一个疑问

问题如下：

An investor purchases a five-year, 4% annual coupon bond for 104.58 and sells it exactly three years later. Immediately after the bond is purchased and before the first coupon is received, interest rates decline to 2.25%, and they remain at that level for the next three years. Assuming that the coupon payments are received and reinvested at 2.25%, the investor’s realized horizon yield is closest to:

选项：

A.2.26%. B.2.31%. C.3.41%.

解释：

C is correct.

The future value of reinvested coupons for three years at 2.25% is 12.2720:

12.2720 = [4 × (1 + 0.0225)²] + [4 × (1 + 0.0225)] + 4

At the end of the third year, the sale price of the bond is 103.3853: 103.3853=4/(1+0.0225)+104/(1+0.0225)²

So, the total return is 115.6573 (= 12.2720 + 103.3853), resulting in a realized three-year horizon yield of 3.41%

104.58=115.6573(1+r)³,r=0.0341

考点：Annualized holding period return

解析：由题干可知，一个五年期的债券持有三年。现在要我们计算三年的持有期收益率。

首先求出3年后卖出债券时所有的Coupon + Coupon Reinvestment，将现金流复利到第三年末。PV=0，PMT=4，N=3，I/Y=2.25，求得FV=12.272

然后求出3年后卖出时的债券价格，要算3年后卖出债券的价格，实际上是将债券剩余2年的现金流折现到第3年末。N=2，PMT=4，I/Y=2.25，FV=100，得到 PV = -103.3853

将以上两个部分相加总：得到持有期总收益为115.6573。

计算年化收益率：104.58 × (1+r)³ =115.6573，求出 r = 3.41%，故选项C正确。