Although short-term interest rate risk is a concern to some investors, other investors have a long-term horizon. Day-to-day changes in bond prices cause unrealized capital gains and losses. A long-term investor is concerned mostly with the total return over the investment horizon. The investor considers both coupon reinvestment risk as well as market price risk in case the bond needs to be sold before the maturity.

The buy-and-hold investor has a higher total return if interest rates rise and a lower total return if rates fall. When interest rates rise, duration measures the immediate drop in value or price. Then, as time passes, the bond price is “pulled to par.” At some point in the lifetime of the bond, those two effects offset each other, and the gain on reinvested coupons is equal to the loss on the sale of the bond. That point is the Macaulay duration statistic.

Here’s the general relationship among interest rate risk (Int_rate), the Macaulay duration (Mac_Dur), and investment horizon (Inv_Hor):

- Inv_Hor > Mac_Dur; coupon reinvestment risk dominates market price risk. Investor’s risk is to lower interest rates.
- Inv_Hor = Mac_Dur; coupon reinvestment risk offsets market price risk.
- Inv_Hor < Mac_Dur; market price risk dominates coupon reinvestment risk. Investor’s risk is to higher interest rates.

The difference between the Macaulay duration of a bond and investment horizon is called the duration gap. Duration gap = (Macaulay Duration) – (Investment horizon)

As time passes, the investment horizon is reduced, the Macaulay duration of the bond also changes, and so does the duration gap.

QuestionAssume that an investor plans to retire in 10 years. The investor buys a newly issued, 10-year, 8% annual coupon payment bond. Macaulay duration is 8.6 years. What is the duration gap at the time of purchase?

A. -1.400

B. -1.425

C. -1.525

SolutionThe correct answer is A.

As the investment horizon is 10 years, duration gap for this bond at the time of purchase is negative.

8.6 – 10 = -1.400

*Reading 54 LOS 54k:*

*Describe the relationships among a bond’s holding period return, its duration, and the investment horizon*