BMAN20072 Investment Analysis 2021/22 Semester 2 Week 2 Problem Set
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BMAN20072 Investment Analysis 2021/22 Semester 2
Week 2 Problem Set
Topic: Optimal Risky Portfolios and Markowitz Portfolio Optimisation
Part A. Non-numerical questions
2.A.1 Diversification
Suppose your risky portfolio consists of two perfectly negatively correlated risky assets. Draw the portfolio opportunity set and optimized capital allocation line with standard deviation in horizontal axis and expected return in vertical axis and indicate the optimal risky portfolio (e.g. slide 18 of Week 2- 1 lecture slides). Suppose that the risk-free rate is 2%. What would be the expected return of this optimal risky portfolio?
2.A.2 Optimal Risky Portfolio and Complete Portfolio
Consider the optimal risky and optimal complete portfolio in slide 20 of Week 2- 1 lecture slides. Suppose risk free rate has decreased from 5% to 1%, and the investor wants to maintain the same utility level under the new risk-free rate. If the investor could extend their opportunity set of risky assets, what would be the characteristics of the risky assets now included in the extended opportunity set. Explain and show in the figure.
2.A.3 Separation Property
What is a separation property and its benefit? Explain. If there are no risk-free assets in the market, how would portfolio managers design an optimal risky portfolio?
Part B. Numerical questions
2.B.1
A pension fund manager is considering a stock fund, a long-term bond fund, and a risk free government bond that yields 8%. The correlation between stock and bond funds is 0.10. Their expected return and standard deviation are as follows:
|
Expected return |
Standard deviation |
|
|
Stock fund Bond fund |
20% 12% |
30% 15% |
a) Solve for the proportion of each asset and for the expected return and standard deviation of the optimal risky portfolio.
b) What is the Sharpe ratio of the best feasible CAL?
c) If you require that your portfolio yield an expected return of 14% and that it be efficient on the best feasible CAL
i. what is the standard deviation of your portfolio?
ii. what is the proportion invested in the risk-free government bond and each of the two risky funds?
2.B.2
You are considering to form a risky portfolio consists of three stocks, A, B and C. Their expected excess returns, standard deviations and correlations are summarized in the below tables.
Expected excess returns and Standard deviations
|
|
Expected excess returns |
Std. Dev. |
|
Stock A |
0.02 |
0.04 |
|
Stock B |
0.03 |
0.05 |
|
Stock C |
0.04 |
0.06 |
Correlation matrix
|
|
A |
B |
C |
|
A |
1 |
0.1 |
0.2 |
|
B |
0.1 |
1 |
0.5 |
|
C |
0.2 |
0.5 |
1 |
Suppose you are considering below two portfolios X and Y.
|
Weights |
X |
Y |
|
A |
0.5 |
0.2 |
|
B |
0.3 |
0.3 |
|
C |
0.2 |
0.5 |
Which one is the better portfolio? X or Y?
2022-07-18