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REALIZED RETURN / CAPM EXPECTATION

Jensen's Alpha Calculator

Compare portfolio return with the CAPM return implied by beta. Review the entered period, benchmark, and risk assumptions alongside the result.

  • 01 Calculated in this tab
  • 02 Values stay in this browser tab
  • 03 Use boundary

Conversion input

Known value

Filter by unit name, symbol, or code. Your current selections remain available.

Scenario inputs

Preparing the calculator...

METHOD / WORKED EXAMPLE

Separate realized return from the CAPM baseline

Jensen's alpha makes the model-implied benchmark visible before showing the residual, helping you audit whether the return, market premium, beta, and horizon actually belong together.

WORKED DEFAULT

Check the calculation with the default inputs

At 13% portfolio return, 10% market return, 4% risk-free rate, and beta 1.2, CAPM expected return is 11.2%, leaving Jensen's alpha of 1.8 percentage points.

  1. Find market premium10% - 4% = 6%
  2. Build CAPM return4% + 1.2 x 6% = 11.2%
  3. Find the residual13% - 11.2% = 1.8%

READ THE RESULT

Interpret the output in context

Positive alpha means the entered return exceeded this particular CAPM expectation; it does not establish causation, persistence, statistical significance, or performance after omitted costs.

ASSUMPTIONS AND LIMITS

Know where the model stops

  • Portfolio, market, and risk-free returns cover the same horizon.
  • Beta was estimated against the entered market benchmark.
  • Return and beta conventions are documented and internally consistent.

Alpha is model- and benchmark-dependent historical attribution, not proof of skill or a forecast of excess return.

CFA Institute: measures of risk-adjusted return

COMMON QUESTIONS

Jensen's Alpha Calculator FAQs

Does positive Jensen's alpha prove manager skill?

No. Positive alpha is a residual from the selected CAPM inputs and sample. It can reflect luck, benchmark mismatch, stale or estimated prices, omitted factors, leverage, nonlinear exposures, fees, or genuine decisions. Assess confidence, persistence, holdings, factor attribution, implementation costs, and multiple market conditions before making any claim about repeatable skill.

Can beta come from a different benchmark?

It should not. Beta measures sensitivity to a particular market-return series, and Jensen's alpha uses that same market in the expected-return equation. Combining beta from one index with the return of another breaks the model's internal link. Re-estimate beta against the selected benchmark over a documented frequency and window before calculating or comparing alpha.

Should returns be gross or net of fees?

Either convention can be analyzed, but portfolio and benchmark treatment must be disclosed and comparisons must remain consistent. Net portfolio return may be most relevant to an investor, while gross return may support manager attribution. Trading costs, taxes, cash flows, and benchmark investability can still create differences that this compact calculation does not isolate.

Use boundary

Calculation path

Build the CAPM expected return from risk-free rate, beta, and market premium, then subtract it from portfolio return.

Calculation path

Jensen's alpha = portfolio return - [risk-free rate + beta x (market return - risk-free rate)].