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youtkr · 2023年08月31日

自己和自己的variance残差项的variance怎么算的?和别人的cov是不是残差项的cov就是0?

NO.PZ2022122601000070

问题如下:

Cortez reviews RiteVal data (Exhibit 2) and preferred two-factor model with global equity and global bonds as the two common drivers of return for all other asset classes.


Using the multifactor model preferred by RiteVal and Exhibit 2, the standard deviation of U.S. real estate is closest to:

选项:

A.23.1% B.

21.0%

C.24.5%

解释:

Correct Answer: A

F1 = Factor 1, Global Equity

F2 = Factor 2, Global Bonds

Var (F1) = 0.0250.5 = 0.1581

Var (F2) = 0.00140.5 = 0.0374

Cov(F1,F2) = σ1σ2ρ1,2 = 0.1518 × 0.374 × 0.33 = 0.002

Real estate factor sensitivities are bre,1 0.6 for sensitivity to global equity and bre,2 0.15 for global bonds. Residual risk variance (given) is Var(εre) = 0.044.

Square root of variance is the standard deviation = 0.231, or 23.1%.

中文解析:

F1 = Factor 1, Global Equity

F2 =因子2,全球债券

Var (F1) = 0.0250.5 = 0.1581

Var (F2) = 0.00140.5 = 0.0374

浸(F1、F2) =σ1,σ2ρ1,2 = 0.1518×0.374×0.33 = 0.002

房地产因素敏感性为bre,全球股票敏感性为1.06,全球债券敏感性为2.0.15。剩余风险方差(给定)Var(εre) = 0.044。


方差的平方根是标准差= 0.231,即23.1%。

如题

1 个答案

笛子_品职助教 · 2023年09月01日

嗨,爱思考的PZer你好:


残差和残差自己的协方差,就是残差的方差。

Square root of variance is the standard deviation = 0.231, or 23.1%.


上面的公式中,除了VAR,其他都可以带入数字,最后可以计算出残差的方差。


残差和其他因子的协方差都是0。否则回归方程写得不正确。

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