5. An insurance company owns a 30-year Treasury bond with a 4.75% coupon rate. The bond has a $100,000 face value and pays its coupon semiannually. Its duration is 16.7891, current market price is $107,700 and its current yield to maturity is 4.29%. The insurance company is concerned that interest rates may increase by 82 basis points. Treasury bond futures on the same bond are currently available with a price of 119.56. a. If interest rates rise by 82 basis points, what will be the impact on the insurance company's Treasury bond value? Will it increase or decrease in value? By how much? Support your answer with appropriate calculations. (4 points) b. If the insurance company hedges its position in the Treasury bond with a Treasury future, what position should it take in the future? Why? (3 points) 2 c. Suppose interest rates rise by the expected 82 basis points and the insurance company has hedged its position as you recommend in b. Calculate the net value of the hedge after the increase in interest rates. (6 points)