Suppose that bond ABC is the underlying asset for a futures contract with settlement six months from now. You know the following about bond ABC and the futures contract: (1) in the cash market, ABC is selling for $80 (par value is $100); (2) ABC pays $8 in coupon interest per year in two semiannual payments of $4, and the next semiannual payment is due exactly six months from now; and (3) the current six-month interest rate at which funds can be loaned or borrowed is 6%.
a. What is the theoretical futures price?
b. What action would you take if the futures price is $83?
c. What action would you take if the futures price is $76?
d. Suppose that bond ABC pays interest quarterly instead of semiannually. If you know that you can reinvest any funds you receive three months from now at 1% for three months, what would the theoretical futures price for six-month settlement be?
e. Suppose that the borrowing rate and lending rate are not equal. Instead, suppose that the current six-month borrowing rate is 8% and the six-month lending rate is 6%. What is the boundary for the theoretical futures price?