R-squared in portfolio analysis: how much of your returns the benchmark explains
R-squared—also written R²—measures the proportion of a portfolio's return variance that can be explained by movements in a benchmark. An R-squared of 1.0 means every variation in the portfolio's return is perfectly explained by the benchmark; an R-squared of 0 means the portfolio's returns move entirely independently of it. R-squared is most useful as a contextual metric: it tells you how much to trust other benchmark-relative metrics such as beta and alpha.
What R-squared measures
R-squared is the square of the correlation coefficient between the portfolio's return series and the benchmark's return series. A correlation of 0.9 produces an R-squared of 0.81, meaning 81% of the portfolio's return variation is associated with benchmark movements. The remaining 19% reflects movements independent of the benchmark—driven by the portfolio's specific holdings, active tilts, or other factors.
The higher the R-squared, the more closely the portfolio tracks the benchmark in its return behaviour. An equity portfolio tracking the MSCI World closely will have an R-squared approaching 1.0. A multi-asset portfolio or one with large active tilts away from the benchmark will have a lower R-squared, meaning a larger fraction of its performance cannot be attributed to benchmark exposure.
The formula
Formula
R² = Corr(Rp, Rb)²
Where:
Rp = portfolio return series
Rb = benchmark return series
Corr(Rp, Rb) = Pearson correlation coefficient between the two series
How to interpret R-squared
R-squared is most valuable as a qualifier for other metrics rather than as a standalone measure. When R-squared is high—above 0.85—the portfolio's beta and alpha calculations are likely to be meaningful, because a large proportion of the portfolio's variance is indeed driven by the benchmark. When R-squared is low—below 0.50—the beta and alpha figures should be interpreted cautiously, because the benchmark does not explain most of the portfolio's behaviour.
A portfolio with a low R-squared relative to a given benchmark is not poorly managed—it may simply be benchmarked against the wrong index. A commodity-heavy portfolio measured against an equity benchmark will have a low R-squared because the two asset classes do not move together. Choosing an appropriate benchmark is a prerequisite for using R-squared meaningfully. See how to choose a benchmark for guidance on that decision.
Note that R-squared is not the same as tracking error. Tracking error measures the standard deviation of the difference between portfolio and benchmark returns—it is a measure of deviation. R-squared measures the proportion of variance explained by the benchmark—it is a measure of co-movement. A portfolio can have a high R-squared and high tracking error simultaneously, or a low R-squared and low tracking error.
Rolling R-squared
The scalar R-squared summarises the relationship over the full period. The rolling R-squared applies the same calculation over a sliding window, showing how the strength of the benchmark relationship evolves over time. A portfolio that has gradually shifted its composition—adding asset classes, changing factor tilts, or reducing benchmark exposure—will show a declining rolling R-squared. Rolling analysis reveals regime-dependent variation in the metric over time.
Limitations
R-squared measures the linear relationship between portfolio and benchmark returns only. Non-linear dependencies—such as those produced by options strategies, volatility targeting, or leverage that scales with market conditions—will not be captured. A portfolio that hedges its benchmark exposure dynamically may show a low R-squared even though it is designed to track the benchmark in most conditions.
R-squared is also sensitive to the measurement period and return frequency. Using weekly returns produces different results than using monthly returns for the same portfolio. The benchmark selection is the single most important input: an R-squared of 0.9 relative to one benchmark can become 0.3 relative to a different one, and neither figure is wrong—they describe different relationships.
R-squared in pfolio
R-squared is not currently displayed as a standalone metric in pfolio Insights. Correlation between the portfolio and the selected benchmark is shown in Insights; R-squared equals the square of that correlation value (R² = ρ²).
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