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Duncan Manz believes that he has found an error in a sample CFA Study Program question. Prior to e- mailing the provider about the error, he discusses his logic with Julia Cook, a fellow finance student at the Hess School of Business. Manz does not believe that the following question provides enough information to completely answer the question. Cook disagrees. Who is correct ?Manz or Cook? And, if Cook is correct, what is the correct answer?
Question: An investor抯portfolio currently consists of 100% of stocks that have a mean return of 18 percent and an expected variance of 0.0625. The investor plans to diversify slightly by replacing 30 percent of her portfolio with U.S. Treasury bills that earn 4.25 percent. Assuming the investor diversifies, what are the expected return and expected standard deviation of the portfolio?
A. Cook is correct. The portfolio's expected return is 18.000% and the expected standard deviation is
B. Manz is correct. There is not enough information to completely answer the question.
C. Cook is correct. The portfolio's expected return is 13.875%and the expected standard deviation is
D. Cook is correct. The portfolio's expected return is 13.875% and the expected standard deviation is
Cook is correct. Since Treasury bills (T-bills) are consideredrisk-free, we know that the standard deviation of this asset and the correlation between T-bills and the other stocks is 0. Thus, we can calculate the portfolio expected return and standard deviation.
Step 1: Calculate the expected return:
Expected ReturnPortfolio= (wT-bills* ERT-bills) + (wStocks* ERStocks)= (0.30) * (0.0425) + (1.00 - 0.30) * (0.18) = 0.13875, or 13.875%.
Step 2: Calculate the expected standard deviation:
When combining a risk-free asset and a risky asset (or portfolio of risky assets), the equation for the standard deviation ofꢀ1,2= [(w12)(ꢀꢀ12) + (w22)(ꢀꢀ22) + 2w1w2ꢀ1ꢀ2r1,2]1/2reduces to:ꢀPortfolio= [(wStocks)(ꢀꢀStocks)] = 0.70 * 0.06251/2= 0.17500, or 17.500%. (Remember to convert variance to standard deviation.)