Jensen's Alpha Calculator

Measure risk-adjusted performance against the Capital Asset Pricing Model. Enter your portfolio's return, the risk-free rate, portfolio beta, and the market's return to see whether it beat or missed its CAPM-implied expected return.

Quick Facts

Formula
α = Rp − [Rf + β(Rm − Rf)]
Rp is portfolio return, Rf is the risk-free rate, β is portfolio beta, and Rm is market return.
Benchmark
Capital Asset Pricing Model (CAPM)
Alpha isolates the return earned above what beta alone would predict against the chosen market benchmark.
Reading it
Alpha > 0 = outperformance
Alpha near zero tracks the benchmark; negative alpha means the portfolio underperformed for its risk level.

Your Results

Calculated
Jensen's Alpha
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Risk-adjusted excess return (α)
CAPM expected return
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Rf + β × (Rm − Rf)
Market risk premium
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Rm − Rf
Performance signal
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Alpha versus the CAPM benchmark

Ready

Enter portfolio return, risk-free rate, beta, and market return, then press Calculate.

What this calculator does

Jensen's Alpha (also called the Jensen measure or simply "alpha") is a risk-adjusted performance metric built on the Capital Asset Pricing Model (CAPM). Instead of just asking "did the portfolio make money," it asks "did the portfolio make more money than its level of market risk (beta) alone would predict?" This calculator runs the standard formula on your inputs and reports the alpha, the CAPM-implied expected return it is measured against, and the market risk premium behind that expectation.

The formula

Jensen's Alpha is defined as:

α = Rp − [Rf + β(Rm − Rf)]

where Rp is the portfolio's actual return over the period, Rf is the risk-free rate (typically a Treasury bill yield for the same period), β is the portfolio's beta relative to the benchmark, and Rm is the benchmark market return for the same period. The bracketed term, Rf + β(Rm − Rf), is the CAPM expected return — the return a portfolio with that beta "should" earn given how the market performed. Alpha is simply the actual return minus that expectation.

Worked example

Suppose a portfolio returned 12% while the risk-free rate was 3%, the market returned 9%, and the portfolio's beta was 1.2. The market risk premium is 9% − 3% = 6%. The CAPM expected return is 3% + 1.2 × 6% = 10.2%. Jensen's Alpha is then 12% − 10.2% = +1.8%. The portfolio beat what its risk level would predict by 1.8 percentage points over the period.

Why beta matters here

Beta measures how sensitive a portfolio's returns are to market-wide moves: a beta of 1.2 means the portfolio tends to move about 20% more than the market in either direction, so it is expected to earn a larger share of any positive market risk premium. Jensen's Alpha uses that expectation as the bar to clear — a high-beta portfolio needs a bigger raw return just to show zero alpha, while a low-beta portfolio can post positive alpha with a comparatively modest return. This is what separates alpha from simply comparing raw returns.

Reading the result

  • Positive alpha means the portfolio (or fund, or manager) delivered returns above what CAPM predicted for its beta — commonly interpreted as value added beyond passive market exposure.
  • Alpha near zero means performance tracked the CAPM expectation closely, consistent with a portfolio that behaves like a levered or de-levered version of the benchmark.
  • Negative alpha means the portfolio underperformed what its risk level would predict, even if the raw return was positive.

Assumptions and limits

This calculator applies the single-period Jensen's Alpha formula exactly as defined above; it does not estimate beta for you, and it does not annualize or average multiple periods. Beta, the risk-free rate, and the market return should all be measured over the same time horizon as the portfolio return for the result to be meaningful. Because alpha is sensitive to the accuracy of beta and the choice of benchmark, analysts typically review it across several periods and alongside other risk-adjusted measures (such as the Sharpe or Treynor ratio) rather than relying on a single calculation. This tool performs computation only and is not personalized investment advice.

Frequently Asked Questions

What is Jensen's Alpha and how is it calculated?
Jensen's Alpha measures the risk-adjusted return a portfolio earned above what the Capital Asset Pricing Model (CAPM) predicted for its level of systematic risk. The formula is α = Rp − [Rf + β(Rm − Rf)], where Rp is the portfolio's actual return, Rf is the risk-free rate, β is the portfolio's sensitivity to the market, and Rm is the market (benchmark) return. A positive alpha means the portfolio outperformed its CAPM-implied expected return; a negative alpha means it underperformed.
What counts as a good Jensen's Alpha?
Any alpha above zero indicates the portfolio beat its CAPM-implied benchmark over the period measured, and a larger positive number reflects greater risk-adjusted outperformance. Alpha near zero suggests the portfolio performed roughly as expected for its beta, while negative alpha means it fell short. Because alpha is calculated from a single period's inputs, a consistent track record across multiple periods is a more reliable signal than any one calculation.
How does beta affect Jensen's Alpha?
Beta sets the CAPM expected return that alpha is measured against: a higher beta raises the expected return when the market return exceeds the risk-free rate, which makes a given portfolio return look less impressive, while a lower beta lowers the bar. Two portfolios with identical raw returns can therefore show very different alpha values if their betas differ, because alpha explicitly adjusts for the amount of market risk each one carried.
What are the limitations of Jensen's Alpha?
Jensen's Alpha depends entirely on the accuracy of beta and the choice of benchmark and risk-free rate, and it assumes CAPM's single-factor view of risk is a complete description of expected return. It also reflects only the period measured, so a single calculation can be swayed by one unusually good or bad stretch. Analysts typically look at alpha across multiple periods and alongside other risk-adjusted measures such as the Sharpe or Treynor ratio rather than relying on one figure alone.

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