Question

An FI has a $230 million asset portfolio that has an average duration of 6.8 years. The average duration of its $190 million in liabilities is 4.3 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 7.3 years. The current market value of the T-bonds is $96,000. 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 10 percent? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616))

  Modified duration years

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.)

  Number of contracts   

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.)

  Change in equity value $   

d.

If interest rates increase 50 basis point, 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.)

  Change in T-bond value $   

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? (Do not round intermediate calculations. Negative value should be indicated by a minus sign. Round your answer to 2 decimal places. (e.g., 32.16))

  Change in interest rates %

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))

  Change in interest rates %

Answer 1

a) Modified duration = duration / (1+ YTM/n) = 7.3 / (1 + 0.10/2) = 6.952 years

b) No. of contracts = (Duration of Assets - k * Duration of Liabilities ) * Value of Assets/ (Delta of option * Duration of T Bond * Market value of the T Bond)

= (6.80 - (190/230)*4.3)*230000000/ (0.3*7.3*96000) = 3553.082 contracts

c) Duration gap = Duration of Assets - (Liabilities/ Assets* Duration of Laibilites) = (6.80 - (190/230)*4.3) = 3.247

Change in Networth = - duration gap * change in interest rate / (1+ interest rate) = -3.247 * 0.005/ (1+ 0.1)=1.4763%

Change in networth = 230 million * 1.4763% = 3395455