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Pavel Korchagin · 2024年01月05日

portfolio的return是按市场E(rp)还是计算的均衡E(rp）？

  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.

（备注：课后题原题，虽然题目形式是问答题，但是建议不用纠结题目形式，了解题目考查角度即可）

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 + 0.096 = 0.196

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 + 0.144 = 0.244

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.

比如这题 Portfolio B 的E(rp）是0.22，市场的E(rp)是0.156,

那么如果去long Portfolio B, 最后获得的收益是0.156还是0.22？

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2 个答案

品职助教_七七 · 2024年10月07日

嗨，从没放弃的小努力你好：


@Rustanchor B的市场收益率0.156低于理论收益率0.22，说明B的市场价格高于理论上的合理价格，为overvalued。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

品职助教_七七 · 2024年01月07日

嗨，从没放弃的小努力你好：


APT算出来的值是理论上应该有的收益率。

表格中给的市场值是当下市场上买入可以获得的收益率。

long Portfolio B获得的值是市场上能获得的值，所以最后获得的收益是0.156。但B理论上应该获得更高的0.22，所以现在市场上获得的收益率显然是少了。这种情况下应该short。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

Rustanchor · 2024年10月07日

所以B不是undervalued吗？不是overvalued。

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