Free Portfolio Alpha Calculator
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 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.
See If You Have Real Alpha
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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.