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Jensen's Alpha Calculator

Measure Jensen's alpha by comparing actual portfolio return with the CAPM expected return from beta, risk-free rate, and market return.

Published

Jensen's alpha
Risk-adjusted outperformance
7.92%
Portfolio's return
20%
CAPM expected return
12.08%
Risk-free rate
2%
Market return
11%
Excess dollar return
$79,200.00

Compared with a 12.08% CAPM expected return, this portfolio produced 20%.

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Results update as you type.

Jensen’s Alpha Calculator

Jensen’s alpha compares what a portfolio actually earned with what the capital asset pricing model would have expected it to earn for the beta risk it took. The calculator starts from beginning and ending portfolio values, so the actual return is based on the change in account value. It then computes a CAPM expected return using the risk-free rate, portfolio beta, and market return. Jensen’s alpha is the actual return minus that expected return.

This makes the page different from a simple gain calculator. A 20 percent gain may be excellent for a low-beta portfolio in a modest market, but ordinary for a very high-beta portfolio in a strong market. Jensen’s alpha tries to isolate the part of performance that is above or below a beta-adjusted benchmark. It is a useful diagnostic for manager review, strategy research, and post-trade analysis, but it is still only as reliable as the benchmark and beta inputs.

Use the Portfolio Beta Calculator before this page if you need to estimate beta from holdings. Use the CAPM calculator if you want to focus on expected return itself. Compare the result with the Information Ratio Calculator when you also want active return per unit of tracking error.

Informational, not investment advice.

What the calculator does

The form asks for beginning portfolio value, ending portfolio value, risk-free rate, portfolio beta, and market rate of return. It rejects a beginning value of zero or less because return cannot be computed from a nonpositive starting base. The risk-free rate and market return are entered as percentages. Portfolio beta is entered as a decimal beta, such as 1.12.

The calculator reports the portfolio’s return, the CAPM expected return, the risk-free rate, the market return, and excess dollar return. The primary label changes depending on the sign of alpha: risk-adjusted outperformance for positive or zero alpha, and risk-adjusted underperformance for negative alpha. Excess dollar return equals beginning value times alpha as a decimal percentage, so it translates the percentage alpha into dollars for the starting portfolio size.

Formula

First compute actual portfolio return:

portfolio return=ending value−beginning valuebeginning value×100\text{portfolio return} = \frac{\text{ending value} - \text{beginning value}}{\text{beginning value}} \times 100

Then compute the CAPM expected return:

CAPM expected return=risk-free rate+portfolio beta×(market return−risk-free rate)\text{CAPM expected return} = \text{risk-free rate} + \text{portfolio beta} \times \left(\text{market return} - \text{risk-free rate}\right)

Jensen’s alpha is actual return minus expected return:

Jensen’s alpha=portfolio return−CAPM expected return\text{Jensen's alpha} = \text{portfolio return} - \text{CAPM expected return}

The calculator keeps rates in percentage points internally. That is why a 20 percent portfolio return minus a 12.08 percent expected return gives 7.92 percent alpha, not 0.0792 displayed as a raw decimal.

Worked example

Use the default values: beginning portfolio value of $1,000,000, ending portfolio value of $1,200,000, risk-free rate of 2 percent, portfolio beta of 1.12, and market return of 11 percent.

The portfolio return is the ending value minus the beginning value divided by the beginning value:

portfolio return=$1,200,000−$1,000,000$1,000,000×100=20%\text{portfolio return} = \frac{\$1{,}200{,}000 - \$1{,}000{,}000}{\$1{,}000{,}000} \times 100 = 20\%

The market risk premium is 11 percent minus 2 percent, or 9 percentage points. Multiply that premium by beta: 1.12 times 9 equals 10.08 percentage points. Add the 2 percent risk-free rate, and the CAPM expected return is 12.08 percent.

Jensen’s alpha is:

Jensen’s alpha=20%−12.08%=7.92%\text{Jensen's alpha} = 20\% - 12.08\% = 7.92\%

The calculator therefore shows risk-adjusted outperformance of 7.92 percent. It also computes excess dollar return as $1,000,000 times 7.92 divided by 100, or $79,200. The note says the portfolio produced 20 percent compared with a 12.08 percent CAPM expected return.

How to interpret alpha

Positive alpha is attractive only after checking context. A single period can be dominated by luck, style tilts, sector concentration, or an unusual benchmark environment. A manager who owns smaller, more volatile companies may look skilled if the benchmark and beta fail to capture those exposures. A negative result can likewise be explainable if the period includes fees, taxes, cash flows, or defensive positioning that the model does not represent.

Jensen’s alpha is strongest when the measurement period, beta estimate, risk-free rate, and market return are aligned. If the portfolio value includes deposits or withdrawals, adjust the return before using the calculator. If the portfolio changed materially during the period, one beta may not describe the whole experience. If the benchmark is wrong, the expected return is wrong.

Limitations and common mistakes

Do not annualize one input but not the others. Do not use a risk-free rate from a different maturity without a reason. Do not compare a global portfolio with a domestic-only market return. Do not treat a positive alpha as proof of repeatable skill unless it persists after fees over enough observations. The formula is transparent, but the result remains a model-based estimate of risk-adjusted performance, not a verdict.

Sources

Frequently asked questions

What does Jensen's alpha measure?
Jensen's alpha measures actual portfolio return minus the return predicted by CAPM for the portfolio's beta. A positive result means the portfolio beat its beta-adjusted expected return for the period entered, while a negative result means it lagged that risk-adjusted benchmark.
What inputs need the same time period?
Beginning value, ending value, risk-free rate, market return, and beta should all describe the same evaluation window as closely as possible. Mixing a one-month portfolio return with an annual market return or stale beta can make the alpha result misleading.
Is Jensen's alpha the same as total return?
No. Total return is the raw percentage change in the portfolio's value. Jensen's alpha subtracts a CAPM expected return that reflects the risk-free rate, market return, and portfolio beta. A high raw return can still produce low alpha if beta was very high.
Can Jensen's alpha be negative?
Yes. Negative alpha means the portfolio earned less than CAPM would have expected for the risk inputs entered. It does not prove the manager lacks skill by itself, because short periods, fees, taxes, benchmark mismatch, and unusual market conditions can influence the result.

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