Consider a futures contract to purchase a coupon-bearing bond whose current price is $875. The futures contract matures in 15 months and the bond matures in 4 years. The bond holder receives an annual coupon of $60 paid semiannually and the next coupon will be paid in 3 months. Thus, if we want to take a long position in the futures on this bond we will have to take into account three coupons until the maturity of the futures (the last coupon will be paid immediately prior to the delivery date). We can borrow and lend money at the following continuously compounded interest rates:
• R3 = 7% per annum for 3 months
• R9 = 9% per annum for 9 months
• R10 = 10% per annum for 10 months
• R15 = 11% per annum for 15 months
Assume that the futures price and the spot price follow the futures-spot parity condition.
a) If the futures price is $905 will you be able to benefit from these prices? If a profit is possible then present the strategy that you can use to obtain this profit.
b) What if the futures price is $910? Can you make any profit? describe how.