Assume a bank currently has net interest income (NII) of $7,000,000. The rates are set for the next year. If interest rates are one percent higher a year from now, the banks NII will fall to $4,500,000. If interest rates are one percent lower a year from now, NII will increase to $9,500,000. The futures price for a T-bond for delivery one year from today is 95-15 ($100,000 face value). If rates go up one percent, it is expected that the T-bond futures price will be 87-25. If rates go down one percent, it is expected that the T-bond futures price will be 103-05.

How would you use futures to hedge the institutions interest rate risk? What is the profit/loss on one contract if rates rise by one percent? SHOW YOUR WORK.

How many contracts would you need to fully hedge your position? SHOW YOUR WORK.

What is the payoff from the combined position (NII plus the profit or loss from the hedge) for a one percent increase in rates?

What is the profit/loss on the futures contracts if rates fall by one percent? SHOW YOUR WORK.

What is the payoff from the combined position (NII plus the profit or loss from the hedge) for a one percent decrease in rates?

Now assume you can purchase a put option on the T-bond future shown above, with an exercise price of 95-15 for a premium of 2-00. How would you use options on interest rate futures to hedge the institutions interest rate risk?

How much would you pay to fully hedge the NII? Show the payoffs from the combined position (net interest income plus the profit or loss from the hedge) for (a) a one percent increase in rates and (b) a one percent decrease in rates.