What is a good R-squared for a mutual fund or ETF?

It depends on what the fund is meant to do. An index fund against its own index has an R-squared close to 1, and anything well below that means it is not tracking. For an actively managed fund, a high R-squared against a broad index means it behaves much like the index, so its fees buy little that is different; a low R-squared means the index is the wrong yardstick, and its alpha and beta against that index say little.

Is a positive alpha proof of skill?

No. An alpha is an estimate with an error band. Unless its t-statistic is well above 2 over a long window, the same alpha could come from luck, and even then it may be exposure to a factor the benchmark leaves out, or part of the risk-free rate when no rate was subtracted.

What is the difference between alpha and excess return?

Excess return is the fund's return minus the benchmark's, with no allowance for risk: a fund with a beta of 1.3 beats its benchmark in most rising markets without any skill. Alpha subtracts beta times the benchmark's return instead, so it compares the fund with a mix of the benchmark and cash that carries the same market exposure.

How many years of data are needed to trust an alpha?

Solve the rule of thumb t ≈ (alpha / residual volatility) × √years for t = 2. A fund whose alpha is a quarter of its residual volatility needs about 64 years; one whose alpha equals half its residual volatility needs about 16. Most track records are far shorter, which is why most published alphas are not statistically distinguishable from zero.

Why is the alpha of a bond fund against the S&P 500 so high?

Because the S&P 500 explains almost none of a bond fund's return, the regression puts nearly all of the bond fund's average return into the intercept. With no risk-free rate subtracted, that includes the interest any short-term Treasury bill would have paid. It is not a sign of skill; a bond index is the right benchmark for a bond fund.

Alpha and R-squared: what they mean, and when alpha is just noise

By Jeffrey Lin · Published 2026-11-06 · Updated 2026-11-06 · Data through Sep 2026

On this page

Key takeaways

Alpha is the return a fund earned beyond what its market exposure (beta) explains: what is left over after paying for riding the market.
An alpha is an estimate from noisy data. The usual test, its t-statistic, asks whether it is large compared with its uncertainty; a reading below about 2 cannot be told apart from zero at the usual 95% confidence.
A low R-squared means the benchmark explains little of the fund's movement, so the alpha is uncertain and mostly collects whatever the benchmark leaves out.
A short track record has the same effect: the evidence builds only slowly with the number of years, so a few years of a large alpha can still be indistinguishable from luck.
MarketHeist does not subtract the interest earned on cash, so for a fund that moves less than the market its alpha also includes part of the cash rate; it is not the textbook (Jensen's) alpha and overstates skill for low-beta holdings.

Definition

Alpha is the part of an investment's average return that its exposure to a benchmark does not explain: the intercept of a regression of its returns on the benchmark's returns. R-squared is the share of the investment's return variance (uncertainty) that the same regression explains, which says how much weight its alpha and beta can bear.

Also known as: Jensen's alpha, alpha (investing), R-squared (investing), coefficient of determination, alpha t-statistic, is alpha statistically significant, excess return over beta.

How it works

Fit a straight line through a fund's monthly returns plotted against a benchmark's, as for beta. The slope is beta. The intercept, where the line crosses zero on the benchmark's axis, is alpha: the fund's average return in a month when the benchmark returned nothing. Annualized, it is read as the return the fund added, or lost, beyond what its market exposure would have produced.

Michael Jensen defined it in 1968 to judge mutual fund managers, inside the capital asset pricing model: subtract the risk-free rate from both the fund's and the market's returns, regress one excess return on the other, and read the intercept. Under the model a fund with no skill has an alpha of zero whatever its beta, because the beta term already pays it for the market risk it took. Jensen found that the average fund's alpha after expenses was negative.

R-squared measures how well the line fits: the share of the fund's return variance that the benchmark explains, from 0 to 1. With a single benchmark it is the correlation squared. An index fund against its own index has an R-squared near 1; a sector fund, gold or a bond fund against the stock market has a much lower one. When R-squared is low the line is a poor description of the fund, and both beta and alpha describe a small part of what happened.

Every estimate from a sample has an error band, and alpha's is wide. Its standard error is roughly the volatility of the regression's residuals divided by the square root of the number of months, so noisy residuals (low R-squared) and few months both widen it. The t-statistic divides the alpha by that standard error. It is close to the information ratio, alpha over residual volatility, times the square root of the number of years, which is why a fund with a respectable-looking alpha and a lot of residual noise needs decades of data before the alpha means much.

Judging alpha from a short, noisy record is like judging a coin from ten tosses: seven heads is not strong evidence that the coin is biased, and the same seven-in-ten over a thousand tosses would be.

Alpha is also only as good as the benchmark. Against a stock index alone, a fund that holds bonds, small companies or a sector with its own drivers shows an alpha that is really exposure to something the index leaves out. Fama and French (1993) and Carhart (1997) added size, value and momentum factors to the regression for that reason, and much of what looked like alpha against the market alone turned out to be factor exposure.

Formula

Jensen's alpha (Jensen 1968)

R_{p, t} - R_{f, t} = α + β (R_{m, t} - R_{f, t}) + ε_{t}

R_p,t: the portfolio's return in period t
R_m,t: the market benchmark's return in period t
R_f,t: the risk-free return in period t, such as a Treasury bill
α: Jensen's alpha: the average excess return not explained by the market exposure
β: beta: the slope on the market's excess return
εₜ: residual: what the line does not explain in period t

MarketHeist's intercept, with a risk-free rate of 0

r_{p, t} = a + β r_{m, t} + ε_{t}, a \approx α + (1 - β) {\bar{R}}_{f}

a: the intercept of the regression on plain monthly total returns; ×12 is the alpha MarketHeist reports
R̄_f: the average risk-free return over the window
(1 − β) R̄_f: the part of the risk-free rate that lands in the intercept when it is not subtracted

The relation is exact when the risk-free rate is constant and close otherwise. For a fund with a beta below 1 the intercept exceeds Jensen's alpha by about (1 − β) times the bill rate; for a beta above 1 it falls short of it.

The t-statistic of alpha and its rule of thumb

t_{α} = \frac{\hat{a}}{SE (\hat{a})}, SE (\hat{a}) = s_{ε} \sqrt{\frac{1}{n} + \frac{{\bar{r}}_{m}^{2}}{\sum {(r_{m, t} - {\bar{r}}_{m})}^{2}}}, t_{α} \approx \frac{α_{ann}}{ω_{ann}} \sqrt{T}

â: the estimated monthly intercept
SE(â): its classical standard error
s_ε: standard deviation of the monthly residuals, with n − 2 degrees of freedom
n: number of months
r̄ₘ: the benchmark's average monthly return
α_ann, ω_ann: annualized alpha and annualized residual volatility; their ratio is the information ratio of the residual return (the appraisal ratio)
T: length of the window in years

A |t| of about 2 corresponds to 95% confidence that the true alpha is not zero, if the residuals are independent and roughly normal. The approximation on the right drops the small second term under the root.

R-squared

R^{2} = 1 - \frac{\sum ε_{t}^{2}}{\sum {(r_{p, t} - {\bar{r}}_{p})}^{2}} = ρ_{p, m}^{2}

r̄_p: the portfolio's average monthly return
ρ_p,m: correlation of the portfolio's and the benchmark's returns (the last equality holds with one benchmark)

Worked example

The utilities sector fund (XLU, the S&P 500's utility companies) regressed on the S&P 500 (SPY), 333 monthly total returns from Jan 1999 to Sep 2026.

Against the S&P 500, XLU had a beta of 0.46 and an annualized alpha of 3.8%. Read at face value, that is a fund that took a fraction of the market's exposure and added 3.8% a year on top of it.

The fit was poor. The R-squared was 20.4%: the S&P 500 explained a small part of XLU's month-to-month movement. XLU was nearly as volatile as the index, 15.2% a year against 15.0%, yet most of its swings were its own, a tracking error of 13.6% around the regression line. Utilities move with interest rates and with their own industry as much as with the stock market, and a single-index intercept collects all of that.

With that much noise around the line, the alpha's t-statistic was 1.43, short of the conventional 2. The 95% confidence band around the alpha runs from below zero to more than double the estimate: 28 years of these returns cannot tell this alpha apart from luck.

Part of the intercept is not skill at all. MarketHeist subtracts no risk-free rate, so the intercept of a fund with a beta below 1 includes about (1 − β) times the Treasury-bill rate it could have earned in cash, and Jensen's alpha on excess returns would be smaller by that amount. Switch the lab to BIL, a Treasury-bill fund, to see the effect in isolation: its whole return shows up as alpha against the S&P 500.

Data through Sep 2026. Reproduce id 1eb5343a09e3236b (this guide, its lab setup and the data month).

Interactive lab

Monthly returns of the fund against the benchmark with the fitted line, and the regression table: alpha with its t-statistic, beta, R-squared and residual tracking error. Switch funds to see a high R-squared, a low one, and an alpha that is only the bill rate.

Monthly returns of XLU against SPY, with the least-squares line. Jan 1999 to Sep 2026.

Measure	XLU on SPY
Beta (slope of the fitted line)	0.46
Alpha (intercept times 12)	3.8%
R-squared	20.4%
Correlation	0.45
t-statistic of beta	9.20
t-statistic of alpha	1.43
Residual standard error (annualized)	13.6%
Volatility of XLU (annualized)	15.2%
Volatility of SPY (annualized)	15.0%
Up capture	54%
Down capture	35%
Months (benchmark up, down)	333 (210, 122)

Ordinary least squares of the monthly returns on the benchmark's with an intercept, risk-free rate 0; classical standard errors. Residual standard error: the root of the residual sum of squares over n - 2, times the square root of 12. Up (down) capture: the average return in the benchmark's up (down) months over the benchmark's average in them. Jan 1999 to Sep 2026.

How MarketHeist computes it

Every choice an implementation has to make, as the code makes it today. The page is checked against the code each time it is built.

Choice	How it is computed	In the code
Data	Monthly total returns (dividends reinvested). Funds younger than the period shown are extended backward with older funds, spliced on returns, not prices.
Window	The worked example and the lab use the common window of the subject and the benchmark, Jan 1999 to Sep 2026 (333 months), ending at the data month of this page; every month is one point of the regression.
Portfolio streams	A fund is its proxy-extended monthly return stream. A built-in portfolio is read as the MarketHeist MCP reads it: its composed stream with its own rebalancing rule and overlay. A custom mix is rebalanced yearly.
Regression	Ordinary least squares of the subject's monthly returns on the benchmark's, with an intercept and a risk-free rate of 0. Beta is the slope; alpha is the intercept times 12; R-squared is the share of the ups and downs of the subject's returns that the line explains; the t-statistics use the classical standard errors; the residual standard error is the root of the residual sum of squares over n - 2, times the square root of 12. Up (down) capture is the subject's average return in the benchmark's up (down) months over the benchmark's average in those months; months with a benchmark return of exactly 0 are in neither.
Regression	Ordinary least squares of the fund's monthly total returns on the benchmark's, with an intercept, over the common window of the two. Alpha is the intercept times 12 (an arithmetic annualization, not compounded).	`ols`packages/shared/engine/factors.ts
Risk-free rate	0. The regression uses plain total returns, so the intercept is not Jensen's alpha: for a beta below 1 it includes roughly (1 − β) times the average Treasury-bill rate, for a beta above 1 it is reduced by roughly (β − 1) times it.
t-statistic	The intercept divided by its classical least-squares standard error, with n − 2 degrees of freedom. No correction for autocorrelated or unevenly spread residuals (no Newey-West adjustment), so with residuals that persist from month to month the true uncertainty is larger than the t-statistic implies.	`ols`packages/shared/engine/factors.ts
R-squared	1 minus the residual sum of squares over the total sum of squares of the fund's returns; not adjusted for the number of regressors (with one benchmark the adjustment is negligible over long windows).
Multi-factor version	The portfolio app's factor exposure panel and the MCP's factor decomposition run the same least-squares routine on several ETF factor spreads at once and report the alpha, its t-statistic and R-squared of that larger model.	`factorDecompose`packages/shared/engine/factors.ts
Engine functions	The functions the portfolio app and the MarketHeist MCP tools run, called here on the same monthly returns.	`ols`packages/shared/engine/factors.ts`pearson`packages/portfolio/engine/correlation.ts

Alpha and R-squared compared with its neighbours

Ways to measure what a fund added beyond its benchmark
Measure	What it is	Accounts for market exposure	Says how reliable it is
Excess return	Fund return minus benchmark return	No: a high-beta fund wins in rising markets	No
Jensen's alpha	Intercept of excess returns on the market's excess returns	Yes, through beta	Only with its t-statistic
Intercept at a risk-free rate of 0 (MarketHeist)	Intercept of plain returns on the benchmark's	Yes, through beta	Only with its t-statistic; includes part of the bill rate
Multi-factor alpha	Intercept after size, value, momentum or other factors	Yes, and for factor tilts	Only with its t-statistic
Information ratio	Average active return over tracking error	No, unless active return is beta-adjusted	Times √years it approximates the t-statistic
R-squared	Share of the fund's movement the benchmark explains	Not a return measure	Tells whether the regression is worth reading

Limitations

Alpha against one index is alpha against that index's omissions. A fund that tilts to small companies, value stocks, bonds or a single industry shows an alpha that a regression with those factors would partly or entirely explain.
The t-statistic assumes residuals that are independent from month to month with a constant spread. Monthly residuals that persist or cluster make it too large, so even a t-statistic above 2 is weaker evidence than it looks.
Results depend on the window. The same fund can show a large alpha over a few years and a small one over decades, and a window chosen because it shows a large alpha is a selected result, not a measured one.
When many funds or strategies are tested, some show a t-statistic above 2 by chance. Picking the top one and quoting its alpha repeats the error that the deflated Sharpe ratio and the plateau test exist to correct.
Alpha here is before taxes and, for portfolios, before trading costs. Fund returns already include their expense ratios.

Frequently asked questions

What is a good R-squared for a mutual fund or ETF?: It depends on what the fund is meant to do. An index fund against its own index has an R-squared close to 1, and anything well below that means it is not tracking. For an actively managed fund, a high R-squared against a broad index means it behaves much like the index, so its fees buy little that is different; a low R-squared means the index is the wrong yardstick, and its alpha and beta against that index say little.
Is a positive alpha proof of skill?: No. An alpha is an estimate with an error band. Unless its t-statistic is well above 2 over a long window, the same alpha could come from luck, and even then it may be exposure to a factor the benchmark leaves out, or part of the risk-free rate when no rate was subtracted.
What is the difference between alpha and excess return?: Excess return is the fund's return minus the benchmark's, with no allowance for risk: a fund with a beta of 1.3 beats its benchmark in most rising markets without any skill. Alpha subtracts beta times the benchmark's return instead, so it compares the fund with a mix of the benchmark and cash that carries the same market exposure.
How many years of data are needed to trust an alpha?: Solve the rule of thumb t ≈ (alpha / residual volatility) × √years for t = 2. A fund whose alpha is a quarter of its residual volatility needs about 64 years; one whose alpha equals half its residual volatility needs about 16. Most track records are far shorter, which is why most published alphas are not statistically distinguishable from zero.
Why is the alpha of a bond fund against the S&P 500 so high?: Because the S&P 500 explains almost none of a bond fund's return, the regression puts nearly all of the bond fund's average return into the intercept. With no risk-free rate subtracted, that includes the interest any short-term Treasury bill would have paid. It is not a sign of skill; a bond index is the right benchmark for a bond fund.

References

Jensen, M. C. (1968) The Performance of Mutual Funds in the Period 1945–1964. Journal of Finance 23(2). Defines alpha as the intercept of a regression of excess returns.
Treynor, J. L. and Black, F. (1973) How to Use Security Analysis to Improve Portfolio Selection. Journal of Business 46(1). Alpha over residual risk, the appraisal ratio.
Fama, E. F. and French, K. R. (1993) Common Risk Factors in the Returns on Stocks and Bonds. Journal of Financial Economics 33(1). Size and value factors beside the market.
Carhart, M. M. (1997) On Persistence in Mutual Fund Performance. Journal of Finance 52(1). Adds momentum; most persistence in fund alphas is explained by factors and costs.
Grinold, R. C. and Kahn, R. N. (2000) Active Portfolio Management. McGraw-Hill, second edition. The information ratio and its link to the t-statistic.

Try it on your own holdings

Open All Weather and see what market factors explain, and what they leave over →

Or ask an assistant connected to the MarketHeist MCP server (https://marketheist.io/mcp), which computes the same figures:

Using MarketHeist.io, regress the utilities fund XLU on SPY with monthly returns: what are the alpha, its t-statistic and the R-squared, and can the alpha be told apart from zero?

Ask an AI assistant

ChatGPT Claude Google AI Mode Perplexity Grok

The prompt opens in a new tab, already filled in. An assistant without the MarketHeist connector answers from its own knowledge, not from the figures on this page.

Historical simulation, not advice. Computed by the MarketHeist portfolio engine from monthly total returns, data through Sep 2026. Markdown version of this page: alpha-and-r-squared.md.