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Darkblanca · 2024年02月05日

Var(F1)和Var(F2)

  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%。

前后数字不一致，能不能统一一下？好多次答案出错都不改了

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1 个答案

笛子_品职助教 · 2024年02月05日

嗨，从没放弃的小努力你好：


前后数字不一致，能不能统一一下？好多次答案出错都不改了

Hello，亲爱的同学~

这里不是前后数字不一致。这里是把方差变为标准差。


解析里的

Var (F1) = 0.0250.5 = 0.1581

Var (F2) = 0.00140.5 = 0.0374

中间少了个^号，实际上是开平方根的计算。


改为

standard error (F1) = 0.025^0.5 = 0.1581

standard error (F2) = 0.0014^0.5 = 0.0374

会更清楚一些。


也感谢同学的提醒。谢谢同学~

如果还有其他问题，也欢迎随时提问，祝学习顺利！

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