R-Squared

Definition

R-squared (R²) measures how much of a fund's movement is explained by the movement of its benchmark. It is expressed on a scale from 0 to 100% (or, equivalently, 0.0 to 1.0):

• R² = 100% — every wiggle in the fund is accounted for by the benchmark. A plain S&P 500 index fund measured against the S&P 500 sits here.
• R² = 0% — the benchmark explains none of the fund's movement. The two might as well be unrelated series of numbers.
• In between — an R² of 85% means the benchmark explains about 85% of the fund's ups and downs; the remaining 15% comes from something else — sector tilts, an options overlay, manager decisions, or plain fund-specific noise.

Mathematically, R-squared is simply correlation squared:

R² = (Correlation between fund and benchmark)²

  Correlation of  1.00  →  R² = 100%
  Correlation of  0.95  →  R² ≈ 90%
  Correlation of  0.71  →  R² ≈ 50%
  Correlation of  0.39  →  R² ≈ 15%

Squaring does two things. It removes the sign — correlations of −0.9 and +0.9 both produce an R² of 81%. And it shrinks middling relationships: a correlation of 0.7, which sounds reasonably strong, squares to an R² of only about 49% — less than half of the fund's movement explained.

R-squared comes out of the same regression that produces a fund's beta and alpha. Beta is the slope of the best-fit line through the fund's returns plotted against the benchmark's; R² measures how tightly the points hug that line. A high R² means the line describes the fund well; a low R² means the points are scattered, and the line — along with the beta and alpha read off it — describes very little.

Why It Matters

R-squared is the gatekeeper statistic. Beta and alpha are quoted everywhere — fact sheets, screeners, comparison tools — but they are only as reliable as the relationship they were measured from, and R² is the number that tells you how reliable that relationship is.

Consider a fund with a published beta of 0.6 against the S&P 500. If its R² is 95%, that beta means what it appears to mean: the fund reliably moves about 60% as much as the market. But if its R² is 40%, the benchmark explains well under half of the fund's movement — the other 60% comes from somewhere else entirely. That "0.6 beta" is mostly noise, a slope drawn through a cloud of scattered points. The same goes for alpha: an alpha measured against a benchmark that barely explains the fund is not skill — it is leftover randomness dressed up as a statistic.

As a rough map of where funds land (illustrative ranges, not fixed rules):

• Broad index funds — R² of roughly 99–100% against their own index. That is the entire point of an index fund: nothing should be left unexplained.
• Diversified dividend and large-cap funds — often roughly 85–95% against the S&P 500, high enough that beta and alpha are meaningful.
• Covered-call and options-overlay funds — frequently lower, because the option overlay reshapes returns in a way a plain equity index does not capture.
• Sector, commodity, and specialty funds — often far lower against a broad benchmark, sometimes under 30%, because most of what drives them is not the broad market at all.

Here is the part investors most often get backwards: a low R² does not mean the fund is bad. It means the benchmark is the wrong yardstick. Judge a FANG+ covered-call income fund against the S&P 500 and you will get a mediocre R², a shaky beta, and an alpha that means nothing — not because the fund is broken, but because you measured it against an index it was never trying to track. Re-run the regression against a FANG+ or Nasdaq-100 benchmark and the R² jumps, and the beta and alpha become readable. A low R² is a message about your choice of ruler, not about the fund.

For income investors this matters directly, because so many income products — covered-call ETFs, sector dividend funds, BDC and REIT funds — are exactly the strategies whose S&P-500-based statistics look strange. Before concluding that an income fund has a "defensive 0.5 beta" or a "negative alpha," check the R² to see whether those numbers measured anything.

Example

The table below shows four illustrative funds, each regressed against the S&P 500. The numbers are representative of how these fund types typically behave, not live quotes:

Walking down the rows:

• The index fund is the baseline. Its R² of ~100% means the regression line fits almost perfectly, so its beta of ~1.0 and alpha of roughly zero (before fees) are precise statements, not estimates.
• The dividend ETF holds large, mature U.S. companies, so the S&P 500 explains about 90% of its movement; the remaining ~10% is its dividend-quality tilt. Its ~0.8 beta is meaningful — the fund genuinely tends to move about 80% as much as the market.
• The covered-call fund is the middle case. An R² of ~85% makes its S&P-based stats usable — but this fund writes calls on the Nasdaq-100, so the S&P 500 is not quite the right ruler. Against a Nasdaq-100 benchmark, its R² would be higher and its beta and alpha would describe the strategy more faithfully.
• The gold miners fund is the cautionary row. Its ~0.4 beta *looks* defensive, but with an R² of ~15%, the S&P 500 explains almost none of what the fund does — gold prices, mining costs, and currency moves drive it. That 0.4 beta is a slope through scattered points, and any "alpha" computed from it is meaningless. The fund is not bad; it is being measured against the wrong index.

Notice the pattern: the beta column alone cannot tell you which numbers to trust. The covered-call fund's 0.9 and the gold fund's 0.4 look equally official on a fact sheet; only the R² column separates a real measurement from statistical debris.

How to Use R-Squared

R-squared is a checking tool, not a scoring tool. Two habits cover most of its practical value:

1. Check R² before quoting beta or alpha — always. Treat it as the prerequisite. A common working threshold is an R² of roughly 70–80% or higher before leaning on a fund's beta or alpha; below that, treat those numbers as unreliable. This one habit prevents the most frequent misreading in fund analysis: calling a fund "low risk" because of a low beta that was never statistically real in the first place.
2. Pick the benchmark that fits the fund. When R² is low, the productive response is not to discard the fund but to change the yardstick. A tech-focused income fund belongs against a tech index; a REIT fund against a REIT index; a gold fund against gold. Once R² is high against the right benchmark, the beta and alpha from that regression actually describe the fund.

R² also pairs naturally with tracking error when evaluating index funds: R² asks "does the benchmark explain this fund?" while tracking error asks "how far does the fund stray from it?" For an index product you want the first near 100% and the second near zero. For actively managed funds, a *very* high R² raises the opposite question — if 98% of an active fund's movement is just the index, you may be paying active fees for what is effectively an index fund, a pattern often called closet indexing.

Common Mistakes

• Quoting beta or alpha without checking R² first. This is the big one. A beta from a low-R² regression is not a smaller-error version of the truth — it can be flatly wrong. Make R² the first number you look at, not the last.
• Reading a low R² as a verdict on the fund. Low R² means the benchmark is the wrong yardstick, nothing more. Plenty of excellent specialty and income funds show a low R² against the S&P 500 simply because they are not broad-market strategies.
• Treating a high R² as automatically good. For an index fund, yes. For an active fund charging active fees, an R² near 100% may mean you are paying for closet indexing. Whether high R² is good depends entirely on what the fund claims to do.
• Confusing R² with correlation. They are related — R² is correlation squared — but not interchangeable. A correlation of 0.7 sounds strong yet leaves more than half of the fund's movement unexplained (R² ≈ 49%).
• Thinking R² measures risk or return. It measures explanatory fit, nothing else. A fund can have an R² of 100% and be extremely volatile, or an R² of 10% and be calm. For risk, look at volatility and standard deviation; for reward per unit of risk, the Sharpe ratio.
• Comparing R² values computed against different benchmarks or windows. Like beta, R² depends on the benchmark and the time period used. An R² measured against the Nasdaq-100 over three years is not comparable to one measured against the S&P 500 over one year.

FAQ

What is a good R-squared for a fund?

It depends on the fund's job. An index fund should show an R² of roughly 99–100% against its own index — anything meaningfully lower suggests it is not tracking well. For a diversified stock fund against a broad benchmark, about 85–95% is typical and high enough to trust its beta and alpha. Below roughly 70%, benchmark-relative statistics get unreliable, and a very low reading mainly tells you to find a better-fitting benchmark.

Is a high R-squared good or bad?

It depends on what you are paying for. For an index fund, high R² is exactly right — tracking the index is the product. For an actively managed fund, an R² near 100% cuts the other way: the manager is adding little beyond the benchmark, and you may be paying active fees for closet index exposure. High R² is a description, not a grade — judge it against the fund's stated strategy.

What does a low R-squared mean for beta?

It means the beta is unreliable. Beta is the slope of a regression line, and R² measures how well that line fits. With a low R² — say 40% — most of the fund's movement has nothing to do with the benchmark, so the slope is drawn through scattered points and the resulting beta is largely noise. A fund showing a beta of 0.6 with an R² of 40% is not a "low-risk 0.6-beta fund"; it is a fund whose market sensitivity that regression failed to measure.

Is R-squared the same as correlation?

No, but they are directly linked: R-squared is the correlation coefficient squared. Correlation runs from −1 to +1 and keeps its sign, telling you the direction of the relationship. R² runs from 0 to 100% and drops the sign, telling you the share of movement explained. Squaring also deflates middling values — a 0.7 correlation becomes an R² of about 49% — which is why R² gives the more sober picture of how much a benchmark really explains.

Why do covered-call ETFs often have lower R-squared?

Two reasons. First, the options overlay reshapes returns — capping upside while collecting premium — so the fund stops moving in lockstep with its underlying index, which lowers R². Second, many covered-call income funds are built on narrower indexes (Nasdaq-100, FANG+, sector baskets), so measuring them against the S&P 500 compounds the mismatch. Their statistics become far more readable when regressed against the index they actually write calls on.

Where can I find a fund's R-squared?

Most fund research pages and fact sheets publish R² in the risk or "modern portfolio theory" statistics section, usually next to beta and alpha and typically measured over three years against a named benchmark. Always note which benchmark and time window were used — an R² without its benchmark is as ambiguous as a beta without one, and figures from different benchmarks are not comparable.