Use the following information to answer parts A-D: Expected return Standard devi
ID: 2801985 • Letter: U
Question
Use the following information to answer parts A-D:
Expected return Standard deviation Bond fund 8% 5% Stock fund 16% 13% Assume the correlation between the two funds is 0.25, the covariance is 35.7, T-bills have a return of 5%, and the optimal portfolio will have an investment of 40% in bonds and 60% in stocks.
A) What is the expected return and standard deviation for the optimal portfolio?
B) What is the Sharpe Ratio for the optimal portfolio?
C) Calculate the standard deviation if the client wanted to achieve an expected return of 10%.
D) To target the 10% return, what proportion of the portfolio would be invested in T-bills, the stock fund and the bond fund?
Expected Return Standard Deviation Bond Fund 8% 5% Stock Fund 16% 13%Explanation / Answer
a)
Expected Returns of the portfolio, E(R) = w1 x R1 + w2 x R2 = 12.80%
Std. Dev. = [(w1 x SD1)^2 + (w2 x SD2)^2 + (2 x w1 x w2 x SD1 x SD2 x corr12)]^(1/2) = 8.52%
where corr12 - correlation between two funds = 0.25
b) Sharpe Ratio = (E(R) - Rf) / SD = (12.80% - 5%) / 8.52% = 0.915
c&d) In order to find standard deviation, we need to find the weights so that the return from the portfolio is 10% using excel solver.
With 75% in investment in Bond and 25% in Stock, we get standard deviation = 5.54%
E(R) SD Weight Bond (B) 8% 5% 40% Stock (S) 16% 13% 60% Portfolio 12.80% 8.52%