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dilly24 · 2024年04月06日

Coefficient是什么？

  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%

请问可以解释一下这道题具体是怎么计算的吗？这里的coefficient指的是什么？应该用哪个公式计算？ 谢谢

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2 个答案

笛子_品职助教 · 2024年04月07日

嗨，从没放弃的小努力你好：


谢谢！这个计算是掌握了的，就是不知道这边的coefficient指的是weight的意思。是因为是factors，而不是个股，所以用coefficient，而不是weight吗？还有没有其他情况题目不是用的weight这个词而是别的单词的情况的呢？


当分析portfolio里的股票时，使用weight。

当分析portfolio里的因子时，使用coefficient。

coefficient是回归系数，又称为因子权重。

Factor，一般对应coefficient 。

如果有别的单词，例如Factor weight，也可以使用，和coefficient 是一个意思。

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加油吧，让我们一起遇见更好的自己！

笛子_品职助教 · 2024年04月06日

嗨，从没放弃的小努力你好：


请问可以解释一下这道题具体是怎么计算的吗？这里的coefficient指的是什么？应该用哪个公式计算？ 谢谢

Hello，亲爱的同学！

计算方法同学可以参考讲义例题：




coefficient是因子权重的意思。

本题的coefficient就是例题里的weight。

本题的market因子，就是例题里的asset X。

本题的market因子对portfolio方差的贡献占比，就是例题里asset X对portfolio方差的贡献占比


本题的：

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


就是例题里的



本题的Portion of total portfolio risk explained by the market factor = 0.001223/(0.0374)2 = 87%

就是例题里的


因子对portfolio方差贡献的题目，是有特定规则解法的，就是原版书的这道题的解法。

本题的解法和例题是完全一样的。

同学可以看看相关基础班视频，具体计算方法，以及如果巧妙记忆，老师都有详细的讲解。


如果看完视频后，还有问题，也欢迎随时提问。

祝学习顺利~

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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