Transparent method
The formula
Worked example
Example inputs
How to interpret the result
Alpha measures performance against a specific benchmark over a specific period, and both of those choices shape the result meaningfully. An alpha figure calculated against one benchmark or time window can look completely different calculated against another, even for the identical underlying investment.
Before you rely on it
What to check
Confirm the benchmark and period used are genuinely appropriate comparisons for the investment being measured before treating a calculated alpha as a meaningful, standalone verdict.
The common error
Where people go wrong with investment alpha calculator
Treating a single alpha figure as a fixed, permanent measure of investment skill. It's calculated against a specific benchmark and period, and both choices can shift the number substantially without anything about the actual investment changing.
Sensitivity evidence
How asset return changes the estimated alpha
| Asset return | Estimated alpha | CAPM expected return | Asset excess return |
|---|---|---|---|
| 8.0% | -1.5% | 9.5% | 4.0% |
| 10.0% | 0.500% | 9.5% | 6.0% |
| 12.0%worked example | 2.5% | 9.5% | 8.0% |
| 14.0% | 4.5% | 9.5% | 10.0% |
| 16.0% | 6.5% | 9.5% | 12.0% |
Every input, tested
Which input moves the estimated alpha most
| Input | Tested from | To | Estimated alpha at each end | Swing |
|---|---|---|---|---|
| Market return | 7.0% | 11.0% | 4.7% to 0.300% | 4.4% (176%) |
| Asset return | 10.0% | 14.0% | 0.500% to 4.5% | 4.0% (160%) |
| Asset beta | 1 | 1.2 | 3.0% to 2.0% | 1.0% (40%) |
| Risk-free rate | 3.0% | 5.0% | 2.4% to 2.6% | 0.200% (8.0%) |
Two variables at once
Estimated alpha by asset return and risk-free rate
| Asset return \ Risk-free rate | 2.0% | 4.0% | 6.0% |
|---|---|---|---|
| 8.0% | -1.7% | -1.5% | -1.3% |
| 10.0% | 0.300% | 0.500% | 0.700% |
| 12.0% | 2.3% | 2.5% | 2.7% |
| 14.0% | 4.3% | 4.5% | 4.7% |
| 16.0% | 6.3% | 6.5% | 6.7% |
Step by step
The worked example, input by input
| Input | Value used |
|---|---|
| Asset return | 12.0% |
| Risk-free rate | 4.0% |
| Asset beta | 1.1 |
| Market return | 9.0% |
| Estimated alpha | 2.5% |
| CAPM expected return | 9.5% |
| Asset excess return | 8.0% |
Where the inputs come from
Asset return and market return are for the same period, the risk-free rate is a Treasury yield for that period, and beta measures the asset's sensitivity to the market. Get beta from a data provider, computed over a long enough period. Enter everything in percent per year. If the period is shorter than a year, annualize first, otherwise the comparison between asset and market will be off.
When the result stops applying
Alpha depends on the benchmark, the beta estimate and the period, so it is sensitive to choices. Most active managers show negative alpha after fees over long periods. A single-factor model like CAPM ignores other known sources of return such as value and size, which can look like alpha. Statistical significance requires many observations.
What to compare it with
Estimate beta on the beta calculator, and judge risk-adjusted performance with the Sharpe and Sortino ratios. The investment fee calculator shows how much of any alpha the fee consumes. If a fund's alpha disappears after fees, a cheap index fund is the better choice.
People also ask
Frequently asked questions
What is a good alpha?
Any consistent positive alpha after fees is good, but it is rare and hard to sustain. Many studies find that most actively managed funds do not deliver positive alpha over long periods.
How is alpha different from excess return?
Excess return is the gain over the risk-free rate, while alpha is the part left after accounting for the market risk taken through beta.
Does a fund's alpha last?
Usually not. Funds with high alpha in one period often fail to repeat it, so a long record matters more than a single strong year.