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金珍荣 · 2023年11月01日

Residual Risk (%)=4.4

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%。

why Residual Risk (%)=4.4?

1 个答案

笛子_品职助教 · 2023年11月02日

嗨,努力学习的PZer你好:


方差的平方根是标准差= 0.231,即23.1%。why Residual Risk (%)=4.4?


Hello,亲爱的同学~

Residual Risk 是指portfolio残差的方差,这是已知条件。

Residual Risk 并不是同学所说的portfolio“方差的平方根”。


这是两个事物,之间是有比较大的区别的。

Residual Risk是portfolio与因子回归的过程中,回归方程里的残差的波动率。

而同学说的方差的平方根,是衡量整个portfolio的波动率

整个portfolio整体的波动率,自然与仅仅是残差的波动率,不同。

我们通常所说:标准差是方差的平方根,这里必须是同一个变量的标准差与方差。

Residual Risk与同学所说的portfolio方差的标准差,并不是同一个变量。因此不存在平方根的关系。

相互之间并不矛盾哦。

----------------------------------------------
努力的时光都是限量版,加油!

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