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7777 · 2023年08月29日

contribution to portfolio variance

  1. CFA III
  2. Equity

NO.PZ2023010903000072

问题如下：

Based on Exhibit 2, the portion of total portfolio risk that is explained by the market factor in Fund 1’s existing portfolio is closest to:


选项：

A.

3%

B.

81%

C.

87%

解释：

The portion of total portfolio risk explained by the market factor is calculated in two steps. The first step is to calculate the contribution of the market factor to total portfolio variance as follows:

The second step is to divide the resulting variance attributed to the market factor by the portfolio variance of returns, which is the square of the standard deviation of returns:

Portion of total portfolio risk explained by the market factor = 0.001223/(0.0374)2

Portion of total portfolio risk explained by the market factor = 87%

为什么计算market 和其他因子的影响的时候不用乘2呢，按照用画图（类似九宫格）的方法来求组合的方差的时候，是要乘2呀，比如2*w1*w2*covariance

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1 个答案

笛子_品职助教 · 2023年08月30日

嗨，从没放弃的小努力你好：


为什么计算market 和其他因子的影响的时候不用乘2呢

这是算单因子，对portfolio风险的贡献。

例如XYZ三个因子构成portfolio

在算X因子工贡献度时，X与Y，X与Z，X与X，就是X对portfolio的风险贡献。

在算Y因子贡献度时，Y与X，Y与Z，Y与Y，属于Y对portfolio的风险贡献。

因此不需要乘以2，否则会重复计算。


按照用画图（类似九宫格）的方法来求组合的方差的时候，是要乘2呀，比如2*w1*w2*covariance

李老师在这里讲解例题的时候，推荐用九宫格的方法记忆。

九宫格里，单因子对portfolio的风险贡献不需要乘以2

如果把九宫格里的9个各自，全部加起来，那是portfolio 总风险，这个时候才有2。

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