Duration is the average time to receipt of the cash flows, weighted by the present value of each cash flow in proportion to the total price of the bond. Other factors held constant, the higher the yield, the lower the PV of a cash flow, therefore, a shorter duration. The greater the frequency of the cash flow, the shorter the duration, because the time to receipt of the cash flows is less. The largest single cash flow is at maturity, and, thus, the maturity has the most effect upon duration. We know Bond 3 has a duration of 10 because it’s a zero-coupon bond. In this question, the bond with the shortest duration would be Bond 5 because its maturity is shorter than the other 6% coupon bonds. The second shortest duration would be Bond 2 because its yield is equal to the highest (6%), and it has the highest frequency (2) of the 6% bonds. Next would be Bond 1 because it also has the 6% yield but a frequency of 1. Bond 4 would come next, because although it has the same cash flows as Bond 1, these would be discounted at the lower yield of 5%. The longest duration would be Bond 3, which is a zero-coupon bond. |
