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小熊猫 · 2023年02月08日

duration gap

NO.PZ2016031001000132

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。

这提问的是duration gap at purchase 不应该是duration - 20吗?(买的时候还有20年到期)

1 个答案

吴昊_品职助教 · 2023年02月08日

嗨,从没放弃的小努力你好:


investment horizon是指投资期,而不是债券的期限。The investor’s investment horizon is eight years. 所以投资期是八年。

比如一个五年期的债券,只持有三年就卖出,那么maturity期限是五年,而investment horizon投资期是三年。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!