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115833 · 2024年03月26日

这道题好难呀.老师可以详细讲解一下吗

NO.PZ2023052301000041

问题如下:

An investor purchases an eight-year, 6.4% annual coupon eurobond priced at par (settlement: 15 June 2031; maturity: 15 December 2039) and sells it after six years. Assuming interest rates rise by 100 bps immediately after purchase, the investor’s rate of return at the end of six years is:

选项:

A.

lower than 6.4%.

B.

equal to 6.4%.

C.

higher than 6.4%.

解释:

A is correct. The future value of reinvested coupon interest is

= FV(0.074,6,6.4,0,0) = 46.245.

The sale price of the bond at the end of six years is

= PV(0.074,2,6.40,100,0) = 98.202,

which results in a six-year horizon yield of 6.32%, which is lower than 6.40%:


B and C are incorrect, because interest rates have risen and the investor’s investment horizon is not long enough to offset the price decline with additional reinvestment return.

这道题好难呀.老师可以详细讲解一下吗

1 个答案
已采纳答案

吴昊_品职助教 · 2024年03月26日

嗨,爱思考的PZer你好:


1、期间的coupon和coupon的再投资收入:持有六年即N=6;以上升100bp的利率进行再投资,则YTM=7.4,一年付息一次coupon为6.4,所以PMT=6.4,一开始PV=0,所以FV算出来是46.245(计算器:N=6,PMT=6.4,PV=0,I/Y=7.4,CPT→FV=46.245)

2、六年后卖出的价格sell price是未来现金流折现求和:未来还剩两年,N=2;YTM=7.4;PMT=6.4;最后面值FV=100,折现得到PV=98.202

(计算器:N=2,FV=100,PMT=6.4,I/Y=7.4,CPT→PV=98.202)

3、有了两笔收入之后(46.245+98.202=144.447),和一开始投资的成本做对比,我们就能算出持有期收益率。一开始投入100,六年之后变成了144.447,100×(1+r)^6=144.447,反求出持有期收益率r即可。r=0.0632=6.32%

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Olivia.W🌸 · 2024年07月22日

第一点不太理解,这个计算出来的FV包含了coupon和coupon 再投资收益?为什么不只是在投资收益呢?应该还要加上6年收到的coupon吧?

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