Portfolio managers document their risk-adjusted efficiency the use of Sharpe, Treynor, data, and Sortino ratios, amongst alternative frequent metrics.
In fact, with numerous measures to make a choice amongst, may capitaltreasury managers be tempted to cherry-pick those who mirror maximum favorably on their efficiency? Most likely, however the opportunity of strategic variety most effective turns into an actual sickness if the efficiency metrics have vulnerable or adverse correlations.
If all of them have prime sure correlations, later there actually isn’t any variety sport to play games. If a just right, or wicked, Sharpe ratio approach matching Treynor, data, and Sortino ratios, later it rarely makes a extra which one (or two) is reported.
So, how do those primary efficiency metrics correlate, and feature their correlations modified over moment?
To respond to those questions, we pulled all energetic mutual capitaltreasury supervisor returns for large-cap fairness finances going again to the Nineteen Fifties. We later calculated every capitaltreasury’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 seems over every decade and over the overall moment duration.
First, over the overall moment duration, Sharpe and Treynor ratios have prime sure correlations as do the guidelines and Sortino ratios. However each Sharpe and Treynor ratios are weakly correlated with the guidelines and Sortino ratios. So, if a capitaltreasury supervisor showcases their Sortino ratio and doesn’t spotlight their Sharpe or Treynor ratio, it will sign that they’re strategically settling on which measures to offer.
Efficiency Metric Correlations: All Classes, 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 |
Then, we tested the rank ordinal correlation of the 4 measures over every decade. The similar development holds somewhat stable from 1950 to 2020. We didn’t see any inordinate diversion within the correlations over the kind of 70 years underneath evaluate.
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: Nineteen 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 |
In the end, we explored the correlations right through recessions to peer 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 lovely matching to what they have been right through non-recession classes.
In all, the consequences display that since Treynor and Sharpe ratios are extremely correlated, whether or not a capitaltreasury supervisor reviews one and no longer the alternative isn’t particularly subject material. The similar holds with the guidelines and Sortino ratios.
However because the Treynor and Sharpe ratios are weakly correlated with the closing two metrics, managers may find a way for strategic reporting. So, if a capitaltreasury supervisor reviews their Sortino or data ratio however is going peaceful on their Sharpe and Treynor ratios, it will mirror a strategic play games and warrant additional investigation.
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