Problem: Suppose the annual yield to maturity on a 1 year zero coupon bond is 2 %, a 2 year zero coupon bond is 3 %, and a 3 year zero coupon bond is 4 %.
(a) Consider a bond of face value 10,000 that pays a 5 % coupon payment on years 1, 2, and 3. It also repays the face value on year 3 in addition. What is the fundamental value of this bond? Does it trade at a discount or premium? Is there a way you could have known whether it traded at a discount or premium without computing its fundamental value?
(b) Suppose the bond is priced at its fundamental value. What is the bond's Macauley duration and modified duration?
(c) Imagine the bond's yield to maturity decreased by a small amount. What would be the percentage change in the bond's price? Is this greater or less than the percentage change in a 3 year zero coupon bond's price if its yield to maturity decreased by the same amount (if it had the same initial yield to maturity)? Why?