问一道题：NO.PZ201710100100000102 第2小题

NO.PZ201710100100000102 问题如下 2. The arbitrage opportunity intifieZapata cexploitewith: A.Strategy 1: Buy $50,000 FunA an$50,000 Funsell short $100,000 Fun B.Strategy 2: Buy $60,000 FunA an$40,000 Funsell short $100,000 Fun C.Strategy 3: Sell short $60,000 of FunA an$40,000 of Funbuy $100,000 Fun C is correct.The expectereturn anfactor sensitivities of a portfolio with a 60% weight in FunA ana 40% weight in FunB are calculateweighteaverages of the expectereturns anfactor sensitivities of Fun A anExpectereturn 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) = 0.9The factor sensitivity of Portfolio 60/40 is inticto thof Funtherefore, this strategy results in no factor risk relative to Portfolio However, FunC’s expectereturn of 3.0% is higher thPortfolio 60/40’s expectereturn of 2.8%. This fferensupports Strategy 3: buying FunC anselling 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=0.02Rf+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=10.5Wa+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 根据表1，是怎么知道用A和B的组合，去和C组合比较和套利呢？为什么不是AC和B，或BC和仅仅是因为题目里面写了A B are well versifie这个地方的原理能下么？

NO.PZ201710100100000102 问题如下 2. The arbitrage opportunity intifieZapata cexploitewith: A.Strategy 1: Buy $50,000 FunA an$50,000 Funsell short $100,000 Fun B.Strategy 2: Buy $60,000 FunA an$40,000 Funsell short $100,000 Fun C.Strategy 3: Sell short $60,000 of FunA an$40,000 of Funbuy $100,000 Fun C is correct.The expectereturn anfactor sensitivities of a portfolio with a 60% weight in FunA ana 40% weight in FunB are calculateweighteaverages of the expectereturns anfactor sensitivities of Fun A anExpectereturn 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) = 0.9The factor sensitivity of Portfolio 60/40 is inticto thof Funtherefore, this strategy results in no factor risk relative to Portfolio However, FunC’s expectereturn of 3.0% is higher thPortfolio 60/40’s expectereturn of 2.8%. This fferensupports Strategy 3: buying FunC anselling 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=0.02Rf+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=10.5Wa+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 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

NO.PZ201710100100000102 问题如下 2. The arbitrage opportunity intifieZapata cexploitewith: A.Strategy 1: Buy $50,000 FunA an$50,000 Funsell short $100,000 Fun B.Strategy 2: Buy $60,000 FunA an$40,000 Funsell short $100,000 Fun C.Strategy 3: Sell short $60,000 of FunA an$40,000 of Funbuy $100,000 Fun C is correct.The expectereturn anfactor sensitivities of a portfolio with a 60% weight in FunA ana 40% weight in FunB are calculateweighteaverages of the expectereturns anfactor sensitivities of Fun A anExpectereturn 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) = 0.9The factor sensitivity of Portfolio 60/40 is inticto thof Funtherefore, this strategy results in no factor risk relative to Portfolio However, FunC’s expectereturn of 3.0% is higher thPortfolio 60/40’s expectereturn of 2.8%. This fferensupports Strategy 3: buying FunC anselling 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=0.02Rf+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=10.5Wa+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 老师， 我看答案中 这一步“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=0.02Rf+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%，用这个方法先算出C组合在APT模型下的预期收益率为1%+0.9*2%=2.8%，”请问既然从题目中已经funA和B是well versifieportfolio，而C不确定。那可不可以跳过上面那些步骤，直接用A B的sensitivity 直接找到可以模拟乘funC sensitivity的配比， 然后根据这个配比算出用A B合成出和相同sensitivity的return = 0.028再用0.028 与C 现在的return 0.03来进行判断和 C之间的低买高卖呢谢谢

NO.PZ201710100100000102

NO.PZ201710100100000102 答案是这么写的根据题干，AB组合符合APT模型，而C不符合，因此存在套利空间。这个是怎么理解？请一下。谢谢