# Jensen’s Alpha Calculator

URL: https://speedycalculator.com/calculators/finance/jensens-alpha/
Last updated: 2026-10-25

> The Jensen's alpha calculator measures how much a portfolio beat (or lagged) the return predicted by the CAPM for its level of market risk (beta) – a classic test of a fund manager's skill.

## Inputs

- Beginning portfolio value
- Ending portfolio value
- Risk-free rate (%)
- Portfolio beta
- Market return (%)

## Results

- Portfolio return
- Expected return (CAPM)
- Jensen's alpha

## 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
```

## Explanation

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.

### Tips

- Use the nominal annual rate and pick the compounding frequency your bank or broker states.
- Small differences in return or fees compound into large differences over decades.
- Run the calculation with a cautious, a central and an optimistic return to see the range of outcomes.
- Past returns do not guarantee future returns – nothing here is investment advice.

### Common mistakes to avoid

- Comparing an APR with an APY or effective rate.
- Ignoring inflation, taxes and fees when judging a real return.
- Entering a percentage as a decimal (5 instead of 0.05 is correct here).

### Inputs explained

FieldWhat to enterBeginning portfolio valueAmount in your currencyEnding portfolio valueAmount in your currencyRisk-free rateIn %Portfolio betaA numberMarket returnIn %

### 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 valueJensen's alpha (%)50,000115.475,00040.07100,0002.4125,000-20.2150,000-35.27200,000-54.1

## 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 %**.

## FAQ

**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.

**What formula does the Jensen's Alpha Calculator use?**
Portfolio return R_p = (ending − beginning) ÷ beginning.


## Sources

- [Corporate Finance Institute – financial ratios](https://corporatefinanceinstitute.com/)