Assignment: Investment Management
SECTION A
Answer ALL questions.
1. There are three assets. Their expected returns, and variances of returns, are described in the table below. The returns on the assets are uncorrelated.
|
|
Expected Return: E(R)
|
Variance of Returns: σ2
|
|
Asset 1
|
0.2
|
0.24
|
|
Asset 2
|
0.24
|
0.6
|
|
Asset 3
|
0.04
|
0
|
a. Plot the assets in the expected return/variance space.
b. Find the optimal risky portfolio, and calculate its expected return and the variance of its returns.
c. Then suppose that an investor's preferences are given by the mean-variance utility function:
U = 3 E(R) - 5σ2
Find the optimal portfolio for this investor.
2. The Bank of England conducted an auction for selling its latest issue of government gilts. The table below gives the selling prices of the gilts for different maturities. All of them are zero coupon gilts and they are expected to pay £1,000 on maturity.
|
Guilt Duration
|
1 Year
|
2 Year
|
3 Year
|
5 Year
|
10 Year
|
|
Auction Price
|
£ 961.54
|
£ 898.63
|
£ 847.77
|
£ 799.10
|
£ 760.32
|
a. Derive and plot the bond yield curve implied by the above prices, assuming that if no bond expires at a specific year then the yield remains the same.
b. What information could an analyst obtain from the above yield curve?
3. Suppose that the returns of the assets in the table below are derived by the two-factor mode
Ri = ai + b1iI1 + b2iI2 + εi
Suppose that the first factor has an expected rate of return of I1=5% and a standard deviation σ1=3%. The second factor has an expected rate of return of I2=12% and a standard deviation σ2=5%. The returns between the two factors and the returns between the idiosyncratic component of each asset and each factor are uncorrelated. The risk-free rate of return is RF = 2%.
|
|
αi
|
b1i
|
b2i
|
σεi
|
|
Asset 1
|
0.4%
|
0.3
|
0.5
|
22%
|
|
Asset 2
|
1.4%
|
0.2
|
0.1
|
9%
|
|
Asset 3
|
-3.0%
|
2.2
|
-0.3
|
4%
|
|
Asset 4
|
3.4%
|
-1.2
|
0.5
|
10%
|
|
Asset 5
|
3.0%
|
2.1
|
0.4
|
29%
|
a. Rank the above assets according to the Sharpe ratio from the most to the least desirable.
b. Do you spot any arbitrage opportunity? If so, how would you exploit it?
SECTION B
Answer ONE of the following questions. Each question carries a weight of 40 marks. If you answer more than one question, only the worst answer will be credited to you.
4. Explain the main differences between CAPM, Markowitz's theory of portfolio selection and the Single-Index model.
5. If you were a hedge-fund manager, what arguments would you use to convince your prospective clients to invest in your company rather than pursue a passive investment strategy?
6. What are the main valuation approaches for equities and under what conditions are they valid?
Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.