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CFApipa · 2022年07月17日

how many unique covariance terms, excluding variances

  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

how many unique covariance terms, excluding variances - 可以仔细讲解一下这句什么意思吗？我觉得这道题和讲义给出的Combination的定义以及例题都不太一样，很难理解...

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1 个答案

星星_品职助教 · 2022年07月17日

同学你好，

“unique covariance terms”指的是不需要考虑顺序，即Cov1,2=Cov2,1，这种情况只能当成一个““unique covariance terms”来考虑；

“excluding variances”指的是不考虑自己和自己的情况，即不考虑Cov1,1（实际就是第一个资产的variance）、Cov2,2等；

这两句话综合一下，题干就可以简化为求 现在有5只股票，其中两两组合有多少种可能。直接计算器按5C2就可以得到答案。

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