Jensen’s Alpha Calculator
Results are estimates based on the values you enter. Recheck your inputs and assumptions before using the output for decisions.
Calculate Jensen's alpha from portfolio return, beta, market return, risk-free rate, and portfolio value.
Jensen’s Alpha Calculator
Free online Jensen’s alpha calculator to measure how much a portfolio outperformed or underperformed the return expected under CAPM. This calculator is useful for investors, portfolio managers, finance students, analysts, advisers, and anyone reviewing whether active portfolio performance was good after adjusting for market risk. Jensen’s alpha is important because a raw return alone does not say whether the portfolio did better than it should have for its beta. Alpha tries to answer that by comparing the actual return with the expected return from the portfolio’s market risk exposure.
This calculator uses five inputs. Portfolio value means the amount used to translate percentage performance into money terms. Portfolio return means the actual return earned by the portfolio over the period. Portfolio beta means the sensitivity of the portfolio to market movements. Market return means the return of the broad market or benchmark over the same period. Risk-free rate means the return available from a near risk-free investment over that period. Once those values are entered, the calculator shows Jensen’s alpha, expected CAPM return, actual ending value, and CAPM expected ending value. These outputs make it easy to compare actual performance with the risk-adjusted benchmark implied by CAPM.
The formula of Jensen’s alpha
Expected CAPM return = Risk-free rate + Beta x (Market return – Risk-free rate)
Jensen’s alpha = Portfolio return – Expected CAPM return
Actual ending value = Portfolio value x (1 + Portfolio return)
CAPM expected ending value = Portfolio value x (1 + Expected CAPM return)
Here portfolio return means the actual return earned by the portfolio, beta means the portfolio’s market sensitivity, market return means the return of the chosen market benchmark, risk-free rate means the low-risk baseline return, expected CAPM return means the return justified by the portfolio’s beta under CAPM, and Jensen’s alpha means the extra performance above or below that expected return.
Solved Example
Example 1: Find Jensen’s alpha if portfolio value is $100,000, portfolio return is 14%, beta is 1.2, market return is 10%, and risk-free rate is 3%.
Solve: Expected CAPM return = 3% + 1.2 x (10% – 3%) = 3% + 8.4% = 11.4%
Jensen’s alpha = 14% – 11.4% = 2.6%
Actual ending value = 100000 x 1.14 = $114,000
CAPM expected ending value = 100000 x 1.114 = $111,400
Example 2: Find the result if portfolio value is $250,000, portfolio return is 9%, beta is 0.8, market return is 11%, and risk-free rate is 4%.
Solve: Expected CAPM return = 4% + 0.8 x (11% – 4%) = 9.6%
Jensen’s alpha = 9% – 9.6% = -0.6%
Actual ending value = 250000 x 1.09 = $272,500
CAPM expected ending value = 250000 x 1.096 = $274,000
Example 3: Find the result if portfolio value is $50,000, portfolio return is 16%, beta is 1.5, market return is 12%, and risk-free rate is 3%.
Solve: Expected CAPM return = 3% + 1.5 x (12% – 3%) = 16.5%
Jensen’s alpha = 16% – 16.5% = -0.5%
Actual ending value = 50000 x 1.16 = $58,000
CAPM expected ending value = 50000 x 1.165 = $58,250
Table of Jensen’s alpha calculator
| Portfolio Return | Beta | Market Return | Risk-free Rate | Jensen’s Alpha |
|---|---|---|---|---|
| 14% | 1.2 | 10% | 3% | 2.60% |
| 13% | 1.0 | 9% | 2% | 4.00% |
| 9% | 0.8 | 11% | 4% | -0.60% |
| 16% | 1.5 | 12% | 3% | -0.50% |
How to use this Jensen’s alpha calculator
Enter the portfolio value in the proper input field. After that, enter the portfolio return, the portfolio beta, the market return, and the risk-free rate for the same period. Then click the calculate button. The calculator will show Jensen’s alpha, expected CAPM return, actual ending value, and CAPM expected ending value in the result box.
This calculator is useful when judging whether a portfolio manager created value beyond what market exposure alone would suggest. A positive alpha generally means the portfolio beat the return justified by its beta, while a negative alpha means the portfolio fell short of that risk-adjusted expectation. Looking at the actual and CAPM expected ending values together also helps convert the percentage difference into a more practical money comparison on the chosen portfolio size.
When using the result, remember that Jensen’s alpha depends on the quality of the beta estimate, the benchmark selection, and the period returns used. A poorly chosen benchmark or unstable beta can make alpha less meaningful. CAPM is also a simplified model and does not capture every source of risk. Even so, Jensen’s alpha remains one of the clearest quick measures of risk-adjusted outperformance. This calculator gives a fast numerical view that supports portfolio review, manager evaluation, finance education, and investment analysis.