Question

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 6.9 percent and a standard deviation of 9.9 percent. The risk-free rate is 3.9 percent, and the expected return on the market portfolio is 11.9 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .44 correlation with the market portfolio and a standard deviation of 54.9 percent? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

11.22%

Explanation:

We need beta coefficient of the security to determine the expected return.

beta = (correlation × standard deviation) ÷ market standard deviation

The share of risk free asset is =

(the market portfolio - portfolio of expected return) ÷ (the market portfolio - risk-free rate)

The share of risk free asset is = (11.9 - 6.9)% ÷ (11.9 - 3.9)%

The share of risk free asset is = 0.625.

As the portfolio has a standard deviation of 9.9%, the standard deviation of market value = Standard deviation ÷ (1 - the share of risk free asset)

The market standard deviation = 9.9% ÷ (1 - 0.625)

The market standard deviation = 26.4%

As we get all the values for beta, we now input the values -

beta = (0.44 × 54.9%) ÷ 26.4%

beta = 0.915

Now we will use Capital asset pricing model to determine the expected return

expected return = Risk free return + (expected market return - risk free return) × beta

expected return = 3.9% + (11.9% - 3.9%) × 0.915

expected return = 3.9% + 7.32%

expected return = 11.22%