# Question

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%.

Answer the below questions.

(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?

Answer the below questions.

(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?

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