An Fl 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 Fl uses put options on T-bonds to hedge against unexpected interest rate increases. The average delta (5) 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? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) 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. (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 FI? (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.) d. If interest rates increase 50 basis points, what will be the change in value of the T-bond option hedge position? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.) 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? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) f. How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) a. Modified duration b. Number of contracts c. Change in equity value d. Change in T-bond value e. Change in interest rates 2.00 years % f. Change in interest rates %

Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Question

Please help with with this assignment. "a-f". Thank you.

 

 

An Fl 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 Fl uses put options on T-bonds to hedge against
unexpected interest rate increases. The average delta (5) 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? (Do not round
intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))
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. (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 FI? (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.)
d. If interest rates increase 50 basis points, what will be the change in value of the T-bond option hedge position? (Enter
your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar
amount.)
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? (Negative value should be indicated by a minus sign. Do not round intermediate calculations.
Round your answer to 2 decimal places. (e.g., 32.16))
f. How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge?
(Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))
a. Modified duration
b. Number of contracts
c. Change in equity value
d. Change in T-bond value
e. Change in interest rates
2.00 years
%
f. Change in interest rates
%
Transcribed Image Text:An Fl 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 Fl uses put options on T-bonds to hedge against unexpected interest rate increases. The average delta (5) 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? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) 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. (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 FI? (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.) d. If interest rates increase 50 basis points, what will be the change in value of the T-bond option hedge position? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.) 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? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) f. How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) a. Modified duration b. Number of contracts c. Change in equity value d. Change in T-bond value e. Change in interest rates 2.00 years % f. Change in interest rates %
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