17) A stock is expected to pay a dividend of $1.50 per share in 2 months and 5 months. The stock price is $50, risk free rate is 8%. An investor has taken a long position in a 6 month forward contract on a stock Three months later the price of the stock is $48 and the risk free rate is 8%. What is the forward price ?

18) Suppose you observe that the S&P 500 Index, S, is at a level of 976.67. The riskless rate of interest is 8% per annum and the dividend yield is 4%. a) What is the theoretical futures price of a six month contract?

19) Determine the optimal hedge ratio for Treasury bonds worth $3,000,000 with a modified duration of 12.45, yielding 11.9 percent if the futures has a price of $90,000, and modified duration of 8.5 years ?

22) Assume that the risk-free interest rate is 9% per annum with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August, and November, dividends are paid at a rate of 5% per annum. In other months, dividends are paid at a rate of 2% per annum. Suppose that the value of the index on July 31 is 1,300. What is the futures price for a contract deliverable on December 31 of the same year? (Hint: Take average dividend yield)