R-Squared

Last updated:

How meaningfully your portfolio tracks the benchmark — and how trustworthy its beta and alpha are.

Quick Answer

What is R-Squared?

R-squared is the fraction of a portfolio's return variance explained by the benchmark's return variance, between 0 and 1. R² = 1.0 means the portfolio moves in lock-step with the benchmark; R² = 0 means no linear relationship at all. R-squared tells you how trustworthy your beta and alpha numbers are.

R² = 1 − SS_residual / SS_total

Formula

R² = 1 − Σ(Rp,i − predictedi)2 / Σ(Rp,i − mean(Rp))2
predictedi = CAPM prediction at observation i · denominator is total variance · numerator is unexplained (residual) variance

R-squared is one minus the fraction of variance not explained by the regression. Equivalently: the square of the correlation between portfolio returns and benchmark returns.

Intuition — what is this number telling you?

R² interprets the rest of the regression. A portfolio with R² of 0.05 vs. the S&P 500 has uncorrelated returns — its beta and alpha numbers vs. that benchmark are essentially meaningless. A portfolio with R² of 0.99 is effectively a leveraged or de-leveraged S&P 500 — there is no stock-picking happening.

Foliolytic's "closet indexer" warning fires when R² > 0.95 with active fees. If you are paying 1% to own something 95% of which is just the index, you are overpaying for management.

Worked example

Step-by-step

You regress portfolio daily returns on S&P 500 daily returns. The correlation coefficient is 0.86.

R² = 0.86² = 0.74

74% of your portfolio's daily return variance is explained by S&P 500 movement. The remaining 26% is idiosyncratic (specific to your holdings).

What's a good R-Squared value?

What R² actually means by range:

Interpretation
0 – 0.3Largely uncorrelated. Beta/alpha vs. this benchmark are noisy.
0.3 – 0.7Modest relationship. Real diversification benefit.
0.7 – 0.9Strong tracking. Most diversified equity portfolios sit here.
0.9 – 0.95Very high tracking. Borderline closet indexer.
> 0.95Closet indexer. Why pay active fees?

Related metrics

Beta  ·  Alpha (Jensen's)  ·  Tracking Error  ·  Diversification Score

Frequently asked questions about R-Squared

What is a good R-squared?

There is no universally "good" R². For a fund claiming to be an index tracker, you want R² near 1.0. For a fund claiming to be uncorrelated alternative, you want R² near 0. Match the value to the stated strategy.

How is R-squared different from correlation?

R² is the square of correlation. Correlation is between −1 and +1; R² is between 0 and 1. R² loses the sign but is the standard reporting metric.

Why does my R-squared matter for alpha?

If R² is low, the regression line that produced your alpha was a poor fit — alpha is then a residual noise term, not skill. Look for at least R² > 0.5 before trusting alpha numbers.

Does Foliolytic show R-squared?

Yes — alongside beta and alpha for every benchmark comparison (S&P 500, VT, factor portfolios).

See R-Squared on your real portfolio

Upload your brokerage CSV — Foliolytic computes R-Squared plus 70+ other metrics using real historical prices, real Treasury yields, and real CPI data. Free, no signup, your data stays in your browser.

Analyze your portfolio free →