Jensen Alpha Calculator
Compare a portfolio return with its CAPM comparison return using four inputs measured over the same period.
How it works
Enter portfolio return, risk free rate, beta, and market return. Returns are percentages over one shared interval. Beta is a coefficient that describes sensitivity to a market benchmark, not a percentage return input.
The calculator finds the CAPM comparison return by adding the risk free rate to beta times the market risk premium. Jensen alpha is the portfolio return less that comparison return. Excess return is portfolio return less the risk free rate. All values keep the input period and return basis.
The assessment label reflects only whether the calculated alpha is positive, zero, or negative. The calculation does not infer the period, annualize returns, estimate beta, or test statistical significance.
For a meaningful comparison, align the portfolio and market return periods, return basis, and benchmark. Use a beta estimated against that benchmark over a compatible window. Do not compare the output across mismatched inputs as if it were a standardized performance record.
Step by step
- Enter portfolio return, risk free rate, beta, and market return.
- Check that the rates use the same period and return basis, and beta uses the chosen benchmark.
- Review the CAPM comparison return, Jensen alpha, and excess return.
Worked example
Enter portfolio return 12%, risk free rate 3%, beta 1.1, and market return 9%. The CAPM comparison return is 3% + 1.1 × (9% − 3%) = 9.6%. Jensen alpha is 12% − 9.6% = 2.4 percentage points, and return above the risk free rate is 12% − 3% = 9 percentage points.
The result is the difference between the entered portfolio return and the CAPM comparison return for these inputs. It does not estimate a regression intercept or show whether the difference is statistically meaningful.
When to use this calculator
Use this calculator to compare a portfolio return with a CAPM return for one stated period when the inputs share a benchmark and return basis.
Use a regression based analysis when you need to estimate alpha from a series of observations or assess statistical uncertainty. This four input calculation does not provide those results.
Common input errors
Do not enter 3 for a 3% return and 0.03 for another rate. Enter all return rates as percentage values, such as 3, over the same period. Beta is entered as a coefficient, such as 1.1, not as 110%.
Do not mix return periods, market benchmarks, currencies, or return conventions. A difference can reflect mismatched inputs rather than portfolio performance. Record the source and date for each rate and beta estimate.
Formula
Jensen alpha = Rp − [Rf + β × (Rm − Rf)]
CAPM comparison return = Rf + β × (Rm − Rf)
Excess over the risk free rate = Rp − Rf
Enter returns as percentages over the same interval and on the same return basis. Beta should use the same market benchmark and a compatible observation window. The calculator does not annualize the inputs.
Limits and assumptions
This calculator applies a single period CAPM comparison to manual inputs. It does not run a time series regression, estimate beta, calculate a standard error, test significance, annualize values, or account for fees, taxes, cash flows, timing, or changing exposures. The result depends on the values, benchmark, and period you choose.
Key terms
- Jensen alpha
- Portfolio return minus the CAPM comparison return calculated from the entered risk free rate, beta, and market return.
- CAPM comparison return
- Rf + β × (Rm − Rf), using the entered risk free rate, beta, and market return.
- Excess return
- Portfolio return minus the entered risk free rate, using the same input period and return basis.
Related measures
CAPM Expected Return Calculator shows the required return from a risk free rate, beta, and market return. Sharpe Sortino Ratio compares portfolio return with total or downside variation. These measures answer different questions from Jensen alpha.
Treynor Ratio also relates excess return to market beta, while Maximum Drawdown summarizes the largest observed peak to trough loss. Each measure uses different inputs and should be interpreted on a compatible period and return basis.
FAQ
What does Jensen alpha calculate?
Jensen alpha is the portfolio return minus the return implied by CAPM from the entered risk free rate, beta, and market return. A positive result means the entered return is above that arithmetic comparison for the stated period. It is not by itself evidence of skill, persistence, or future performance.
How is Jensen alpha calculated here?
The calculator applies the displayed CAPM equation to four numbers you enter. It does not estimate beta or alpha from a historical return series. Enter the portfolio return, risk free rate, and market return as percentages, and beta as a coefficient.
How should I interpret a positive or negative result?
A positive alpha means the portfolio return is above the CAPM comparison return; a negative alpha means it is below; zero means they are equal at the entered precision. The label follows the sign of the calculated value. It is not a statistical test and does not use a significance threshold.
Which inputs need to match?
Use rates from the same interval and return basis, and use beta matched to the same market benchmark and a compatible estimation window. For example, do not compare a monthly portfolio return with an annual market return. The calculator does not convert periods or currencies.
What does this calculation leave out?
The calculation uses four manually entered values and does not model fees, taxes, cash flows, changing beta, benchmark choice, or timing within the period. It does not estimate a regression intercept, standard error, statistical significance, manager skill, or future return.
Related tools
CAPM Expected Return Calculator calculates a required return from beta and market assumptions. Treynor Ratio relates excess return to beta, while Sharpe Sortino Ratio uses total or downside variation. Maximum Drawdown measures the depth of observed peak to trough losses.