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sherry_lee · 2021年04月27日

权重为什么用相关系数？

  1. CFA III
  2. Equity

NO.PZ2019012201000065

问题如下：

Based on Exhibit 2, theportion of total portfolio risk that is explained by the market factor in Fund1’s existing portfolio is closest to:

选项：

A.

3%

B.

81%

C.

87%

解释：

The portion oftotal 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 totalportfolio variance as follows:


Where

CVmarket factor = contribution of the market factor to totalportfolio variance

xmarket factor = weight of the market factor in theportfolio

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 isto divide the resulting variance attributed to the market factor by theportfolio variance of returns, which is the square of the standard deviation ofreturns:

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

Portion of totalportfolio risk explained by the market factor = 87%

​权重为什么用相关系数？

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2 个答案

maggie_品职助教 · 2021年05月13日

嗨，爱思考的PZer你好：


这里的coefficient是多因素模型的回归系数，即组合的投资收益在多大程度上取决于各个因子。

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努力的时光都是限量版，加油！

maggie_品职助教 · 2021年04月28日

嗨，努力学习的PZer你好：


同学你好，这里和我们上课讲过的例子稍稍有些不同，我们上课讲的例子是以资产来看的，所以计算的是资产的weighting，方差和相关系数，而这个题目是从risk factor的角度来看的，是把收益回归成以risk factor为变量的方程，方程可以表达为y=a+1.08*market factor+0.098*size factor-0.401*Value factor+0.034*Momentum factor+E，coefficient系数就是这个因子的变动程度，也可以理解为是这个因子的weight.

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

sherry_lee · 2021年05月12日

所以这里的相关系数，是factor和组合收益的相关系数？

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