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Long-Term Mean-Variance Optimization Under Mean-Reverting Equity Returns

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  • Michael Preisel

Abstract

This paper studies the mean-variance optimal portfolio choice of an investor pre-committed to a deterministic investment policy in continuous time in a market with mean-reversion in the risk-free rate and the equity risk-premium. In the tradition of Markowitz, optimal policies are restricted to a subclass of factor exposures in which losses cannot exceed initial capital and it is shown that the optimal policy is characterized by an Euler-Lagrange equation derived by the method of Calculus of Variations. It is a main result, that the Euler-Lagrange equation can be recast into a matrix differential equation by an integral transformation of the factor exposure and that the solution to the characteristic equation can be parametrized by the eigenvalues of the associated lambda-matrix, hence, the optimization problem is equivalent to a spectral problem. Finally, explicit solutions to the optimal policy are provided by application of suitable boundary conditions and it is demonstrated that - if in fact the equity risk-premium is slowly mean-reverting - then investors committing to long investment horizons realize better risk-return trade-offs than investors with shorter investment horizons.

Suggested Citation

  • Michael Preisel, 2023. "Long-Term Mean-Variance Optimization Under Mean-Reverting Equity Returns," Papers 2309.07488, arXiv.org, revised Mar 2024.
    • Handle: RePEc:arx:papers:2309.07488
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    References listed on IDEAS

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