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Lynn · 2020年02月26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.

Portfolio B 用one factor model 算 ER = 22%。 现实市场价格反映ER=15%,证明B价格被低估。我的理解应该买入B因为是低估的资产。

1 个答案

丹丹_品职答疑助手 · 2020年02月26日

同学你好,本题考查的是APT的应用,根据题干b的收益率应当为22%,而实际利率是15%,所以b的收益率被低估。资产价格和收益率呈反向变动关系,所以债券的价格应被高估,从而应该卖出B。通过构造公式,按照加和为1的比例配置组合A和C的资产可以形成B[wa*fator sensitivitya+(1-wa)*factor sensitivityc=factor sensitivityb,求出wa=0.5.按比例买入组合A和组合C,卖出组合B,可进行套利。希望可以帮到你。