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How meaningfully your portfolio tracks the benchmark — and how trustworthy its beta and alpha are.
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_totalR² = 1 − Σ(Rp,i − predictedi)2 / Σ(Rp,i − mean(Rp))2R-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.
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.
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 R² actually means by range:
| R² | Interpretation |
|---|---|
| 0 – 0.3 | Largely uncorrelated. Beta/alpha vs. this benchmark are noisy. |
| 0.3 – 0.7 | Modest relationship. Real diversification benefit. |
| 0.7 – 0.9 | Strong tracking. Most diversified equity portfolios sit here. |
| 0.9 – 0.95 | Very high tracking. Borderline closet indexer. |
| > 0.95 | Closet indexer. Why pay active fees? |
Beta · Alpha (Jensen's) · Tracking Error · Diversification Score
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.
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.
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.
Yes — alongside beta and alpha for every benchmark comparison (S&P 500, VT, factor portfolios).
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