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Stella · 2021年12月20日

能中文解释一下答案吗

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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).

请用中文解释一下答案解析力的意思

1 个答案

源_品职助教 · 2021年12月21日

嗨,爱思考的PZer你好:


是正确的。

表述三是正确的。只要在基于因子的VCV模型中使用的因素没有一个是冗余的,并且没有一个资产回报是完全由公共因素决定的,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矩阵方法可能导致一些投资组合错误地表现为无风险,如果任何资产收益可以完全由公共因子决定,或一些因子是冗余的。


A是不正确的,因为VCV矩阵的收缩估计相对于样本VCV矩阵会提高估计的效率,因为它的均方误差(MSE)通常小于(无偏)样本VCV矩阵的MSE。

这种情况下,效率意味着更小的MSE。


B是不正确的,因为虽然提出的方法是不可靠的,但原因不是样本VCV矩阵有偏和不一致;相反,它是公正和一致的。

相反,VCV矩阵的估计不可靠,因为观测的数量不是至少10倍的资产(例如,用十年的月度数据返回,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)。



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NO.PZ202105270100000501 不仅仅是翻译原文,就是彻底一下statement3是想表达个什么意思

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