NO.PZ201710100100000102
问题如下：
2. The arbitrage opportunity identified by Zapata can be exploited with:
选项：
A.Strategy 1: Buy $50,000 Fund A and $50,000 Fund B; sell short $100,000 Fund C.
B.Strategy 2: Buy $60,000 Fund A and $40,000 Fund B; sell short $100,000 Fund C.
C.Strategy 3: Sell short $60,000 of Fund A and $40,000 of Fund B; buy $100,000 Fund C
解释：
C is correct.
The expected return and factor sensitivities of a portfolio with a 60% weight in Fund A and a 40% weight in Fund B are calculated as weighted averages of the expected returns and factor sensitivities of Funds A and B: Expected return of Portfolio 60/40 = (0.60)(0.02) + (0.40)(0.04) = 0.028, or 2.8% Factor sensitivity of Portfolio 60/40 = (0.60)(0.5) + (0.40)(1.5) = 0.9
The factor sensitivity of Portfolio 60/40 is identical to that of Fund C; therefore, this strategy results in no factor risk relative to Portfolio C. However, Fund C’s expected return of 3.0% is higher than Portfolio 60/40’s expected return of 2.8%. This difference supports Strategy 3: buying Fund C and selling short Portfolio 60/40 to exploit the arbitrage opportunity.
考点：APT模型
解析：
根据题干，AB组合符合APT模型，而C不符合，因此存在套利空间。
首先求单因子的APT模型，公式写为：E(R)=Rf+βλ，代入AB组合的已知数：
Rf+0.5λ=0.02
Rf+1.5λ=0.04，
两个方程两个未知数，得Rf=1%，λ=2%。
根据E(R)=1%+β*2%，C组合在APT模型下的预期收益率为1%+0.9*2%=2.8%，而现在表格中给出的C组合的实际收益率为3%。所以C组合在市场上的实际收益率3%是高于APT模型的预期收益率，那么投资者可以通过long C组合的实际收益率，同时short APT模型下通过AB合成的C组合，来获得无风险收益率。
因此我们要找到AB组合的权重，使得合成后新组合的factor sensitivy=C组合的factor sensitivy，列出方程：
Wa+Wb=1
0.5Wa+1.5Wb=0.9
因此Wa=60%, Wb=40%
所以通过long1个C组合，short （60%的A组合+40%的B组合），可以获得套利机会。因此符合这样的头寸和投资比例的只有C选项。
老师，APT得到的不是合理收益率水平吗？既然C现在的收益率水平3%是大于均衡收益率2.8%的，不是说明收益率被高估应该卖出才是吗？
我有点搞不清头寸方向，烦请老师解答，谢谢
