Question

Problem 6:

You have an investment horizon of 10 years. Which of the following has more interest rate risk?

(1) Invest in a 12-year zero and sell it after 10 years.

(2) invest in a 10-year sequence of 1-year zeros (when one 1-year zero matures, roll the money over into the next one-year zero, for 10 years).

Explain your answer.

Answer 1

Option 1 has more interest rate risk: (1) Invest in a 12-year zero and sell it after 10 years.

zero coupon bonds pay no interest. they have only one cash flow par value of bond which is paid at maturity. so, duration of a zero coupon bond is equal to its maturity.

if you hold the zero till its maturity then you will certainly get its par value. but if you sell it before its maturity then depending at market interest rate at that time price of the bond could be higher or lower than your purchase price.

1-year zeros have duration of 1 year only and at maturity you will certainly get its par value. it has less interest rate risk because duration is lower and you are holding the bond till maturity. also there is a high probability of volatile interest rate in 12 years than in 1-year.