Question

A portfolio that combines the risk-free asset and the market portfolio has an expected return of 6.5 percent and a standard deviation of 9.5 percent. The risk-free rate is 3.5 percent, and the expected return on the market portfolio is 11.5 percent. Assume the capital asset pricing model holds. What expected rate of return would a security earn if it had a .40 correlation with the market portfolio and a standard deviation of 54.5 percent?

Answer 1

Answer: Step 1) Find share of market in the Portfolio

(11.5-3.5)x+3.5=6.5

8x=3

x=3/8

x=0.375

=37.5%

SD of market portfolio= 0.375x+0=9.5

x=9.5/0.375

=25.33%

correl = cov / (std 1 * std2)

0.4=COV/0.2533*0.545

COV= 0.2533*0.545*0.4=0.05

cov of 2 assets = b1 * b2 * variance of market

0.05=B1*1*0.2533^2

B of security=0.0032

Capm Model

3.5+0.0032(11.5-3.5)=3.5256% expected return

Explanation:

Step 1) Find the share of market in the portfolio in order to find market SD

Step 2)  Find Covariance betweens security and market by using both SDS and correlation

Step 3) Find Beta of Security using Co variance

Step 4) Use the Beta in CAPM model in order to find expected return