Longest Duration Bond

C

Duration is a measure of the sensitivity of the bond price to changes in interest rates. It takes into account both the time to maturity of the bond and the size of the coupon payments.

In general, a bond with a longer maturity will have a longer duration, and a bond with a higher coupon will have a shorter duration. This is because a higher coupon payment reduces the present value of the bond's future cash flows, making the bond less sensitive to changes in interest rates.

Using this information, we can analyze the given bonds and determine which one has the longest duration:

A. 5 year, 10 percent coupon bond This bond has a relatively high coupon payment, which means it will have a shorter duration than a bond with a lower coupon payment. Additionally, its shorter maturity also contributes to a shorter duration.

B. 5 year, 15 percent coupon bond This bond has an even higher coupon payment than the previous bond, which means it will have an even shorter duration. Its shorter maturity also contributes to a shorter duration.

C. 10 year, zero percent coupon bond This bond has a longer maturity than the previous two bonds, which means it will have a longer duration. Additionally, because it has no coupon payments, all of its value is derived from the final principal payment at maturity. This makes it very sensitive to changes in interest rates, which also contributes to a longer duration.

D. 10 year, 10 percent coupon bond This bond has the longest maturity of all the bonds, which means it will have the longest duration. However, its relatively high coupon payment will reduce its duration somewhat compared to the zero coupon bond.

Therefore, the bond with the longest duration is C. 10 year, zero percent coupon bond.