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咩咩 · 2021年12月05日

为什么Portfolio B 是overvalued portfolio

  1. CFA II
  2. Portfolio

NO.PZ2021101401000003

问题如下：

Assume that the following one-factor model describes the expected return for portfolios:

E(Rp)=0.10+0.12βp,1E{(R_p)}=0.10+0.12\beta_{p,1}

Also assume that all investors agree on the expected returns and factor sensitivity of the three highly diversified Portfolios A, B, and C given in the following table:

Assuming the one-factor model is correct and based on the data provided for Portfolios A, B, and C, determine if an arbitrage opportunity exists and explain how it might be exploited.

选项：

解释：

According to the one-factor model for expected returns, the portfolio should have these expected returns if they are correctly priced in terms of their risk:

Portfolio A

E(RA) = 0.10 + 0.12βA,1 = 0.10 + (0.12)(0.80) = 0.10 + 0.10 = 0.20

Portfolio B

E(RB) = 0.10 + 0.12βB,1 = 0.10 + (0.12)(1.00) = 0.10 + 0.12 = 0.22

Portfolio C

E(RC) = 0.10 + 0.12βC,1 = 0.10 + (0.12)(1.20) = 0.10 + 0.14 = 0.24

In the table below, the column for expected return shows that Portfolios A and C are correctly priced but Portfolio B offers too little expected return for its risk, 0.15 or 15%. By shorting Portfolio B (selling an overvalued portfolio) and using the proceeds to buy a portfolio 50% invested in A and 50% invested in C with a sensitivity of 1 that matches the sensitivity of B, for each monetary unit shorted (say each euro), an arbitrage profit of €0.22 -€0.15 = €0.07 is earned.

为什么Portfolio B 是overvalued portfolio

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1 个答案

星星_品职助教 · 2021年12月05日

同学你好，

按照题干中给出的APT公式，将A、B、C的β逐个代入，得到的就是这个portfolio应该有的合理收益率。然后再和目前的expected return进行比较，可以发现A、C定价合理。

只有B的合理定价应为0.22，但实际的expected return却是0.156，即return比合理的要低。

这说明这个portfolio被卖的太贵了，才把收益率压低了。即价格被高估，也就是overvalued。

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