Long-Term Mean-Variance Optimization Under Mean-Reverting Equity Returns
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910354578079744 |
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| author | Preisel, Michael |
| author_facet | Preisel, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07488 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Long-Term Mean-Variance Optimization Under Mean-Reverting Equity Returns Preisel, Michael Mathematical Finance 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. |
| title | Long-Term Mean-Variance Optimization Under Mean-Reverting Equity Returns |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2309.07488 |