duration gap

问题如下：

An investor purchases an annual coupon bond with a 6% coupon rate and exactly 20 years remaining until maturity at a price equal to par value. The investor’s investment horizon is eight years. The approximate modified duration of the bond is 11.470 years. The duration gap at the time of purchase is closest to:

选项：

A.

-7.842.

B.

3.470.

C.

4.158.

解释：

C is correct.

The duration gap is closest to 4.158. The duration gap is a bond’s Macaulay duration minus the investment horizon. The approximate Macaulay duration is the approximate modified duration times one plus the yield-to-maturity. It is 12.158 (= 11.470 × 1.06).

Given an investment horizon of eight years, the duration gap for this bond at purchase is positive: 12.158 – 8 = 4.158. When the investment horizon is less than the Macaulay duration of the bond, the duration gap is positive, and price risk dominates coupon reinvestment risk.

考点：duration gap

解析：duration gap = Macaculay duration - investment horizon = Modified duration × (1+y) - investment horizon = 11.470 × 1.06 - 8 = 4.1582，故选项C正确。