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Jm · 2021年03月14日

为什么第五年的carrying value 还是 100?

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.

没有解释为什么carrying value一直是100

第五年的carrying value不应该是用原来的YTM折现得到吗?

1 个答案
已采纳答案

吴昊_品职助教 · 2021年03月14日

嗨,努力学习的PZer你好:


同学你好:

bond的carrying value是账面价值。

如果债券期初是溢价购买的,在债券的一生中,Carrying value逐渐降低,向面值100靠近。债券到期时Carrying value就是100. 如果债券期初是折价购买的,在债券的一生中,Carrying value逐渐上升,向面值100靠近。债券到期时Carrying value就是100。如果债券是平价发行的,投资者买的时候就是以Par Value买到。不存在购买价格向Par value靠拢这个问题,债券的Carrying Value在这只债券的一生中都是100。

回到这道题中,这道题是以面值购买,7% annual coupon payment bond at a price equal to par value。也正因为是以面值购买,所以账面价值就一直都是100,即carrying value=100。你也可以用一开始的7%进行折现,coupon rate也是7%,所以折现结果永远是面值100。

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努力的时光都是限量版,加油!

广超 · 2022年09月27日

老师,为什么课上的例题就需要再算一下第五年的债券carrying value?而且和期初购买价格不同?

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