NO.PZ202105270100000501
问题如下：
Which of the following statements made by Bader’s research assistant is correct?
选项：
A.Statement 1 B.Statement 2 C.Statement 3解释：
C is correct.
Statement 3 is correct. As long as none of the factors used in a factor-based VCV model are redundant and none of the asset returns are completely determined by the common factors, there will not be any portfolios that erroneously appear to be riskless. Therefore, a factor-based VCV matrix approach may result in some portfolios that erroneously appear to be riskless if any asset returns can be completely determined by the common factors or some of the factors are redundant.
A is incorrect because shrinkage estimation of VCV matrices will increase the efficiency of the estimates versus the sample VCV matrix, because its mean squared error (MSE) will in general be smaller than the MSE of the (unbiased) sample VCV matrix. Efficiency in this context means a smaller MSE.
B is incorrect because, although the proposed approach is not reliable, the reason is not that the sample VCV matrix is biased and inconsistent; on the contrary, it is unbiased and consistent. Rather, the estimate of the VCV matrix is not reliable because the number of observations is not at least 10 times the number of assets (i.e., with 10 years of monthly return data, there are only 120 observations, but the rule of thumb suggests there should be at least 200 observations for 20 asset classes).
表述三是正确的。只要基于因素的风险现值模型中使用的所有因素都不是冗余的，而且没有任何资产回报完全由公共因素决定，就不会有任何投资组合错误地看起来是无风险的。因此，基于因子的VCV矩阵方法可能导致某些投资组合错误地看似无风险，如果任何资产收益完全由公共因子决定，或某些因子是多余的。
A是错误的，因为相对于样本VCV矩阵，收缩估计VCV矩阵会增加估计的效率，因为其均方误差(MSE)一般会小于(无偏)样本VCV矩阵的MSE。在这种情况下，效率意味着较小的MSE。
B是错误的，因为虽然所提出的方法是不可靠的，但原因不是样本VCV矩阵有偏差和不一致;相反，它是无偏的和一致的。相反,VCV矩阵的估计不可靠,因为观测的数量不满足至少10倍于资产数目的要求(例如,用十年的月度数据回测,只有120年的观察,但经验法则表明应该有至少200观察20资产类别)。
如果任何资产收益完全由公共因子决定，或某些因子是多余的。那么基于因子的VCV矩阵方法可能导致某些投资组合错误地被认为是无风险的。
能解析一下这个中间推导过程吗
1、为什么资产收益由完全由公共因子决定，那么基于因子的VCV矩阵方法可能导致某些投资组合错误地被认为是无风险的。
2、为什么某些因子是多余的，那么基于因子的VCV矩阵方法可能导致某些投资组合错误地被认为是无风险的。
