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phoebeqp · 2023年06月02日

No.PZ2017092702000072

  1. CFA I
  2. Quantitative

NO.PZ2017092702000072

问题如下：

Given a portfolio of five stocks, how many unique covariance terms, excluding variances, are required to calculate the portfolio return variance?

选项：

A.

10

B.

20

C.

25

解释：

A is correct.

A covariance matrix for five stocks has 5 × 5 = 25 entries. Subtracting the 5 diagonal variance terms results in 20 off-diagonal entries. Because a covariance matrix is symmetrical, only 10 entries are unique (20/2 = 10)

根据五个股票两两组合，去掉自己和自己组合，一共是5*4/2=10种

是要求这个portfolio的variance，那就应该知道五个数的variance, 还有五个数两两组合的covariance。

covariance是10个，但是不是还有五个variance吗，应该是15个才对啊？

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星星_品职助教 · 2023年06月02日

同学你好，

本题的题干中已说明了不需要考虑那5个自己的variance。

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