Great year, bad Sharpe? A note on the joint distribution of performance and risk-adjusted return
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866914848901693440 |
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| author | Smerlak, Matteo |
| author_facet | Smerlak, Matteo |
| contents | Returns distributions are heavy-tailed across asset classes. In this note, I examine the implications of this well-known stylized fact for the joint statistics of performance (absolute return) and Sharpe ratio (risk-adjusted return). Using both synthetic and real data, I show that, all other things being equal, the investments with the best in-sample performance are never associated with the best in-sample Sharpe ratios (and vice versa). This counter-intuitive effect is unrelated to the risk-return tradeoff familiar from portfolio theory: it is, rather, a consequence of asymptotic correlations between the sample mean and sample standard deviation of heavy-tailed variables. In addition to its large sample noise, this non-monotonic association of the Sharpe ratio with performance puts into question its status as the gold standard metric of investment quality. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2302_08829 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Great year, bad Sharpe? A note on the joint distribution of performance and risk-adjusted return Smerlak, Matteo Statistical Finance Physics and Society General Finance Portfolio Management Returns distributions are heavy-tailed across asset classes. In this note, I examine the implications of this well-known stylized fact for the joint statistics of performance (absolute return) and Sharpe ratio (risk-adjusted return). Using both synthetic and real data, I show that, all other things being equal, the investments with the best in-sample performance are never associated with the best in-sample Sharpe ratios (and vice versa). This counter-intuitive effect is unrelated to the risk-return tradeoff familiar from portfolio theory: it is, rather, a consequence of asymptotic correlations between the sample mean and sample standard deviation of heavy-tailed variables. In addition to its large sample noise, this non-monotonic association of the Sharpe ratio with performance puts into question its status as the gold standard metric of investment quality. |
| title | Great year, bad Sharpe? A note on the joint distribution of performance and risk-adjusted return |
| topic | Statistical Finance Physics and Society General Finance Portfolio Management |
| url | https://arxiv.org/abs/2302.08829 |