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CFApipa · 2022年10月10日

老师,这道题算的是capital/gain loss,是不是和horizon yield完全不一样?

NO.PZ2016031001000111

问题如下:

An investor purchases a nine-year, 7% annual coupon payment bond at a price equal to par value. After the bond is purchased and before the first coupon is received, interest rates increase to 8%. The investor sells the bond after five years. Assume that interest rates remain unchanged at 8% over the five-year holding period.

The capital gain/loss per 100 of par value resulting from the sale of the bond at the end of the five-year holding period is closest to a:

选项:

A.

loss of 8.45.

B.

loss of 3.31.

C.

gain of 2.75.

解释:

B is correct.

The capital loss is closest to 3.31 per 100 of par value. After five years, the bond has four years remaining until maturity and the sale price of the bond is 96.69, calculated as:

7(1.08)1+7(1.08)2+7(1.08)3+107(1.08)4=96.69\frac7{{(1.08)}^1}+\frac7{{(1.08)}^2}+\frac7{{(1.08)}^3}+\frac{107}{{(1.08)}^4}=96.69

The investor purchased the bond at a price equal to par value (100). Because the bond was purchased at a price equal to its par value, the carrying value is par value. Therefore, the investor experienced a capital loss of 96.69 - 100 = -3.31.

考点:capital gain(loss)

解析:一开始是以面值100购入债券,当收到第一笔coupon前,利率上涨至8%,五年后投资者又将债券卖出。现在题目要我们求的是capital gain(loss)。capital gain(loss)衡量的是债券售价和carrying value之间的差距,这道题的carrying value就是100,那我们只要算出selling price,两项相减即可。利用计算器计算债券售价:N=4,PMT=7,I/Y=8,FV=100,求得PV= -96.69。求得的96.69是债券第五年卖出的sale prcie,债券在第五年能卖多少钱,取决于未来现金流折到第五年共有多少。故capital loss = 96.69-100 = -3.31,故选项B正确。

老师,这道题算的是capital/gain loss,是不是和horizon yield完全不一样?

Capital Gain/Loss = Sell Price - Carrying Value, 不包括求coupon的future value

而Horizon Yield的计算里面,包括了求Bond本身的future value,以及coupon payments的future value,也就是reinvestment value?

1 个答案
已采纳答案

吴昊_品职助教 · 2022年10月10日

嗨,从没放弃的小努力你好:


是的,CG/L和horizon yield不是一个概念。

1、求CG/L,只需要分别计算selling price和carrying value。两者的差是CG/L。

2、而horizon yield是债券一开始的投入和最后的产出之间的对比,好比一开始付出去PV,到期可以收回FV(包含coupon+coupon reinvestment,如果债券中间卖出还有一个卖出的价格。)然后根据:PV(1+r)^n=FV,求一个年化的收益率。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

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