## R-squared

R-squared represents the “goodness of fit” of a manager to its benchmark. R-squared is the percentage of variation in a manager’s returns explained by the benchmark’s returns.

## How Is it Useful?

R-squared is used primarily as a cross-check on the appropriateness of the benchmark. Many other statistics such as alpha, beta, information ratio, and up/down capture use a passive benchmark as a reference point. If the R-squared of a manager to the benchmark is too low, the usefulness of all these other benchmark-relative metrics diminishes.

## What Is a Good Number?

Generally speaking, in “efficient” asset classes like large cap stocks and investment grade bonds, analysts look for higher R-squared numbers in the +85% range. For “inefficient” asset classes like small cap, foreign, or emerging market stocks, investors would be more liberal and accept lower R-squared numbers in the +70% range. The assumption with inefficient asset classes is that managers should be more active and not track the benchmark too closely. Suffice it to say, if the R-squared is 50% or less, metrics like alpha, beta, or up/down capture will be of limited use.

## What Are the Limitations?

R-squared is of limited value as a stand-alone metric. It doesn’t measure outperformance or underperformance. It just describes how closely the manager tracked the benchmark. R-squared is best used as a preliminary cross-check to the benchmark’s appropriateness.

## What Do the Graphs Show Me?

In the two graphs below, the black line is identical. It is a rolling, three-year return for the benchmark. Superimposed over the benchmark is a high- R-squared manager in blue (upper) and a low- R-squared manager in red (lower). As the benchmark black line zigs and zags, the blue manager is moving almost in lockstep with it. The majority of the movement in the manager can thus be explained or attributed to the movements in the benchmark. In contrast, the red manager doesn’t seem to track the benchmark very well at all. The movement of the red manager seems to be independent of the benchmark. This results in a low R-squared. Therefore, it wouldn’t be very useful to rely on other benchmark-relative metrics (e.g. alpha) when looking at the red manager.

## What Are Typical Values?

Below are typical R-squared ranges for six peer groups over 10 years. Within traditional asset classes, most managers can attribute the majority of the variation in performance to movements in the broad market. The good news for those managers is that the other performance-based metrics like alpha, information ratio, up/down capture, etc. will be relevant and useful. For the managers in the bottom quartile of R-squared, it might be more useful to look for a more appropriate benchmark or to examine non-benchmark relative metrics like the Sharpe ratio and pain ratio for performance analysis.

Math Corner:

R-squared literally takes the correlation of a manager versus a benchmark and squares it. Squaring correlation removes the directional aspect of correlation. It is impossible to have a negative R-squared. This is intentional, as the sole point of R-squared is to determine what percentage, from 0% to 100%, of the variation of a manager’s return is explained by the benchmark.

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