Portfolio managers report their risk-adjusted efficiency utilizing Sharpe, Treynor, info, and Sortino ratios, amongst different common metrics.
In fact, with varied measures to decide on amongst, may fund managers be tempted to cherry-pick those who replicate most favorably on their efficiency? Maybe, however the potential for strategic choice solely turns into an actual drawback if the efficiency metrics have weak or unfavorable correlations.
If all of them have excessive constructive correlations, then there actually is not any choice sport to play. If a very good, or unhealthy, Sharpe ratio means comparable Treynor, info, and Sortino ratios, then it hardly makes a distinction which one (or two) is reported.
So, how do these main efficiency metrics correlate, and have their correlations modified over time?
To reply these questions, we pulled all energetic mutual fund supervisor returns for large-cap fairness funds going again to the Fifties. We then calculated every fund’s Sharpe, Treynor, Sortino, and data ratio on a one-year rolling foundation. With this information, we explored how the rank ordinal correlation between the metrics appears to be like over every decade and over the complete time interval.
First, over the complete time interval, Sharpe and Treynor ratios have excessive constructive correlations as do the knowledge and Sortino ratios. However each Sharpe and Treynor ratios are weakly correlated with the knowledge and Sortino ratios. So, if a fund supervisor showcases their Sortino ratio and doesn’t spotlight their Sharpe or Treynor ratio, it could sign that they’re strategically deciding on which measures to current.
Efficiency Metric Correlations: All Durations, 1950 to 2023
| Sharpe Ratio | Treynor Ratio | Data Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.95 | 0.25 | 0.24 |
| Treynor Ratio | 0.95 | 1 | 0.24 | 0.23 |
| Data Ratio | 0.25 | 0.24 | 1 | 0.99 |
| Sortino Ratio | 0.24 | 0.23 | 0.99 | 1 |
Subsequent, we examined the rank ordinal correlation of the 4 measures over every decade. The identical sample holds pretty regular from 1950 to 2020. We didn’t see any inordinate divergence within the correlations over the roughly 70 years beneath evaluation.
Efficiency Metric Correlations: Fifties
| Sharpe Ratio | Treynor Ratio | Data Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.95 | 0.11 | 0.09 |
| Treynor Ratio | 0.95 | 1 | 0.01 | -0.01 |
| Data Ratio | 0.11 | 0.01 | 1 | 0.99 |
| Sortino Ratio | 0.09 | -0.01 | 0.99 | 1 |
Efficiency Metric Correlations: Sixties
| Sharpe Ratio | Treynor Ratio | Data Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.97 | 0.35 | 0.32 |
| Treynor Ratio | 0.97 | 1 | 0.36 | 0.33 |
| Data Ratio | 0.35 | 0.36 | 1 | 0.98 |
| Sortino Ratio | 0.32 | 0.33 | 0.98 | 1 |
Efficiency Metric Correlations: Nineteen Seventies
| Sharpe Ratio | Treynor Ratio | Data Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.98 | 0.38 | 0.33 |
| Treynor Ratio | 0.98 | 1 | 0.37 | 0.32 |
| Data Ratio | 0.38 | 0.37 | 1 | 0.98 |
| Sortino Ratio | 0.33 | 0.32 | 0.98 | 1 |
Efficiency Metric Correlations: Nineteen Eighties
| Sharpe Ratio | Treynor Ratio | Data Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.97 | 0.25 | 0.23 |
| Treynor Ratio | 0.97 | 1 | 0.23 | 0.20 |
| Data Ratio | 0.25 | 0.23 | 1 | 0.98 |
| Sortino Ratio | 0.23 | 0.20 | 0.98 | 1 |
Efficiency Metric Correlations: Nineties
| Sharpe Ratio | Treynor Ratio | Data Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.92 | 0.26 | 0.26 |
| Treynor Ratio | 0.92 | 1 | 0.22 | 0.21 |
| Data Ratio | 0.26 | 0.22 | 1 | 0.99 |
| Sortino Ratio | 0.26 | 0.21 | 0.99 | 1 |
Efficiency Metric Correlations: 2000s
| Sharpe Ratio | Treynor Ratio | Data Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.97 | 0.27 | 0.25 |
| Treynor Ratio | 0.97 | 1 | 0.26 | 0.24 |
| Data Ratio | 0.27 | 0.26 | 1 | 0.99 |
| Sortino Ratio | 0.25 | 0.24 | 0.99 | 1 |
Efficiency Metric Correlations: 2010s
| Sharpe Ratio | Treynor Ratio | Data Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.93 | 0.41 | 0.4 |
| Treynor Ratio | 0.93 | 1 | 0.44 | 0.43 |
| Data Ratio | 0.41 | 0.44 | 1 | 0.99 |
| Sortino Ratio | 0.40 | 0.43 | 0.99 | 1 |
Lastly, we explored the correlations throughout recessions to see in the event that they fell aside on the most crucial moments. Of the seven recessions because the Fifties, once more we discovered that the correlations stayed fairly just like what they have been throughout non-recession durations.
In all, the outcomes present that since Treynor and Sharpe ratios are extremely correlated, whether or not a fund supervisor experiences one and never the opposite just isn’t particularly materials. The identical holds with the knowledge and Sortino ratios.
However because the Treynor and Sharpe ratios are weakly correlated with the latter two metrics, managers may have the chance for strategic reporting. So, if a fund supervisor experiences their Sortino or info ratio however goes silent on their Sharpe and Treynor ratios, it could replicate a strategic play and warrant additional investigation.
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All posts are the opinion of the writer. As such, they shouldn’t be construed as funding recommendation, nor do the opinions expressed essentially replicate the views of CFA Institute or the writer’s employer.
Picture credit score: ©Getty Photos / Uwe Krejci
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