1. [Hedge Equity Portfolio]It is July 16. A company has a portfolio of stocks worth $12 million. The beta of theportfolio is 1.5. The company would like to use the CME December futures contract onthe S&P 500 to change the beta of the portfolio to 1.2 during the period July 16 toNovember 16. The index futures price is currently 1,000 and each contract is on $250 timesthe index.
(a) What position should the company take?(2pts)
(b) On Nov. 1st, the level of S&P 500 is 1200 and the futures price is 1203. What is value of the position taken in (a) ?(6pts)
(c) Suppose that the company changes its mind and decides to increase the beta of theportfolio from 1.5 to 1.7. What position in futures contracts should it take?(2pts)
2. [Forward Valuation w/ No Income] A 1-year long forward contract on a non-dividend-paying stock is entered into when the stock price is $40 and the risk-free rate of interest is 12% per annum with continuous compounding.
a) What are the forward price and the initial value of the forward contract?(2pts)
b) Six months later, the price of the stock is $46 and the risk-free interest rate is still 12%. What are the forward price and the value of the forward contract? (2-2pts)
3. [Future Valuation with Dividend Income]A stock index currently stands at 340. The risk-free interest rate is 9% per annum (with continuous compounding) and the dividend yield on the index is 5% per annum. What should the futures price for a 4-month contract be?
4. [Future Valuation with Storage Cost]The spot price of silver is $15 per ounce. The storage costs are $0.24 per ounce per yearpayable quarterly in advance. Assuming that interest rates are 10% per annum for allmaturities, calculate the futures price of silver for delivery in 9 months.
5. [Future Evaluation with Varying Interest Rate]An index is 1,200. The three-month risk-free rate is 3% per annum and the dividend yieldover the next three months is 1.2% per annum. The six-month risk-free rate is 3.5% perannum and the dividend yield over the next six months is 1% per annum. Estimate the futures price of the index for three-month and six-month contracts. All interest rates and dividend yields are continuously compounded.(Hint: Match the risk-free rate with the dividend yield and corresponding maturity)