题目
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.
答案
C
解析
： 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. ： 这道题目问的是投资者以6%的票面利率购买一种年息债券，并以与票面价值相等的价格购买20年直至到期。投资者的投资期限是八年。债券的修正久期约为11.470年。购买时的久期缺口最接近： C是正确的。久期缺口最接近4.158。久期缺口是债券的麦考利久期减去投资期限。麦考利久期的近似值是修正后的久期乘以1再加上到期收益率。它是12.158（=11.470×1.06）。假设投资期限为8年，购买时债券的久期缺口为正：12.158–8=4.158。当投资期限小于债券的麦考利久期时，久期缺口为正，价格风险主导息票再投资风险。