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pepperhyp · 2023年06月20日

如何理解该题目因子系数就是权重？

  1. CFA III
  2. Equity

NO.PZ2019012201000065

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:


Where

CVmarket factor = contribution of the market factor to total portfolio variance

xmarket factor = weight of the market factor in the portfolio

xj = weight of factor j in the portfolio

Cmf,j = covariance between the market factor and factor j

The variance attributed to the market factor is as follows:

CVmarket factor = (1.080 × 0.00109 × 1.080) + (1.080 × 0.00053 × 0.098) + (1.080 × 0.00022 × –0.401) + (1.080 × –0.00025 × 0.034)

CVmarket factor = 0.001223

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%

如上述所述，如何理解

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1 个答案

笛子_品职助教 · 2023年06月20日

嗨，爱思考的PZer你好：


如上述所述，如何理解

Hello，亲爱的同学！


本题的因子系数，就等同于例题里的股票权重。

解题思路就是把因子系数当做权重，然后沿用例题的计算方法。


原因在于：


股票的权重是W，股票用S表示：

则portfolio return = w1*S1 + w2*S2 +...+wn*Sn + residual


因子的系数是C，因子用F表示：

则portfolio return = C1*F1 + C2*F2 + ...Cn*Fn + residual


我们看到，基于权重和股票的表达式，与基于系数和因子的表达式，形式上是相同的。


所以我们计算S1的方差对portfolio 方差的贡献时，与计算F1的方差对portfolio方差的贡献时，所用的计算方法也是相同的。

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