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luckylxl · 2025年04月02日

解题思路没看懂

NO.PZ2023052301000041

问题如下:

An investor purchases an eight-year, 6.4% annual coupon eurobond priced at par 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.

 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%:


这二步没看明白,可以详细说一下吗

1 个答案

吴昊_品职助教 · 2025年04月02日

嗨,努力学习的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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