Question

Suppose the risk-free rate is 6%. A stock with a beta of 1.5 has an expected rate of return of 12%. If CAPM holds and all securities are correctly priced, the expected return of a stock with a beta of

a.0.8
b.10.8%
c.9.2%
d.8%
e.7.2%

Answer 1

Using the CAPM formula and the given information, we calculated the market return and subsequently the expected return for a stock with a beta of 0.8 to be approximately 8%.

Step-by-step explanation:

The question pertains to the Capital Asset Pricing Model (CAPM), which is used to determine the expected return of a stock given its risk, represented by beta, compared to the overall market.

The formula for CAPM is given by:

Expected return = Risk-free rate + Beta * (Market return - Risk-free rate)

We are given the risk-free rate (6%), the beta of the stock (0.8), and the expected return of another stock with a beta of 1.5 (12%). To find the expected return of the stock with a beta of 0.8, we need to find the market return. This can be determined using the information of the given stock with a beta of 1.5.

Rearranging the CAPM formula:

Market return = (Expected return - Risk-free rate) / Beta + Risk-free rate

Market return = (12% - 6%) / 1.5 + 6%

Market return = 4% / 1.5 + 6%

Market return = 2.67% + 6%

Market return = 8.67%

Now, plug in the beta of 0.8 to find the expected return of the stock:

Expected return = 6% + 0.8 * (8.67% - 6%)

Expected return = 6% + 0.8 * 2.67%

Expected return = 6% + 2.14%

Expected return = 8.14%

Thus, the closest answer to the expected rate of return for the stock with a beta of 0.8 is 8.0%.