NO.PZ2023040601000001
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.
老师，您好！
答案解析的思路是算出其中错误定价的组合，然后short价格高并long价格低的。
我的思路如下：
Yes, there's an arbitrage opportunity. We can short 2 units of B and long 1 unit A and 1 unit C. Then, for the factor risk is hedged, but the expected return is 0.2+0.24-0.15*2 = 0.14.
即直接根据因子的敏感性对冲，short 2个B并同时long A和C各一份（或者如答案中多空都减半也行），得到的单位收益率都一样7%。
但是，感觉两种解答还是有所不同，能不能解释一下？谢谢了！
