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 (ö) 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 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? (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)) 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))

Answer 1

1. What is the modified duration of the T-bonds if the current level of interest rates is 9 percent? MD= D/1+.09 = 8.5/1.09 = 9.2650 years 2.How many put option contracts should FI purchase to hedge its exposure against rising interest rates? The face value of the T-bonds is $100,000. _IDA-KD/A N,= S*-D*B = [8.0-6.66.86)]*$290,000,000/[(-.1)*(-8.5)*(91,000)] = 8,713.1222 or 8,713 contracts 3.If interest rates increase 50 basis points, what will be the change in value of the equity of the FI? DGAP = 8 - (250/290)*6.6 = 2.31 Assuming R for the assets is similar to R for the underlying bonds, the change in equity value is -DGAP*A"(AR/(1+R)) = -2.31*($290,000,000) "0.005/1.09) = -$3,072.935.77 4.What will be the change in value of the T-bond option hedge position? AP = Np(8*-MD BAR) = 8,713*(-.1*-9.2650*$91,000*0.005) = 3,673,030.50 gain 5. 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? Premium on the put options = 8713*1.10"1000 = $9,584,300 AR = $9,584,300*1.09/($290,000,000-2.31) = -0.01559 or -1.56 percent 6.How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge? Use the equation in part (4) above and solve for AR. Then AR = $9,584,300/[8,713-1*-9.2650*$91,000] = 0.01304 or 1.30 percent

1. What is the modified duration of the T-bonds if the current level of interest rates is 9 percent? MD= D/1+.09 = 8.5/1.09 = 9.2650 years 2.How many put option contracts should FI purchase to hedge its exposure against rising interest rates? The face value of the T-bonds is $100,000. _IDA-KD/A N,= S*-D*B = [8.0-6.66.86)]*$290,000,000/[(-.1)*(-8.5)*(91,000)] = 8,713.1222 or 8,713 contracts 3.If interest rates increase 50 basis points, what will be the change in value of the equity of the FI? DGAP = 8 - (250/290)*6.6 = 2.31 Assuming R for the assets is similar to R for the underlying bonds, the change in equity value is -DGAP*A"(AR/(1+R)) = -2.31*($290,000,000) "0.005/1.09) = -$3,072.935.77 4.What will be the change in value of the T-bond option hedge position? AP = Np(8*-MD BAR) = 8,713*(-.1*-9.2650*$91,000*0.005) = 3,673,030.50 gain 5. 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? Premium on the put options = 8713*1.10"1000 = $9,584,300 AR = $9,584,300*1.09/($290,000,000-2.31) = -0.01559 or -1.56 percent 6.How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge? Use the equation in part (4) above and solve for AR. Then AR = $9,584,300/[8,713-1*-9.2650*$91,000] = 0.01304 or 1.30 percent