Portfolio managers report their risk-adjusted performance using Sharpe, Treynor, Information and Sortino metrics, amongst others.
Of course, when selecting different metrics, might fund managers be tempted to pick out people who have essentially the most positive impact on their performance? Perhaps, however the potential for strategic selection only becomes an actual problem when performance metrics have weak or negative correlations.
If all of them have high positive correlations, there really is not any selection game. If or bad Sharpe ratio means similar Treynor, Information, and Sortino ratios, then it makes little difference which (or two) is reported.
So how are these key performance metrics related and have their correlations modified over time?
To answer these questions, we used all lively mutual fund manager returns for large-cap stock funds dating back to the Fifties. We then calculated each fund’s Sharpe, Treynor, Sortino and Information Ratio on a rolling one-year basis. Using this data, we examined what the rank order correlation between metrics looks like across each decade and across the complete time period.
First, the Sharpe and Treynor ratios show high positive correlations over the complete period, as do the Information and Sortino ratios. But each the Sharpe and Treynor ratios correlate only weakly with the Information and Sortino ratios. So if a fund manager presents his Sortino ratio and doesn’t highlight his Sharpe or Treynor ratio, this may occasionally be a signal that he’s strategically selecting the metrics to present.
Performance metrics correlations: All time 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 order correlation of the 4 measures across each decade. The same pattern stays fairly stable from 1950 to 2020. We didn’t find any excessive divergence within the correlations within the roughly 70 years examined.
Performance metrics correlations: Fifties
| 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 metrics correlations: Nineteen Sixties
| 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 metrics correlations: Nineteen Seventies
| 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 metrics correlations: Eighties
| 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 metrics correlations: Nineties
| 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 metrics 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 metrics 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 examined relationships during recessions to see whether or not they fell apart at essentially the most critical moments. Even within the seven recessions because the Fifties, we found that the correlations remained fairly just like those in non-recession periods.
Overall, the outcomes show that it is just not particularly vital whether a fund manager reports one fairly than the opposite because Treynor and Sharpe ratios are highly correlated. The same applies to the knowledge and Sortino ratios.
However, since the Treynor and Sharpe metrics are only weakly correlated with the latter two metrics, managers could have the chance for strategic reporting. So if a fund manager reports his Sortino or Information ratio but doesn’t comment on his Sharpe and Treynor ratios, this might reflect a strategic play and warrant further investigation.
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Photo credit: ©Getty Images / Uwe Krejci
