1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund. The correlation coefficient between the stock and bond fund is 0.15, the probability distributions of the securities are shown below. You can use Excel to do this problem. Security Stock fund (S) Bond fund (B) T-bills (T) Expected return 15% 99 5.5% Standard deviation 32% 23% 0% a. Graph the opportunity set between the stock and bond fund starting with 0% in the stock fund and increasing it to 100% in increments of 10%. At each weight paring show the expected return, standard deviation, and Sharpe ratio of the risky portfolio. b. What is the proportional weight of the risky portfolio in the stock and bond funds which optimizes the expected Sharpe ratio of the risky portfolio? c. What is the proportional weight of the risky portfolio in the stock and bond funds which has the minimum expected variance for the risky portfolio? For this min-variance portfolio what is the expected return and standard deviation of the risky portfolio?
1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund. The correlation coefficient between the stock and bond fund is 0.15, the probability distributions of the securities are shown below. You can use Excel to do this problem. Security Stock fund (S) Bond fund (B) T-bills (T) Expected return 15% 99 5.5% Standard deviation 32% 23% 0% a. Graph the opportunity set between the stock and bond fund starting with 0% in the stock fund and increasing it to 100% in increments of 10%. At each weight paring show the expected return, standard deviation, and Sharpe ratio of the risky portfolio. b. What is the proportional weight of the risky portfolio in the stock and bond funds which optimizes the expected Sharpe ratio of the risky portfolio? c. What is the proportional weight of the risky portfolio in the stock and bond funds which has the minimum expected variance for the risky portfolio? For this min-variance portfolio what is the expected return and standard deviation of the risky portfolio?
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a
long-term government and corporate bond fund, and the third is a T-bill money market fund. The
correlation coefficient between the stock and bond fund is 0.15, the probability distributions of the
securities are shown below. You can use Excel to do this problem.
Security
Stock fund (S)
Bond fund (B)
T-bills (T)
Expected return
15%
99
5.5%
Standard deviation
32%
23%
0%
a. Graph the opportunity set between the stock and bond fund starting with 0% in the stock
fund and increasing it to 100% in increments of 10%. At each weight paring show the
expected return, standard deviation, and Sharpe ratio of the risky portfolio.
b. What is the proportional weight of the risky portfolio in the stock and bond funds which
optimizes the expected Sharpe ratio of the risky portfolio?
c. What is the proportional weight of the risky portfolio in the stock and bond funds which has
the minimum expected variance for the risky portfolio? For this min-variance portfolio what
is the expected return and standard deviation of the risky portfolio?
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