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Alex · 2023年07月20日

如何理解residual risk？

  1. CFA III
  2. Capital Market Expectations

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%。

请问这里的residual risk是不是默认就是variance而非标准差？在何老师其他视频和题目里面好像又明确说residual risk是标准差

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源_品职助教 · 2023年07月20日

嗨，从没放弃的小努力你好：


经典题补充讲义里的这道题的确是当做方差而非标准差处理的。

但是补充讲义收录了一些考纲修改前的题目，

我又翻了下最新的原版书教材，三级CME 学科里并没有对Residual Risk给出明确的建议，

那还是把它当做方差来记忆吧。考试应该不会专门考这个知识点了。


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