Show all work please! 32. There are only two assets available to investors: 1) A
ID: 2794472 • Letter: S
Question
Show all work please!
32. There are only two assets available to investors: 1) A stock fund with an expected return of 12% and a return standard deviation of 20%; and 2) A bond fund with an expected return of 7% and a return standard deviation of 8%. The correlation between the stock fund’s return and the bond fund’s return is -0.2. Mary is a risk-averse investor. Answer the following questions:
a. If Mary invests 5% of her portfolio wealth in the stock fund and 95% in the bond fund (She invests nothing in the risk free asset). What is the expected return and standard deviation of her portfolio?
b. If Mary invests 100% of her portfolio wealth in the bond fund, what is the expected return and standard deviation of her portfolio?
c. Which portfolio between a) and b) would Mary prefer? Explain your answer.
Explanation / Answer
Answer a) Portfolio Return =
(Weight of stock fund x return on stock fund ) + Weight of bond fund x return on bond fund)
= (0.05*0.12)+(0.95*0.07) = 7.25%
Portfolio Standard deviation = [(Weight of stock fund x St.d on stock fund )^2 + (Weight of bond fund x St.d on bond fund) + (2*Weight of stock fund x St.d on stock fund xWeight of bond fund x St.d on bond fund) ]^1/2
Porfolio st. deviation = [(0.0001) +(0.005776)-0.0003]^1/2 = [0.005572]^1/2 = 7.465%
Answer b) If 100% is invested in bond fund the porfolio st. deviation and return will equla bond fund return and st. deviation ie 7% and 8%
Answer c) Out of the two opton I will prefer the first option because in option 1 we have a higher return and lower st.deviation as compared to option of 100% bond fund.The st. devaition of portfolio reduces because the bonds and stocks are negatively correlated.Hence we get the diversification benefit in option 1.