Portfolio managers report their risk-adjusted efficiency utilizing Sharpe, Treynor, info, and Sortino ratios, amongst different well-liked metrics.
After all, with numerous measures to decide on amongst, would possibly fund managers be tempted to cherry-pick people who mirror 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 adverse correlations.
If all of them have excessive constructive correlations, then there actually isn’t any choice recreation to play. If a superb, or unhealthy, Sharpe ratio means related 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 Nineteen Fifties. We then calculated every fund’s Sharpe, Treynor, Sortino, and knowledge ratio on a one-year rolling foundation. With this knowledge, we explored how the rank ordinal correlation between the metrics seems over every decade and over the total time interval.
First, over the total 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 choosing 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 underneath assessment.
Efficiency Metric Correlations: Nineteen 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: Nineteen 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: 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: 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 important moments. Of the seven recessions because the Nineteen Fifties, once more we discovered that the correlations stayed fairly much 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 stories one and never the opposite 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 might have the chance for strategic reporting. So, if a fund supervisor stories their Sortino or info ratio however goes silent on their Sharpe and Treynor ratios, it could mirror a strategic play and warrant additional investigation.
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