Question

Which of the following investments has the lowest duration? Assume time to maturity are fixed at 10 years for all investment.

a) A zero-coupon bond with 20% yield to maturity

b) A 15% annual coupon paying bond with 6% yield to maturity

c) A 3% annual coupon paying bond with 15% yield to maturity

d) A 15% annual coupon paying bond with 15% yield to maturity

Answer 1

Option - (d)......... A 15% annual coupon paying bond with 15% yield to maturity.

Explanation:-

Option - (a) is WRONG

Zero - coupon bond will always have highest bond duration. Discounting rate of 20% is highest among the given options hence, we can safely eliminate this option.

Option - (c) is WRONG

Investments with lower coupon will have higher duration. Hence this is a wrong option

Now, between, (b) and (d)

Having a high coupon will decrease the bond duration. In (b) and (d) we have same coupon amounts but they are discounted at 6% or 15%. Discounting at a higher rate will decrease the bond duration compared a lower discount rate. Because, initial years will receive a higher weight compared to last years with higher rate of discounting ( ytm).

Thus .................Final answer should be ...............Option - (d)