Estimation of Out-of-Sample Sharpe Ratio for High Dimensional Portfolio Optimization
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918087755825152 |
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| author | Meng, Xuran Cao, Yuan Wang, Weichen |
| author_facet | Meng, Xuran Cao, Yuan Wang, Weichen |
| contents | Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the in-sample estimated covariance to evaluate the out-of-sample Sharpe, especially in the high dimensional settings. In this paper, we propose a novel method to estimate the out-of-sample Sharpe ratio using only in-sample data, based on random matrix theory. Furthermore, portfolio managers can use the estimated out-of-sample Sharpe as a criterion to decide the best tuning for constructing their portfolios. Specifically, we consider the classical framework of Markowits mean-variance portfolio optimization {under} high dimensional regime of $p/n \to c \in (0,\infty)$, where $p$ is the portfolio dimension and $n$ is the number of samples or time points. We propose to correct the sample covariance by a regularization matrix and provide a consistent estimator of its Sharpe ratio. The new estimator works well under either of the following conditions: (1) bounded covariance spectrum, (2) arbitrary number of diverging spikes when $c < 1$, and (3) fixed number of diverging spikes with weak requirement on their diverging speed when $c \ge 1$. We can also extend the results to construct global minimum variance portfolio and correct out-of-sample efficient frontier. We demonstrate the effectiveness of our approach through comprehensive simulations and real data experiments. Our results highlight the potential of this methodology as a useful tool for portfolio optimization in high dimensional settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03954 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimation of Out-of-Sample Sharpe Ratio for High Dimensional Portfolio Optimization Meng, Xuran Cao, Yuan Wang, Weichen Statistics Theory Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the in-sample estimated covariance to evaluate the out-of-sample Sharpe, especially in the high dimensional settings. In this paper, we propose a novel method to estimate the out-of-sample Sharpe ratio using only in-sample data, based on random matrix theory. Furthermore, portfolio managers can use the estimated out-of-sample Sharpe as a criterion to decide the best tuning for constructing their portfolios. Specifically, we consider the classical framework of Markowits mean-variance portfolio optimization {under} high dimensional regime of $p/n \to c \in (0,\infty)$, where $p$ is the portfolio dimension and $n$ is the number of samples or time points. We propose to correct the sample covariance by a regularization matrix and provide a consistent estimator of its Sharpe ratio. The new estimator works well under either of the following conditions: (1) bounded covariance spectrum, (2) arbitrary number of diverging spikes when $c < 1$, and (3) fixed number of diverging spikes with weak requirement on their diverging speed when $c \ge 1$. We can also extend the results to construct global minimum variance portfolio and correct out-of-sample efficient frontier. We demonstrate the effectiveness of our approach through comprehensive simulations and real data experiments. Our results highlight the potential of this methodology as a useful tool for portfolio optimization in high dimensional settings. |
| title | Estimation of Out-of-Sample Sharpe Ratio for High Dimensional Portfolio Optimization |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2406.03954 |