What this calculator does
Beating the market is not impressive if the portfolio simply carried more market risk. Jensen's alpha subtracts what CAPM says the portfolio should have returned given its beta, leaving whatever the manager actually added.
The hurdle rises with beta. A portfolio with a beta of 1.12 in a market returning 11 per cent needed 12.1 per cent just to break even. A 10 per cent return therefore produces an alpha of −2.08 per cent, despite being a positive return.
The formula
The portfolio return is calculated from beginning and ending values. The CAPM-required return is the risk-free rate plus beta times the market risk premium, and alpha is the difference between the two.
| Term | Meaning |
|---|---|
| Alpha | Return above what beta alone would justify. |
| CAPM-required return | The benchmark: risk-free rate plus beta times the market premium. |
| Beta | The portfolio's sensitivity to market movements, which sets the hurdle. |
The inputs explained
| Field | What to enter |
|---|---|
| Beginning portfolio value ($) | Portfolio value at the start of the period. |
| Ending portfolio value ($) | Portfolio value at the end of the period. |
| Portfolio beta | The portfolio beta against the market. |
| Risk-free rate (%) | The risk-free rate over the period. |
| Market rate of return (%) | The market return over the same period. |
When to use it
Evaluating a fund manager
Alpha separates skill from simply having taken more market risk.
Assessing your own portfolio
Beating the index with a high-beta portfolio is not necessarily outperformance.
Comparing managers with different mandates
Alpha normalises for the level of market exposure each carried.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How much return does a 1.12 beta require?
Three ending values against the same CAPM hurdle.
Questions
Why can a positive return give a negative alpha?
Because alpha is measured against what the portfolio should have earned given its risk, not against zero. A portfolio with a beta above 1 in a rising market is expected to beat the market, so merely matching it is underperformance.
Does alpha prove skill?
Not from one period. Alpha is noisy, and with enough managers some will show positive alpha by chance alone. Persistent alpha over many periods is far more convincing than a single strong year.
How does it relate to the Treynor ratio?
Both adjust for beta. Alpha gives the outperformance in percentage points; Treynor gives excess return per unit of beta as a ratio. Alpha is the more direct answer to whether value was added.
Is it sensitive to the benchmark chosen?
Very. A small-cap portfolio measured against a broad market index will show spurious alpha when small caps outperform. Choosing an appropriate benchmark matters as much as the arithmetic.
For beta-adjusted return as a ratio, see the Treynor ratio calculator. For the model setting the hurdle, see the CAPM calculator.