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shuangzili · 2021年11月22日

看不懂这道题的解题

  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

可以详细讲一下吗？ 我觉得用20 C 5就可以算。 但还想听一下具体的解题思路。
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1 个答案

星星_品职助教 · 2021年11月23日

同学你好，

这道题应该是用 5C2 来计算。

题目意思是现在有5只股票，其中两两组合有多少种可能（题干中的“unique covariance terms”说明了不需要考虑顺序，即Cov1,2=Cov2,1，只能当成一个““unique covariance terms”来考虑）。

所以就是5C2，直接按计算器就可以了，顺序为输入“5”，按“2nd”+最右侧一列的加号键，再输入“2”，直接按等号即可得到结果10。

类似的题目都可以按照上述思路处理，是比较快捷的方法。

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