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咖啡巧克力 · 2023年12月17日

利率增加100bps,为何RI变成了5.4%? 另外,为何FV不包含当期利息?

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(0.054,6,6.4,0,0) = 46.245.

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

= PV(0.054,2,6.40,100,0) = 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.

利率增加100bps,为何RI变成5.4%? 另外,为何FV不包含当期利息?谢谢

咖啡巧克力 · 2023年12月18日

如果按照利率升至7.4%来分析,答案是否应该是高于6.4%?持有6年后卖出还剩下2年到期,利率升高对再投资收益的正向影响更大。

4 个答案

pzqa015 · 2023年12月24日

嗨,爱思考的PZer你好:


interest rates rise by 100 bps immediately after purchase,所以,Ytm由6.4%上涨1%变成7.4%

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pzqa015 · 2023年12月19日

嗨,爱思考的PZer你好:


题目中对债券等描述是eight-year, coupon rate of 6.4% and priced at par value。那么定价时YTM理解就是等于6.4℅,那么购买后利率增加1%,为何YTM需要减小1%?

--

 FV(0.054,6,6.4,0,0) = 46.245.和 PV(0.054,2,6.40,100,0) = 98.202, 括号里面写错了,ytm应该是0.074而不是0.054,但是计算结果没错。

也就是说购买后利率增加1%,ytm增加1%而不是减少1%,变成了7.4%

是total return减少了,但没减少1%。

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SEVEN澤🐻 · 2023年12月23日

老师好,请问YTM=0.074是怎么得到的?

咖啡巧克力 · 2023年12月23日

因为交割后,利率上升了100个bps

pzqa015 · 2023年12月18日

嗨,努力学习的PZer你好:


Price at par,意味着coupon rate=ytm,买入后利率上涨1%,所以Ytm增加1%,前面说了,解析力写错了,是7.4%而不是5.4%。

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pzqa015 · 2023年12月17日

嗨,努力学习的PZer你好:


买入后利率增加,则实际的持有收益是变小的。也就是这道题问的rate of return是变小的。

因为根据债券价格等于未来现金流折现求和,买入后如果利率上涨,则未来卖出的FV是下降的,所以rate of return是低于期初ytm的,也就是这道题的6.4%。

如果买入后利率不变,那么持有期的rate of return就是买入时的ytm 6.4%。


 FV(0.054,6,6.4,0,0) = 46.245.和 PV(0.054,2,6.40,100,0) = 98.202, 括号里面写错了,应该是0.074而不是0.054,但是计算结果没错,

也就是说FV(0,0.074,6,6.4,0)=46.245;PV(0.074,2,6.4,100,0)=98.202

----------------------------------------------
努力的时光都是限量版,加油!

咖啡巧克力 · 2023年12月18日

题目中对债券等描述是eight-year, coupon rate of 6.4% and priced at par value。那么定价时YTM理解就是等于6.4℅,那么购买后利率增加1%,为何YTM需要减小1%?

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