Alpha is the part of a portfolio's return that its exposure to the market does not explain. A fund packed with market-sensitive stocks ought to beat the index in a rising year and lose more in a falling one, so comparing its return with the index alone rewards or punishes it for risk rather than skill. Alpha removes that effect. The standard version, Jensen's alpha, uses the fund's beta to estimate what its market exposure alone would have earned and reports the gap in percentage points, usually per year. A positive alpha means the portfolio did better than its beta implied, a negative one means worse, and zero means it earned what its risk predicted. The stocks hub covers the fund basics behind these numbers.
How is Jensen's alpha calculated?
Jensen's alpha is a portfolio's actual return minus the return the capital asset pricing model predicts for a portfolio with the same beta.
The part in the outer parentheses is the predicted return. It starts from what a riskless investment paid over the period, normally a short-term Treasury bill, then adds the market's return above that rate multiplied by the portfolio's beta. A fund with a beta of 1.2 is expected to collect 1.2 times the market's excess return; a fund with a beta of 0.8, eight-tenths of it. Every input has to cover the same months and use the same benchmark. Michael Jensen proposed the measure in a 1968 study of mutual funds, estimating it as the intercept of a regression of each fund's excess returns on the market's, and analysts still estimate it from a run of returns rather than a single annual figure.
Worked example: Jensen's alpha for two funds in the 12 months to September 30, 2026
The market return is the S&P 500's 15.74% total return for the 12 months to September 30, 2026, from Vanguard's S&P 500 ETF profile. The risk-free rate is 3.81%, the average 3-month Treasury yield over the same months in FRED's daily series. That puts the market's excess return at 11.93 percentage points. The two funds are hypothetical.
| Step | Fund A, beta 1.2 | Fund B, beta 0.8 |
|---|---|---|
| Beta × market excess return | 1.2 × 11.93 = 14.32 | 0.8 × 11.93 = 9.54 |
| Predicted return, adding 3.81% | 18.13% | 13.35% |
| Actual return after fees | 17.50% | 14.00% |
| Compared with the S&P 500 | 1.76 points ahead | 1.74 points behind |
| Jensen's alpha | −0.63 points | +0.65 points |
Fund A beat the index and still shows a negative alpha, because a beta of 1.2 should have delivered even more in a year when stocks rose this much. Fund B lagged the index but earned more than its milder exposure predicted.
A single year shows the arithmetic, not the manager's skill. In any one year a fund can land well away from its predicted return because a few holdings had unusual news, so an alpha means more when it holds up across many years and market conditions. Jensen tested for that and found "very little evidence that any individual fund was able to do significantly better than that which we expected from mere random chance." The risk-free rate should be the average bill yield over the same months as the returns, not the latest auction result. T-bill rates today shows current yields, and what is the risk-free rate explains which rate to pick.
How is alpha different from beta?
Beta measures how much of the market's movement a portfolio carries, while alpha measures the return left over once that exposure has been accounted for.
| Measure | What it tells you | Units | Typical value for an S&P 500 index fund |
|---|---|---|---|
| Alpha | Return above or below what the portfolio's beta predicted | Percentage points a year | Just below 0, by roughly its costs |
| Beta | Sensitivity to the benchmark's moves | A ratio, with the benchmark at 1 | 1.00 against its own index |
| Return minus the index | Raw outperformance, with no allowance for risk | Percentage points | Slightly negative |
| R-squared | Share of the portfolio's variation the benchmark explains | 0 to 1 | About 1 |
| Tracking error | How widely returns stray from the index's | Percentage points a year | Close to 0 |
| Sharpe ratio | Return above Treasury bills for each unit of total volatility | A ratio | Close to the index's own |
Both numbers come out of the same regression. Beta is the slope of the line through a fund's excess returns plotted against the market's, and alpha is the intercept: the excess return the fund would have earned in a period when the market's was zero. A wrong beta therefore produces a wrong alpha. R-squared shows how far to trust either one, because when the benchmark explains little of a fund's movement, alpha may just be picking up exposures the benchmark leaves out. For that reason researchers often measure alpha against several factors at once. The Fama-French three-factor model adds a small-minus-big company size factor and a high-minus-low book-to-market value factor to the market's return over one-month Treasury bills, so a fund that leans toward small or cheap stocks does not get credit for skill it did not show. Tracking error and the Sharpe ratio have their own entries.
Why do most active funds show negative alpha after fees?
The average actively managed dollar must earn the market's return before costs, so after fees and trading costs the average active fund falls behind.
William Sharpe set out the arithmetic in 1991. Index investors as a group hold the market and earn its return. Active investors together hold everything else, which is also the market, so before costs their average dollar earns the same. Active management costs more, so after costs the average active dollar must trail the average passive one, and every point of cost comes off alpha point for point. Weighted by assets, the Investment Company Institute's 2025 figures put the average expense ratio of actively managed stock mutual funds at 0.64% a year and that of index stock mutual funds at 0.05%, and the funds' own trading costs sit outside both numbers. Had Fund A in the example charged 0.64%, it earned about 18.14% before fees, an alpha of roughly zero; the fee alone made it negative.
| Study | Period | Result |
|---|---|---|
| Jensen, 115 US mutual funds | 1945 to 1964 | Average alpha about −1.1% a year after all expenses and −0.4% before management expenses; 76 of the 115 funds were below zero after expenses |
| SPIVA U.S. Mid-Year 2026, large-cap funds against the S&P 500 | 10 years to June 30, 2026 | 83.33% underperformed, and 95.39% on S&P's risk-adjusted measure |
| Same report, average large-cap fund | 10 years to June 30, 2026 | 14.66% a year weighted by assets and 13.07% with every fund weighted equally, against 15.51% for the S&P 500 |
| Same report, survivorship | 20 years to June 30, 2026 | 36.52% of the 690 large-cap funds that existed at the start were still operating at the end |
SPIVA counts funds that merged or closed during a period as underperformers and uses returns after fees, excluding sales loads, so closed funds cannot flatter the results. The asset-weighted shortfall of 0.85 points a year compounds: $10,000 growing at 15.51% a year for 10 years reaches about $42,286, while at 14.66% it reaches about $39,275, roughly $3,011 less. The compound interest calculator runs the same comparison at other rates.
None of this means no manager has skill. It means the average active dollar must trail the market once costs are paid, and that spotting the minority with real positive alpha before the fact is hard. Index funds explained weighs that choice, and ETFs vs mutual funds vs index funds compares the ways to own a fund.
Where do you see alpha?
Alpha shows up on fund risk-statistics pages, in index fund results, in manager commentary and, loosely, in marketing for strategies that promise extra return.
- Fund statistics pages. Research sites and some fund companies print alpha beside beta, R-squared, standard deviation and the Sharpe ratio, typically from three years of monthly returns against a named benchmark. Check that benchmark first: a small-company fund's alpha against the S&P 500 mostly measures how small companies did.
- Index fund results. Vanguard's S&P 500 ETF returned 15.29% a year at net asset value over the 10 years to September 30, 2026, against 15.33% for the index, and its beta against the index over the latest 36 months was 1.00. That works out to an alpha of about −0.04 points a year, close to its 0.03% expense ratio. The average S&P 500 index fund listed on the same profile returned 14.75%, 0.58 points a year behind the index it follows.
- Manager commentary. Shareholder letters and pitch decks sometimes call any return above the benchmark alpha. Unless the calculation adjusts for beta, read it as raw outperformance.
- Tax alpha. Advisers and robo-advisers use the phrase for extra after-tax return from harvesting losses, a different idea from Jensen's measure that tax-loss harvesting explains.
What mistakes do people make with alpha?
The most common is calling any return above an index alpha without first adjusting for how much market risk the portfolio took on.
- Skipping the beta adjustment. Fund A in the example beat the S&P 500 and still fell short of what its risk implied, while Fund B lagged and came out ahead.
- Using a benchmark that does not fit. Alpha is only as meaningful as the index behind it. A fund of foreign or small-company stocks needs a yardstick holding the same kind of stocks, as benchmark index explains.
- Mixing periods. A three-year beta, a one-year return and this week's bill yield do not belong in one formula. Use the same window for every input.
- Treating a short record as skill. Even over 10 to 20 years Jensen found few funds whose alpha stood out from what luck alone would produce, so a year or two proves even less.
- Comparing gross with net figures. Alpha before fees flatters a manager. What an investor keeps is alpha after fees, the basis SPIVA uses.
- Looking only at surviving funds. S&P notes that funds usually close or merge after continued poor performance, so an average of the survivors overstates alpha.