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Alpha is the return you earned that can't be explained by market exposure. Upload your portfolio and find out whether your selection and timing actually beat a passive index with the same beta — or whether your gains were just the market carrying you.
What is Jensen's alpha?
Alpha is the excess return your portfolio earns above what its beta would predict. If your beta is 1.2 and the market returned 10%, CAPM predicts you'd return 12% — alpha is whatever you got above that. Positive alpha means real skill (or luck); zero alpha means you're matching the market for the risk you took.
α = your return − (Rf + β × (Rₘ − Rf)) · positive = real edgeWant the deeper math? Learn the math behind Jensen's Alpha →
What Is Jensen's Alpha?
Alpha is the return your portfolio earned beyond what CAPM predicted based on your beta. It isolates the portion of performance attributable to your skill — security selection, timing, sizing, rebalancing — from the portion attributable to simply being exposed to the market.
Michael Jensen's 1968 paper on mutual-fund performance introduced alpha as the way to separate manager skill from market luck. The finding, then and now: after fees, most active managers post negative alpha. Passive index investing works because generating positive alpha is genuinely hard.
α = Rportfolio − [Rrisk-free + β × (Rbenchmark − Rrisk-free)]
Actual return minus CAPM-predicted return given your beta
The bracketed term is what CAPM says your portfolio "should" have earned given its beta exposure. Alpha is your deviation from that prediction — positive means you beat the model, negative means the model beat you.
A Concrete Example
Suppose you ran a portfolio for the last 12 months with the following characteristics:
- Portfolio return: +18%
- Portfolio beta vs S&P 500: 1.3
- S&P 500 return: +11%
- Risk-free rate: 4.5%
CAPM predicted return: 4.5% + 1.3 × (11% − 4.5%) = 4.5% + 8.45% = 12.95%.
Your actual return was 18%. Alpha = 18% − 12.95% = +5.05%.
That's genuinely strong. You outperformed by 5 percentage points after adjusting for the fact that your 1.3 beta meant you should have been somewhat ahead of the benchmark anyway. Had your beta been 0.8 instead of 1.3 while still returning 18%, your alpha would be even higher (around +8.3%) — you earned amplified returns with less-than-market exposure, which is the holy grail.
Statistical Significance Matters
A single year of positive alpha proves nothing. Returns are noisy and luck compounds. Foliolytic reports alpha's t-statistic alongside the value itself, so you know whether the signal is real.
| T-Statistic | Interpretation |
|---|---|
| < 1.0 | Effectively noise. Alpha could easily be zero. |
| 1.0 – 1.96 | Suggestive but not statistically significant at 95%. |
| 1.96 – 2.58 | Statistically significant at 95% confidence — alpha is likely real. |
| > 2.58 | Significant at 99% — strong evidence of genuine skill (or persistent bias, depending on context). |
Rule of thumb: you need at least 24–36 months of data and a t-stat above 2.0 before positive alpha can be distinguished from luck. Most retail investors who think they have alpha actually don't — they've just been on the right side of a trending market.
Real Jensen's Alpha vs the S&P 500 Right Now
Alpha is easiest to grasp with real assets. Below is the annualized Jensen's alpha of several well-known holdings measured against the S&P 500 (SPY), computed by Foliolytic from its own daily price database over the trailing 3-year and 5-year windows ending July 23, 2026, using the 13-week Treasury bill as the risk-free rate.
| Asset (vs SPY) | 3Y α (ann.) | 5Y α (ann.) | 5Y β | 5Y t-stat |
|---|---|---|---|---|
| BRK-B (Berkshire) | +3.1% | +4.6% | 0.58 | 0.72 |
| AAPL (Apple) | +1.3% | +5.9% | 1.22 | 0.68 |
| QQQ (Nasdaq-100) | +1.8% | +1.3% | 1.26 | 0.39 |
| VTI (Total US Market) | −0.3% | −1.0% | 1.01 | −1.10 |
| MSFT (Microsoft) | −11.5% | −3.9% | 1.15 | −0.45 |
| GLD (Gold) | +19.4% | +13.0% | 0.15 | 1.57 |
| TLT (20Y+ Treasuries) | −12.0% | −14.8% | 0.07 | −2.09 |
Read this table with the beta column in mind. Berkshire is the textbook alpha story: a beta of just 0.58 — barely more than half the market's swings — paired with positive alpha, which is genuine value added rather than leverage. Gold shows the largest "alpha" (+19.4% annualized over 3 years), but its beta is essentially zero, and that exposes a limitation of single-factor CAPM: it attributes all non-market return to alpha, so an uncorrelated asset like gold or long Treasuries shows a large alpha that is really a separate return stream, not skill. TLT is the mirror image — near-zero beta and a deeply negative alpha because long bonds were crushed in the 2021–2026 rate cycle.
Notice how few of these clear the significance bar from the section above: only TLT has a 5-year t-statistic beyond ±2.0. Even Berkshire's and Apple's positive alpha, over five full years, is not statistically distinguishable from luck at the 95% level — a humbling reminder of how much data it takes to prove skill rather than measure it.
Computed by Foliolytic by regressing each asset's daily excess returns against SPY's over windows ending July 23, 2026 (roughly 750 trading days for 3Y, 1,250 for 5Y), using its own price database and the 13-week T-bill as the risk-free rate. Same regression the calculator runs on your portfolio — see methodology. Figures refresh when this page is next updated.
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Open the AnalyzerFrequently Asked Questions
What is Jensen's alpha?
Jensen's alpha measures the portion of a portfolio's return that is NOT explained by its beta exposure to the benchmark. It's the difference between your actual return and the return CAPM predicted based on your beta. Positive alpha means your security selection and timing added value beyond passive index exposure. Negative alpha means a passive index fund with your beta would have beaten you.
How is alpha calculated?
Alpha = Rportfolio − [Rrisk-free + β × (Rbenchmark − Rrisk-free)]. The bracketed term is the CAPM-expected return given your beta. If you earned 15% annualized with beta 1.2, and the benchmark did 10% with risk-free at 4%, CAPM predicted 4% + 1.2 × (10% − 4%) = 11.2%. Your alpha is 15% − 11.2% = +3.8% — meaningful outperformance.
What is a good alpha?
Positive alpha is good, but context matters. Over long periods (5+ years), sustained positive alpha is genuinely rare. Most actively managed equity funds post negative alpha after fees — that's why indexing works. An annualized alpha of +1% to +3% after a full market cycle is strong for a retail investor. +5% or higher sustained is hedge-fund territory. Be skeptical of short-term alpha; anything less than 24 months of data has high statistical noise.
Is alpha the same as outperformance?
No. Raw outperformance (portfolio return − benchmark return) isn't risk-adjusted. If you beat the S&P 500 by 5% but did it with beta 1.5, you took 50% more risk. Alpha strips out the beta contribution so you can see genuine value-added. A portfolio with low outperformance but high alpha is often better than a portfolio with high outperformance but low alpha — the first took less risk to get there.
Does Foliolytic test alpha for statistical significance?
Yes. Foliolytic reports the t-statistic for alpha alongside the value itself. A t-stat above 2.0 (roughly) means the alpha is statistically distinguishable from zero at the 95% confidence level. Short portfolios or noisy return series often show positive alpha by chance — the t-stat tells you whether the signal is real. This is the same test used in academic finance research.
Does gold or Berkshire Hathaway have positive alpha versus the market?
As of July 2026, Foliolytic's price database shows Berkshire Hathaway (BRK-B) with an annualized Jensen's alpha of about +3.1% over three years and +4.6% over five, on a beta of just 0.58 — the classic profile of genuine value added rather than leverage. Gold (GLD) shows an even larger alpha (+19.4% over three years) but on a near-zero beta of 0.15, which reveals a quirk of single-factor CAPM: it labels all of an uncorrelated asset's return as alpha even though that return is really a separate factor, not skill. Long Treasuries (TLT) show the opposite — a deeply negative alpha after the 2021–2026 rate cycle.