Response to the following problem:
An FI has a $200 million asset portfolio that has an average duration of 6.5 years. The average duration of its $160 million in liabilities is 4.5 years. Assets and liabilities are yielding 10 percent. The FI uses put options on T-bonds to hedge against unexpected interest rate increases. The average delta () of the put options has been estimated at 0.3 and the average duration of the T-bonds is seven years. The current market value of the T-bonds is $96,000. Put options on T-bonds are selling at a premium of $1.25 per face value of $100.
a. What is the modified duration of the T-bonds if the current level of interest rates is 10 percent?
b. How many put option contracts should the FI purchase to hedge its exposure against rising interest rates? The face value of the T-bonds is $100,000.
c. If interest rates increase 50 basis points, what will be the change in value of the equity of the FI?
d. If interest rates increase 50 basis point, what will be the change in value of the T-bond option hedge position?
e. What must be the change in interest rates before the change in value of the balance sheet (equity) will offset the cost of placing the hedge?
f. How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge?