5. DURATION OF INVERSE FLOATERS Assume that LIBOR rates are risk free. Suppose you have a 10 year note that pays a quarterly coupon of (10% 2 x 3mo LIBOR), divided by 4 since this is a quarterly coupon. Such a note is called an inverse floater. Suppose the face value is $100, the first LIBOR amount has not yet been fixed, and a flat rate curve of 4% quarterly compounded. (a) What is the price of the bond? (Hint: Replicate with floating rate bonds, coupon bonds and zero coupon bonds). (b) What is the modified duration? (Hint: Find price as a function of interest rate, and take the derivative). (c) Compare the modified duration to the maturity. Do you find this surprising? 5. DURATION OF INVERSE FLOATERS Assume that LIBOR rates are risk free. Suppose you have a 10 year note that pays a quarterly coupon of (10% 2 x 3mo LIBOR), divided by 4 since this is a quarterly coupon. Such a note is called an inverse floater. Suppose the face value is $100, the first LIBOR amount has not yet been fixed, and a flat rate curve of 4% quarterly compounded. (a) What is the price of the bond? (Hint: Replicate with floating rate bonds, coupon bonds and zero coupon bonds). (b) What is the modified duration? (Hint: Find price as a function of interest rate, and take the derivative). (c) Compare the modified duration to the maturity. Do you find this surprising