A manager wishes to construct a portfolio by investing 25% in a stock half as volatile as the market

By Investopedia Staff AAA
Q:

A manager wishes to construct a portfolio by investing 25% in a stock half as volatile as the market, 25% in a stock twice as volatile as the market, 25% in the market itself, and finally, 25% into Treasury bills. If the market risk premium is 5% and the risk free rate is 3%, what's the expected return from this portfolio?
a) 6.75%
b) 7.38%
c) 8.00%
d) 4.75%

A:

The correct answer is: b)
Step 1. Find Portfolio Beta
Beta of the Portfolio
= (.25)(.5)+(.25)(2)+(.25)(1)+(.25)(0)
= 0.125 + 0.5 + 0.25 + 0
= 0.875

Step 2. Find E(R)
E(R) = Rf + B(Rm - Rf)
= 3% + (0.875)(5%)
= 7.38%
Note that the market risk premium is the difference between the expected market return on a market portfolio, and the risk-free rate. In this case, we were given the market risk premium, so further calculation was not needed.
2005 CFA Level 1 LOS: 12.1.D.h


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