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玛卡巴卡 · 2021年09月18日

equity

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NO.PZ201809170400000504

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:

C is correct.

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:

CVmarket  factor=j=1nXmarket  factorXjCmf,jCV_{market\;factor}={\textstyle\sum_{j=1}^n}X_{market\;factor}X_jC_{mf,j}

=Xmarket  factorj=1nXjCmf,j=X_{market\;factor}{\textstyle\sum_{j=1}^n}X_jC_{mf,j}

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%

这里的market也算是一个风险因子么?这怎么理解呢?

1 个答案

笛子_品职助教 · 2021年09月20日

嗨,爱思考的PZer你好:


在本题,market也算是一个风险因子。题目问的就是,market factor 贡献给投资组合的方差,在投资组合的总方差中, 占比多少。

为何把market也算是风险因子:因为投资组合的总风险是绝对风险,投资组合的总风险中,就有一部分波动是源自市场的波动。


本题在原版书例题中有一道类似的,只不过把风险因子换成了asset,理解方式和计算原理均一致。见以下截图(来自基础班讲义245到246页)。





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