Alpha Calculator

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Beating the Market Isn't the Same as Beating What You Should Have Earned

A portfolio that returned 12% sounds good until you account for how much risk it took to get there. Jensen's Alpha asks a sharper question: given the portfolio's beta (its sensitivity to market moves), what return should it have earned based on the market's actual performance and the risk-free rate — and did it beat or miss that expected figure?

The Formula

Expected Return = Rf + Beta × (Rm − Rf)
Alpha = Rp − Expected Return

Rp is the portfolio's actual return, Rf is the risk-free rate, Beta measures the portfolio's volatility relative to the market, and Rm is the market's return. The expected return line comes from the Capital Asset Pricing Model (CAPM); alpha is simply the gap between actual and expected.

What a Positive or Negative Alpha Means

  • Positive alpha — the portfolio outperformed what its risk level would predict, often cited as evidence of manager skill (though it could also reflect luck over a short period).
  • Negative alpha — the portfolio underperformed its risk-adjusted expectation, common among actively managed funds after fees.
  • Zero alpha — the portfolio performed exactly in line with what its beta would predict, given how the market actually moved.

Worked Example

A portfolio returned 12%, the risk-free rate was 3%, the portfolio's beta is 1.2, and the market returned 10%:

Jensen's Alpha calculation
StepValue
Expected Return = 3% + 1.2 × (10% − 3%)11.40%
Actual Portfolio Return12.00%
Alpha = 12% − 11.40%0.60%

A positive alpha of 0.60% here means the portfolio slightly outperformed what its beta of 1.2 would have predicted given how the market moved.

How to Use This Calculator

  1. Enter the Portfolio Return for the period.
  2. Enter the Risk-Free Rate for the same period.
  3. Enter the portfolio's Beta.
  4. Enter the Market Return for the period.
  5. Select Calculate to see the alpha and its interpretation.

Related Calculations

Need the beta figure first? Calculate it with the Beta Calculator, or check risk-adjusted return a different way with the Sharpe Ratio Calculator.