Hedging with Futures and Options – Practice Problem

Hedging with Futures and Options – Practice Problem

Assume a bank currently has net interest income (NII) of $4,000,000. The rates are set for the next year. If interest rates are one percent higher a year from now, the bank’s NII will fall to $2,875,000. If interest rates are one percent lower a year from now, NII will increase to $5,125,000.
The futures price for a T-bond for delivery one year from today is 98-12 ($100,000 face value). If rates go up one percent, it is expected that the T-bond futures price will be 95-18. If rates go down one percent, it is expected that the T-bond futures price will be 101-06.
How would you use futures to hedge the institution’s 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? SHOW YOUR WORK.

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? SHOW YOUR WORK.

Now assume you can purchase a put option on the T-bond future shown above, with an exercise price of 98-12 for a premium of 1-00.
How would you use options on interest rate futures to hedge the institution’s interest rate risk?

How much would you pay to fully hedge the NII? SHOW YOUR WORK.

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 (b) a one percent decrease in rates and (c) no change in rates. SHOW YOUR WORK.

Based on your answers, when would it be better to hedge with options than futures?

Hedging with Futures and Options – Practice Problem
Assume a bank currently has net interest income (NII) of $4,000,000. The rates are set for the next year. If interest rates are one percent higher a year from now, the bank’s NII will fall to $2,875,000. If interest rates are one percent lower a year from now, NII will increase to $5,125,000.
The futures price for a T-bond for delivery one year from today is 98-12 ($100,000 face value). If rates go up one percent, it is expected that the T-bond futures price will be 95-18. If rates go down one percent, it is expected that the T-bond futures price will be 101-06.
How would you use futures to hedge the institution’s interest rate risk? Sell T-bond futures.
What is the profit/loss on one contract if rates rise by one percent? SHOW YOUR WORK.
Profit of $2,812.50.

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

What is the payoff from the combined position (NII plus the profit or loss from the hedge) for a one percent increase in rates? SHOW YOUR WORK.
$4,000,000

What is the profit/loss on the futures contracts if rates fall by one percent? SHOW YOUR WORK.
Loss of $2,812.50.

What is the payoff from the combined position (NII plus the profit or loss from the hedge) for a one percent decrease in rates? SHOW YOUR WORK.
$4,000,000

Now assume you can purchase a put option on the T-bond future shown above, with an exercise price of 98-12 for a premium of 1-00.
How would you use options on interest rate futures to hedge the institution’s interest rate risk?
Buy put options on T-bond futures.
How much would you pay to fully hedge the NII? SHOW YOUR WORK.
$400,000

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 (b) a one percent decrease in rates and (c) no change in rates. SHOW YOUR WORK.
(a) $3,600,000

(b) $4,725,000

(c) $3,600,000

Based on your answers, when would it be better to hedge with options than futures?