Applying CAPM to Find Risk Premium, Required Return, and Beta

Summary

The document applies the Capital Asset Pricing Model to a simple set of return assumptions. It explains that an asset’s expected return equals the risk-free rate plus its beta multiplied by the market risk premium. The key step is to express both market and asset returns in excess of the risk-free rate when solving for beta or calculating a required return.

With the stated risk-free rate of 4% and expected market return of 12%, the market risk premium is 8%. For beta 1.5, CAPM gives a required return of 16%; for a stock with an expected return of 11.2%, it implies beta 0.9. These are arithmetic illustrations of the model, not evidence that CAPM accurately predicts returns. The exchange does not discuss estimation uncertainty, alternative asset-pricing models, or whether the assumptions are appropriate for any particular investment.

Key ideas

• CAPM relates expected asset return to the risk-free rate and the market risk premium scaled by beta.
• The stated market risk premium is 8% after subtracting the 4% risk-free rate from the 12% market return.
• A beta of 1.5 implies a required return of 16% under the given assumptions.
• An expected return of 11.2% implies a beta of 0.9 under the same assumptions.

Tags

# finance - using CAPM


# finance - using CAPM












The risk-free rate is 4%, and the expected return on the market portfolio is 12%. Using the Capital Asset Pricing Model:

a. What is the risk premium on the market?

b. what is the required return on an investment with a beta of 1.5?

c. if the expected return on stock X is 11.2%, what is its beta, according to the capital asset pricing model?

## Answer by Richi Wa (score 1)

https://quant.stackexchange.com/a/15516

The CAPM states that $$ E[r-r_f] = \beta E[r_M-r_f], $$ thus $$ E[r] = r_f + \beta E[r_M-r_f], $$ where $r$ is the return of the asset and $r_M$ is the market return, $r_f$ is the risk free rate. Thus you have to substract the risk free rate from the expectations as $E[r-r_f] =E[r]-r_f $. The answers are

- $8\%$ as in the other answer

- $4\% + 1.5* 8\% = 16\%$

- $11.2\%-4\% =\beta*8\%$ thus $\beta=0.9$.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.