R-Squared
Home › Glossary › R-Squared
R-squared (R²) measures what percentage of an investment’s price movement is explained by movements in its benchmark. It ranges from 0 to 100. An R-squared of 100 means the investment moves in perfect lockstep with the benchmark. An R-squared of 0 means the benchmark explains none of the investment’s behavior.
R-squared doesn’t tell you whether an investment is good or bad. It tells you whether beta — and any risk metric built on it — is actually a reliable measure for that investment. It’s the quality check on your risk model.
The R-Squared Formula
In regression terms: you regress the investment’s returns against the benchmark’s returns. R-squared is the proportion of the total variance in the investment’s returns that the regression (the benchmark) explains. The residuals — what’s left over — represent the portion driven by factors other than the benchmark.
Equivalently:
If a stock’s correlation with the S&P 500 is 0.85, its R-squared is 0.85² = 0.72, meaning 72% of the stock’s return variance is explained by the market. The remaining 28% is driven by company-specific factors — earnings surprises, management changes, sector-specific trends, and so on.
How to Interpret R-Squared
| R-Squared Range | Interpretation | Implication for Beta |
|---|---|---|
| 85–100 | Investment closely tracks the benchmark | Beta is highly reliable |
| 70–85 | Strong but imperfect relationship | Beta is useful but not the whole story |
| 40–70 | Moderate benchmark influence | Beta is a rough guide only — other factors dominate |
| Below 40 | Weak or no meaningful relationship | Beta is unreliable — don’t use it for risk assessment |
The critical threshold most practitioners use is around 70. Above 70, beta is a meaningful risk measure and CAPM-based analysis is reasonably valid. Below 70, the investment is driven primarily by idiosyncratic factors, and beta-based metrics like the Treynor ratio and Jensen’s alpha lose their interpretive power.
R-Squared in Practice
Index Funds vs. Active Funds
An S&P 500 index fund will typically have an R-squared of 99–100 relative to the S&P 500 — by design, it mirrors the benchmark. An actively managed large-cap fund might show R-squared of 85–95, depending on how much the manager deviates from the index.
A sector fund or concentrated stock-picker might have R-squared of 50–75 against a broad market index. This doesn’t mean the fund is worse — it means the broad market is the wrong benchmark, or the fund’s returns are driven by factors the benchmark doesn’t capture.
Identifying Closet Indexers
R-squared is one of the most effective tools for spotting closet indexers — funds that charge active management fees but closely replicate the benchmark. If a fund has R-squared above 95 relative to its benchmark and charges active fees, you’re essentially paying 1%+ for what an index fund delivers at 0.03–0.10%. Check R-squared before paying for active management.
Choosing the Right Benchmark
Low R-squared often doesn’t mean an investment is behaving randomly — it may mean you’re using the wrong benchmark. A real estate fund compared to the S&P 500 might show R-squared of 30. Compare it to a REIT index, and R-squared might jump to 85. Always match the benchmark to the investment’s actual mandate and asset class.
R-Squared and Beta: The Critical Connection
Beta tells you the magnitude of an investment’s sensitivity to the benchmark. R-squared tells you how much that sensitivity actually matters.
Consider two stocks, both with a beta of 1.2:
| Stock | Beta | R-Squared | What It Means |
|---|---|---|---|
| Stock A | 1.2 | 88 | Reliably moves 1.2× the market — beta is trustworthy |
| Stock B | 1.2 | 25 | Beta of 1.2 is statistically meaningless — stock dances to its own tune |
Stock A’s beta is actionable. If you expect the market to rally 10%, you can reasonably expect Stock A to rally about 12%. Stock B’s beta is noise. The market might rally 10% and Stock B could drop 5%, rise 30%, or do anything in between. The beta of 1.2 is a statistical artifact, not a useful prediction.
This is why you should always check R-squared before relying on beta, the Treynor ratio, or Jensen’s alpha. These metrics are only as good as the underlying regression fit.
R-Squared Across Investment Types
| Investment Type | Typical R² vs. Broad Market |
|---|---|
| S&P 500 index fund | 99–100 |
| Large-cap actively managed fund | 85–97 |
| Large-cap individual stock | 30–70 |
| Sector ETF | 60–85 |
| Small-cap stock | 15–50 |
| Bond fund vs. equity benchmark | 0–15 |
| Gold | 0–10 |
| Market-neutral hedge fund | 0–15 |
Notice that low R-squared can be a feature, not a bug. Gold and market-neutral strategies have near-zero R-squared against equities — which makes them valuable diversifiers precisely because they don’t move with the stock market. Low R-squared in this context means uncorrelated return streams, which is exactly what reduces portfolio standard deviation.
R-Squared and Alpha Interpretation
When a fund reports positive alpha, R-squared helps you evaluate whether that alpha is meaningful:
High R-squared + positive alpha: The fund closely tracks the benchmark and still manages to outperform. This is genuine, benchmark-relative skill. The alpha is statistically meaningful because the regression fit is strong.
Low R-squared + positive alpha: The “alpha” might be misleading. The benchmark doesn’t explain much of the fund’s returns, so measuring excess return against that benchmark is questionable. The apparent alpha could simply reflect exposure to factors the benchmark doesn’t capture — not skill.
This is why the information ratio (which measures alpha per unit of tracking error) is more informative than alpha alone. But even the information ratio loses meaning when R-squared is very low — you’re measuring active return against the wrong reference point.
Limitations of R-Squared
Doesn’t indicate direction. R-squared tells you how much variance is explained, not whether the relationship is positive or negative. You need correlation or beta for that. In practice, this rarely matters for long-only equity investments (they almost always have positive correlation with the market), but it’s relevant for alternative strategies.
Can be artificially high. Any two time series that trend upward over time will show correlated returns to some degree. Using price levels instead of returns inflates R-squared. Always calculate R-squared from returns, not price levels.
Benchmark-dependent. R-squared is entirely a function of the benchmark chosen. A fund might have low R-squared against the S&P 500 but high R-squared against a more appropriate benchmark. Don’t conclude that an investment is “uncorrelated with markets” based on R-squared against a single index — test multiple benchmarks.
Time-period sensitive. R-squared can shift meaningfully depending on the measurement window. During crises, correlations tend to spike (everything falls together), which temporarily pushes R-squared higher. During calm markets, idiosyncratic factors dominate and R-squared may be lower. A single R-squared figure doesn’t capture this dynamic.
Doesn’t capture nonlinear relationships. R-squared measures linear fit. Some investments — options-based strategies, catastrophe bonds, convertibles — have nonlinear relationships with their benchmarks. R-squared will understate the true connection because it only captures the linear component.
Frequently Asked Questions
What is a good R-squared?
It depends on what you’re trying to do. If you want beta and alpha to be meaningful, you need R-squared above 70 — ideally above 85. If you’re looking for diversification, you want low R-squared (below 30) to ensure the investment provides uncorrelated returns. There’s no universally “good” number — it depends on the analytical context.
Does R-squared measure performance?
No. R-squared measures how closely an investment tracks a benchmark — not whether it performs well. An index fund with R-squared of 99 and a terrible year still has high R-squared. A hedge fund with R-squared of 5 and fantastic returns still has low R-squared. R-squared is a diagnostic tool for your risk model, not a performance measure.
How is R-squared different from correlation?
R-squared is the square of correlation. Correlation ranges from –1 to +1 and captures both strength and direction. R-squared ranges from 0 to 1 (or 0 to 100) and captures only strength — it doesn’t tell you if the relationship is positive or negative. A correlation of –0.80 and +0.80 both produce an R-squared of 64.
Can R-squared change over time?
Yes, significantly. During market crises, correlations spike and R-squared tends to increase across almost all assets. During stable periods, idiosyncratic factors reassert themselves and R-squared may decline. Rolling R-squared (calculated over a moving window) is useful for tracking how the benchmark relationship evolves over time.
Should I check R-squared before looking at beta?
Always. Beta is only meaningful when R-squared is high enough for the benchmark to be a relevant explanatory factor. A beta of 1.5 with R-squared of 15 tells you almost nothing useful. Check R-squared first, then interpret beta — and by extension, the Treynor ratio and alpha — accordingly.