is important for practical applications.

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  • Maxime Markov & Vladimir Markov, 2023. "Optimal portfolio allocation with uncertain covariance matrix," Papers 2311.07478, arXiv.org.
    • Handle: RePEc:arx:papers:2311.07478
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    1. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
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