Question

An Fl has a $290 million asset portfolio that has an average duration of 8.0 years. The average duration of its $250 million in liabilities is 6.6 years. Assets and liabilities are yielding 9 percent. The Fl uses put options on T-bonds to hedge against unexpected interest rate increases. The average delta (d) of the put options has been estimated at -0.1 and the average duration of the T-bonds is 8.5 years. The current market value of the T-bonds is $91,000. Put options on T-bonds are selling at a premium of $1.10 per face value of $100. a. What is the modified duration of the T-bonds if the current level of interest rates is 9 percent? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616)) b. How many put option contracts should the Fl purchase to hedge its exposure against rising interest rates? The face value of the T- bonds is $100,000. (Do not round intermediate calculations. Round your answer to the nearest whole number.) c. If interest rates increase 50 basis points, what will be the change in value of the equity of the Fl? (Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to the nearest dollar amount.)

Answer 1

Answer:-

a) MD = D/(1+0.09) = 8.5/1.09 = 7.798 years

7.798 years is modified duration (MD) of the T-bonds if the current level of interest rates is 9 percent.

D =  the average duration of the T-bonds is 8.5 years

b)

N_p = {[8 - 6.6(.80)]×290,000,000}/[(-0.1)( - 8.5)×91,000]

N_p =324,800,000/77,350

N_p = 4199 contracts

c) Assuming R for the assets is similar to R for the underlying bonds, the change in equity value is

DGAP*A*((R/(1+R)) = -2.9($290,000,000)(.005/1.09) = -$3,868,600

d)P = Np(*-MD*B*R) = 4199[(-0.1) *(-7.798)*$91,000*0.005 = $1,489,842.991 gain

As HOMEWORKLIB RULES rule we can give answer for four option only