The risk-free rate is 1.5% and the expected return on the market portfolio is 9%. If the CAPM holds, what is the beta on stock YMH with an expected return of 9.68%?

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BlackTom AI · Accepted Answer

This problem uses the CAPM relationship, which links expected return to the risk-free rate, the market return, and the asset's beta. 
First, identify the given quantities: the risk-free rate R_f is 1.5%, the expected market return E[R_m] is 9%, and the stock YMH has an expected return E[R_i] of 9.68%. 
Next, write the CAPM formula: E[R_i] = R_f + beta_i × (E[R_m] − R_f). We need to solve for beta_i. 
Compute the market risk premium: E[R_m] − R_f = 9% − 1.5% = 7.5%. 
Compute the stock’s excess return over the risk-free rate: E[R_i] − R_f = 9.68% − 1.5% = 8.18%. 
Now divide the stock’s excess return by the market risk premium to obtain beta: beta_i = 8.18% / 7.5% = 1.090666..., which is approximately 1.09 when rounded to two decimal places. 
If you consider rounding choices, you could note that 1.0907 rounds to 1.091 or 1.09 depending on the precision convention used. 
In summary, the calculation follows directly from the CAPM equation by isolating beta and using the provided rate values to compute the ratio of the stock’s over‑risk-free return to the market’s over‑risk-free return. 
The key steps are identifying the market premium, computing the stock’s excess return over the risk-free rate, and performing the division to obtain beta.

COEC_V 371 001 002 2025W1 Lecture 5 Practice Quiz: Part 1

The risk-free rate is 1.5% and the expected return on the market portfolio is 9%. If the CAPM holds, what is the beta on stock YMH with an expected return of 9.68%?

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