USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)

-Refer to Exhibit 9.18. What is the required rate of return for Stock X based on the capital asset pricing model (CAPM)?
A) 15.5%
B) 17.3%
C) 21.3%
D) 26.5%
E) 30.5%

Question

USE THE INFORMATION BELOW FOR THE FOLLOWING PROBLEM(S)
 
-Refer to Exhibit 9.18. What is the required rate of return for Stock X based on the capital asset pricing model (CAPM)?
A) 15.5% 
B) 17.3% 
C) 21.3% 
D) 26.5% 
E) 30.5%

Quizplus · Accepted Answer

To calculate the required rate of return for Stock X based on the CAPM, we need to use the formula: 
required rate of return = risk-free rate + beta x (market rate of return – risk-free rate)

The risk-free rate is given as 5%. The market rate of return is 12%. To calculate beta, we first need to calculate the covariance between the stock and the market, as well as the variance of the market:

Covariance = Σ[(R(stock) - Avg R(stock)) * (R(market) - Avg R(market))] / N-1

Var(market) = Σ[(R(market) - Avg R(market))^2] / N-1

Using the data in the table, we can calculate the covariance between the stock and the market as -0.00052 and the variance of the market as 0.025.

Beta = Covariance / Var(market) = -0.00052 / 0.025 = -0.0208

Plugging these values into the CAPM formula, we get: 
required rate of return = 5% + (-0.0208) * (12% - 5%) = 21.3%

Therefore, the best choice is C.