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CAPM calculator and formula

By Jude Wallis

CAPM required return is the risk-free rate plus beta times the market risk premium. A 4 percent risk-free rate, a beta of 1.2 and a 10 percent market return produce 11.2 percent.

CAPM required return

11.20%

A 6.00 point market premium, scaled by beta 1.20.

Risk-free rate
4.00%
Market risk premium
6.00 points
Beta times the premium
7.20 points
%

The return available without market risk, in the same currency as the cash flows.

Sensitivity to market moves. One receives the full market premium.

%

The expected return on the market the beta was measured against.

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The formula

E(Ri)=Rf+βi(E(Rm)−Rf)E(R_i) = R_f + \beta_i\left(E(R_m) - R_f\right)

RfR_f is the risk-free rate. E(Rm)E(R_m) is the expected market return. βi\beta_i is beta. The term in parentheses is the market risk premium.

A base rate and a scaled premium

Begin with the return available without market exposure. Subtract that from the expected market return to form the premium. Multiply the premium by beta. Add the base rate once.

With a 4 percent risk-free rate and a 10 percent market return, the premium is 6 points. A beta of 1.2 turns that into 7.2 points of compensation, and adding the 4 percent base gives 11.2 percent.

How the CAPM formula works is the explainer. This page is the working identity.

Beta scales the premium, not the market return

A beta of 1 receives the full premium. A beta of 1.2 receives 1.2 times that premium. A beta of 0.8 receives 0.8 times it. The second example keeps the same 4 and 10 percent rates and cuts beta to 0.8, which produces 8.8 percent.

Beta is sensitivity to market moves, not a promise that the asset rises in every rising market. How unlevered beta works separates the business sensitivity from the financing effect when debt has changed the equity beta.

Only systematic risk is priced here

CAPM assumes investors can hold broad portfolios. Company-specific surprises are treated as diversifiable, so they do not earn an extra expected return in this formula. The risk that remains is systematic risk.

That is why the line rises with beta rather than with total volatility. An asset can bounce around for company-specific reasons and still have a modest CAPM return if those moves have little relationship with the market.

Risk and return places that distinction beside diversification.

What this page is not doing

It does not estimate beta from a return series, pick a market index, or forecast a realised return. The output is the return the stated inputs imply.

Add the risk-free rate once, after the premium has been scaled. Adding it a second time is the usual slip. This is educational material, not financial advice.

Worked examples

Beta above one

The risk-free rate is 4 percent, beta is 1.2 and the expected market return is 10 percent. What is the CAPM required return?

  1. Market premium: 10−4=610 - 4 = 6 percentage points.
  2. Beta times the premium: 1.2×6=7.21.2 \times 6 = 7.2 points.
  3. Add the risk-free rate once: 4+7.2=11.24 + 7.2 = 11.2 percent.

The CAPM required return is 11.2 percent. The market premium is 6 points and beta 1.2 scales it to 7.2 points.

Beta below one

Keep the risk-free rate at 4 percent and the market return at 10 percent, but set beta to 0.8. What is the CAPM required return?

  1. The market premium is still 10−4=610 - 4 = 6 percentage points.
  2. Beta times the premium: 0.8×6=4.80.8 \times 6 = 4.8 points.
  3. Add the risk-free rate once: 4+4.8=8.84 + 4.8 = 8.8 percent.

The CAPM required return is 8.8 percent. The same 6 point premium is scaled by beta 0.8.

Adding the risk-free rate twice

The premium is already market return minus the risk-free rate. After beta scales that difference, the risk-free rate is added once as the base.

Writing Rf+β×E(Rm)R_f + \beta \times E(R_m) skips the subtraction and overstates the result whenever beta is not zero. The first example would then read 16 percent instead of 11.2 percent.

Common questions

Is CAPM expected return a forecast?

Read it as a model-implied required return for the stated inputs. Realised return can differ widely.

Does a higher beta always raise the CAPM return?

When the assumed market premium is positive, yes. If the premium were zero, beta would not change the result.

Where does unlevered beta fit?

When you need the business beta without the financing effect. The unlever beta calculator is that conversion. This page then prices the equity beta you actually hold.

Keep reading

This page is educational material, not financial advice. The figures come from the formula shown and assume the inputs you enter hold for the whole term. Your own rate, fees, taxes and timing will differ, so treat the output as arithmetic to check a decision against, not as a recommendation.