We are given the risk-free rate, the beta of Stock A and Stock B, and the required return of Stock A. We need to find the required return of Stock B. We can use the Capital Asset Pricing Model (CAPM) to solve this problem. The CAPM formula relates the expected return of an asset to its beta, the risk-free rate, and the market risk premium.

1. Problem Description

We are given the risk-free rate, the beta of Stock A and Stock B, and the required return of Stock A. We need to find the required return of Stock B. We can use the Capital Asset Pricing Model (CAPM) to solve this problem. The CAPM formula relates the expected return of an asset to its beta, the risk-free rate, and the market risk premium.

2. Solution Steps

First, we can write the CAPM equation:

$E(R_i) = R_f + \beta_i (E(R_m) - R_f)$

Where:

$E(R_i)$ is the expected return of asset i

$R_f$ is the risk-free rate

$\beta_i$ is the beta of asset i

$E(R_m)$ is the expected return of the market

$E(R_m) - R_f$ is the market risk premium

We know the following values:

$R_f = 5.5\%$

$\beta_A = 1.0$

$\beta_B = 1.4$

$E(R_A) = 12\%$

We can use the information about Stock A to find the market risk premium:

$E(R_A) = R_f + \beta_A (E(R_m) - R_f)$

$12\% = 5.5\% + 1.0 (E(R_m) - R_f)$

$12\% - 5.5\% = E(R_m) - R_f$

$6.5\% = E(R_m) - R_f$

Now we know the market risk premium is 6.5%.

We can use this value to find the required return for Stock B:

$E(R_B) = R_f + \beta_B (E(R_m) - R_f)$

$E(R_B) = 5.5\% + 1.4 (6.5\%)$

$E(R_B) = 5.5\% + 9.1\%$

$E(R_B) = 14.6\%$

3. Final Answer

The required return of Stock B is 14.6%.

a. 14.6%