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米妮涵 · 2023年03月26日

权重换成系数

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%

讲义例题是有权重的,这道题只有系数,解题思路是怎样的?

1 个答案

笛子_品职助教 · 2023年03月27日

嗨,从没放弃的小努力你好:


讲义例题是有权重的,这道题只有系数,解题思路是怎样的?

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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