Assignment Questions -
Q1. It is now January. The current interest rate is 4%. The June futures price for gold is $1,346.30, while the December futures price is $1,351. Is there an arbitrage opportunity here? If so how would you exploit it?
Q2. The multiplier for a futures contract on the stock-market index is $250. The maturity of the contract is one year, the current level of the index is 800, and the risk-free interest rate is .5% per month. The dividend yield on the index is .2% per month. Suppose that after one month, the stock index is at 810.
a. Find the Cash flow from the mark-to-market proceeds on the contract. Assume that the parity condition holds exactly.
b. Find the one-month holding-period return if the initial margin on the contract is $10,000.
Q3. You are a corporate treasurer who will purchase $1 million bonds for the sinking fund in three months. You believe rates soon will fall and would like to repurchase the company's sinking fund bonds, which are currently selling below par, in advance of requirements. Unfortunately, you must obtain approval from the board of directors for such a purchase, and this can take up to two months.
a. What actions can you take in the futures market to hedge and adverse movements in bond yields and prices until you actually can buy the bonds?
b. Will you be long or short? Why?
Q4. Consider the following information regarding the performance of a money manager in a recent month. The table presents the actual return of each sector of the manager's portfolio column (1), the fraction of the portfolio allocated to each sector in column (2), the benchmark or neutral sector allocations in column (3), and the returns of sector indexes in column (4).
|
Actual
Return
|
Actual
Weight
|
Benchmark
Weight
|
Index
Return
|
|
EQUITY
|
2.5%
|
0.60
|
0.70
|
1.5 %(S&P 500)
|
|
BONDS
|
1.3
|
0.20
|
0.35
|
0.7 (AGGREGATE BOND INDEX)
|
|
CASH
|
1
|
0.20
|
0.5
|
0.5
|
a. What was the manager's return in the month? What was her over- or underperformance?
b. What was the contribution of security selection to relative performance?
c. What was the contribution of asset allocation to relative performance? Confirm that the sum of selection and allocation contributions equals her total "excess" return relative to the bogey.
Q5. Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 9% and 17%, respectively. The beta of A is .9, while that of B is 1.2. The T-bill rate is currently 4%, while the expected rate of return of the S&P 500 index is 12%. The standard deviation of portfolio A is 18% annually, while that of B is 27%, and that of the index is 20%.
a. If you currently hold a market-index portfolio, would you choose to add either of these portfolios to your holdings? Explain.
b. If instead you could invest only in bills and one of these portfolios, which would you choose?
Q6. During a particular year, the T-bill rate was 2.65%, the market return was 6%, and a port-folio manager with beta of 1.5 realized a return of 14%. Evaluate the manager based on the portfolio alpha.
Q7. A corporation has issued a $100 million issue of floating-rate bonds on which it pays an interest rate .75% over the LIBOR rate. The bonds are selling at par value. The firm is worried that rates are about to rise, and it would like to lock in a fixed interest rate on its borrowings. The firm sees that dealers in the swap market are offering swaps of LIBOR for 3%. What swap arrangement will convert the firm's borrowings to a synthetic fixed-rate loan? What interest rate will it pay on that synthetic fixed-rate loan?
Q8. Consider that IBM is trading at $144 and Exxon Mobil is trading at $ 88. In your portfolio you own $2,000,000 of IBM and 7,000,000 of. Exxon Mobil has an annualized volatility of 43 % and IBM's annualized volatility is 18%. The correlation between the two stocks is 33%
Calculate
a. The 10 day 99% Var for each stock
b. The 5 day 95 % Var for the two-stock portfolio
c. The diversification benefit of holding IBM stock at the 99% confidence interval for 10 days
Q9. Bonus Question!
In addition to the above you also own Citi group shares which trade at $78. And have a volatility of 22 % The correlation of Citi to IBM is 17 % and to Exxon Mobil 15 %.
Calculate and explain the diversification benefit of having 3 stocks.
Note Question 8 is mandatory, and then choose another 5.