Portfolio managers report their risk-adjusted performance using Sharpe, Treynor, information, and Sortino ratios, among other popular metrics.
Of course, with various measures to choose among, might fund managers be tempted to cherry-pick those that reflect most favorably on their performance? Perhaps, but the potential for strategic selection only becomes a real problem if the performance metrics have weak or negative correlations.
If they all have high positive correlations, then there really is no selection game to play. If a good, or bad, Sharpe ratio means similar Treynor, information, and Sortino ratios, then it hardly makes a difference which one (or two) is reported.
So, how do these major performance metrics correlate, and have their correlations changed over time?
To answer these questions, we pulled all active mutual fund manager returns for large-cap equity funds going back to the 1950s. We then calculated each fund’s Sharpe, Treynor, Sortino, and information ratio on a one-year rolling basis. With this data, we explored how the rank ordinal correlation between the metrics looks over each decade and over the full time period.
First, over the full time period, Sharpe and Treynor ratios have high positive correlations as do the information and Sortino ratios. But both Sharpe and Treynor ratios are weakly correlated with the information and Sortino ratios. So, if a fund manager showcases their Sortino ratio and doesn’t highlight their Sharpe or Treynor ratio, it may signal that they are strategically selecting which measures to present.
Performance Metric Correlations: All Periods, 1950 to 2023
| Sharpe Ratio | Treynor Ratio | Information Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.95 | 0.25 | 0.24 |
| Treynor Ratio | 0.95 | 1 | 0.24 | 0.23 |
| Information Ratio | 0.25 | 0.24 | 1 | 0.99 |
| Sortino Ratio | 0.24 | 0.23 | 0.99 | 1 |
Next, we examined the rank ordinal correlation of the four measures over each decade. The same pattern holds fairly steady from 1950 to 2020. We didn’t see any inordinate divergence in the correlations over the roughly 70 years under review.
Performance Metric Correlations: 1950s
| Sharpe Ratio | Treynor Ratio | Information Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.95 | 0.11 | 0.09 |
| Treynor Ratio | 0.95 | 1 | 0.01 | -0.01 |
| Information Ratio | 0.11 | 0.01 | 1 | 0.99 |
| Sortino Ratio | 0.09 | -0.01 | 0.99 | 1 |
Performance Metric Correlations: 1960s
| Sharpe Ratio | Treynor Ratio | Information Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.97 | 0.35 | 0.32 |
| Treynor Ratio | 0.97 | 1 | 0.36 | 0.33 |
| Information Ratio | 0.35 | 0.36 | 1 | 0.98 |
| Sortino Ratio | 0.32 | 0.33 | 0.98 | 1 |
Performance Metric Correlations: 1970s
| Sharpe Ratio | Treynor Ratio | Information Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.98 | 0.38 | 0.33 |
| Treynor Ratio | 0.98 | 1 | 0.37 | 0.32 |
| Information Ratio | 0.38 | 0.37 | 1 | 0.98 |
| Sortino Ratio | 0.33 | 0.32 | 0.98 | 1 |
Performance Metric Correlations: 1980s
| Sharpe Ratio | Treynor Ratio | Information Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.97 | 0.25 | 0.23 |
| Treynor Ratio | 0.97 | 1 | 0.23 | 0.20 |
| Information Ratio | 0.25 | 0.23 | 1 | 0.98 |
| Sortino Ratio | 0.23 | 0.20 | 0.98 | 1 |
Performance Metric Correlations: 1990s
| Sharpe Ratio | Treynor Ratio | Information Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.92 | 0.26 | 0.26 |
| Treynor Ratio | 0.92 | 1 | 0.22 | 0.21 |
| Information Ratio | 0.26 | 0.22 | 1 | 0.99 |
| Sortino Ratio | 0.26 | 0.21 | 0.99 | 1 |
Performance Metric Correlations: 2000s
| Sharpe Ratio | Treynor Ratio | Information Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.97 | 0.27 | 0.25 |
| Treynor Ratio | 0.97 | 1 | 0.26 | 0.24 |
| Information Ratio | 0.27 | 0.26 | 1 | 0.99 |
| Sortino Ratio | 0.25 | 0.24 | 0.99 | 1 |
Performance Metric Correlations: 2010s
| Sharpe Ratio | Treynor Ratio | Information Ratio | Sortino Ratio | |
| Sharpe Ratio | 1 | 0.93 | 0.41 | 0.4 |
| Treynor Ratio | 0.93 | 1 | 0.44 | 0.43 |
| Information Ratio | 0.41 | 0.44 | 1 | 0.99 |
| Sortino Ratio | 0.40 | 0.43 | 0.99 | 1 |
Finally, we explored the correlations during recessions to see if they fell apart at the most critical moments. Of the seven recessions since the 1950s, again we found that the correlations stayed pretty similar to what they were during non-recession periods.
In all, the results show that since Treynor and Sharpe ratios are highly correlated, whether a fund manager reports one and not the other is not especially material. The same holds with the information and Sortino ratios.
But since the Treynor and Sharpe ratios are weakly correlated with the latter two metrics, managers could have the opportunity for strategic reporting. So, if a fund manager reports their Sortino or information ratio but goes silent on their Sharpe and Treynor ratios, it may reflect a strategic play and warrant further investigation.
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All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.
Image credit: ©Getty Images / Uwe Krejci
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