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我来自螃蟹星球 · 2020年02月03日

问一道题:NO.PZ2015121810000003

问题如下:

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

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.

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1 个答案

星星_品职助教 · 2020年02月04日

这是问答题