 ### Hedging with Futures and Options Practice Problem

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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?

How many contracts would you need to fully hedge your position?

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?

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 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 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. .

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

“The values of some stocks are dependent on the bond market. When investors are not interested in junk bonds, the values of stocks ripe for leveraged buyouts decline”. Discuss.

which of the following \$1,000 face-value securities has the lowest yield to maturity?,

a bond which has a yield to maturity greater than its coupon interest rate will sell for a price

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