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Alice_090 · 2022年03月04日

问P114例题

  1. CFA III
  2. Capital Market Expectations

NO.PZ2018091901000056

问题如下：

An investor is considering adding three new securities to her internationally focused fixed income portfolio. She considers the following non-callable securities:

1-year government bond

10-year government bond

10-year BBB rated corporate bond

She plans to invest equally in all three securities being analyzed or will invest in none of them at this time. She will only make the added investment provided that the expected spread/premium of the equally weighted investment is at least 1.5 percent (150bp) over the 1-year government bond. She has gathered the following information:

Using only the information given, calculate the expected total risk premium of the three securities and determine the investor’s probable course of action.

选项：

A.

invest equally in all three securities

B.

do not invest equally in all three securities

C.

uncertain

解释：

B is correct.

The average spread (over 1-year government bond) at issue is [0 + 1 + (1 + 0.75 + 0.55)] = 3.3%/3 = 1.1%.

As the 1.1% is less than 1.5%, the investor will not make the investment.

解析：1-year government bond没有任何风险溢价，所以它的SPREAD就是0。

相比较于1-year government bond，10-year government bond的SPREAD是1%。

相比较于1-year government bond，10-year corporate bond的SPREAD是1% + 0.75% + 0.55%。

又因为这三类债券投资权重相等，所以直接求算数平均就可以求得投资的SPREAD，即

[0 + 1 + (1 + 0.75 + 0.55)] = 3.3%/3 = 1.1%.又因为这个SPREAD小于投资者想要的回报率1.5%，所以投资者不会去做投资。

抱歉想在这里请教一道课本上的例题，可以麻烦老师讲一下P114题目上reinvestment rate为什么是1%么？题目是写的2年2%,难道是因为2年只再投资了一次coupon，所以是1%么？那5年，7年的怎么理解呢？

谢谢老师

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2 个答案

源_品职助教 · 2022年03月07日

嗨，爱思考的PZer你好：


前两年是1%就是原版书的一个假设。同学可以看下原版书原文，这里并没有任何解释。

后面每年2%，不是假设，是可以正常推导出来的。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

源_品职助教 · 2022年03月06日

嗨，努力学习的PZer你好：




前两年增加的幅度幅度是1%，而非2%，这是个粗略值，之后每年增加才是2%。

RI前两年年总共上涨是1% 可以这样想。

如果是在0时刻就上涨了2%，那么第一年就有个2%，第二年也有个2%，所以总共就是4%

如果实在1时刻上涨了2%，那么就只有1个2%（也就是从第一年到第二年末的2%）

所谓2%，它只是一个年化收益率的概念，落实到题目里，需要将其天化。

但是题目没有告诉我们具体的涨息的时间点，所以这个天化就没法具体来算。

从结果来看，原版书是假设第二年年末才涨到2%，也就是之前很长一段时间的都没有享受到这个2%，

从一个平滑的观点看，原版书告诉我们，其实头2年只上涨了1%。

其实原版书这里没有对1%做出详细的解释，可以直接当成是原版书自己的一个假设，因为真实怎么长的，其实谁也不知道。


因为投资期是T0时刻，所以从从第二年之后，每过1年，就有个2%，因为它是再投资，每年都会投资一次。

举个例子，在2021年到2022年间，利率提高了2%，那么之后没过完整的一年，都会享受到这2%

所以，22年到23年这一年，再投资收益是完整享受到这2%的。所以这一年就会有这么个2%

那23年到24年，又过了一年，就又一次享受到了这2%，就又多了2%。以此类推。

说回5年，就是前两年的1%再加上（5-3）×2%，七年就是1%+（7-2）×2%（线性模式）

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加油吧，让我们一起遇见更好的自己！

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