[Hedge Equity Portfolio] It is July 16. A company has a portfolio of stocks worth $12million. The beta of the portfolio is 1.5. The company would like to use the CME Decemberfutures contract on the S&P 500 to change the beta of the portfolio to 1.2 during the periodJuly 16 to November 16. The index futures price is currently 1 000 and each contract is on$250 times the index.1.(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 ofthe 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 is12% per annum with continuous compounding.a)What are the forward price and the initial value of the forward contract? (2pts)Six months later the price of the stock is $46 and the risk-free interest rate is still12%. What are the forward price and the value of the forward contract? (2-2pts)b)3. [Future Valuation with Dividend Income] A stock index currently stands at 340. Therisk-free interest rate is 9% per annum (with continuous compounding) and the dividendyield 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. Thestorage costs are $0.24 per ounce per year payable quarterly in advance. Assuming thatinterest rates are 10% per annum for all maturities calculate the futures price of silver fordelivery in 9 months.5. [Future Evaluation with Varying Interest Rate] An index is 1 200. The three-monthrisk-free rate is 3% per annum and the dividend yield over the next three months is 1.2% perannum. The six-month risk-free rate is 3.5% per annum and the dividend yield over the nextsix months is 1% per annum. Estimate the futures price of the index for three-month and six-Article From Yahoo! Finance Education Center month contracts. All interest rates and dividend yields are continuously compounded.(Hint:Match the risk-free rate with the dividend yield and corresponding maturity)Article From Yahoo! Finance Education Center
