A positive alpha means the manager delivered more than the market exposure alone explains; a negative alpha means investors would have done better with an index fund at the same risk.
How to use the Jensen’s Alpha Calculator
- Beginning portfolio value
- Ending portfolio value
- Risk-free rate
- Portfolio beta
- Market return
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the beginning and ending portfolio values, the risk-free rate, the portfolio’s beta and the market return.
Inputs explained
| Field | What to enter |
|---|---|
| Beginning portfolio value | Amount in your currency |
| Ending portfolio value | Amount in your currency |
| Risk-free rate | In % |
| Portfolio beta | A number |
| Market return | In % |
What each result means
- Portfolio return = ([Ending portfolio value]÷[Beginning portfolio value] – 1)×100
- Expected return (CAPM) = [Risk-free rate] + [Portfolio beta]×([Market return] – [Risk-free rate])
- Jensen’s alpha = [Portfolio return] – [Expected return (CAPM)]
Example values
How the main result changes when Beginning portfolio value changes and everything else stays at the example values above:
| Beginning portfolio value | Jensen’s alpha (%) |
|---|---|
| 50,000 | 115.4 |
| 75,000 | 40.07 |
| 100,000 | 2.4 |
| 125,000 | -20.2 |
| 150,000 | -35.27 |
| 200,000 | -54.1 |
Formula
Portfolio return R_p = (ending − beginning) ÷ beginning
Expected return = R_f + β × (R_m − R_f)
Jensen's alpha α = R_p − expected return
Worked example
Inputs: Beginning portfolio value: $100,000; Ending portfolio value: $113,000; Risk-free rate: 4 %; Portfolio beta: 1.1; Market return: 10 %.
Results: Portfolio return = 13 %; Expected return (CAPM) = 10.6 %; Jensen's alpha = 2.4 %.
Frequently asked questions
What is Jensen's alpha?
The return above the CAPM-predicted return for the portfolio's beta.
Is a positive alpha good?
Yes, it suggests the manager added value beyond market risk.
Where do I find beta?
From financial data sites or by regression against a market index.