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highsix · 2020年03月07日

问一道题：NO.PZ2019012201000065 [ CFA III ]

  1. CFA III
  2. Equity

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%

这道题的解析看不懂，能不能麻烦说一下为什么要这样做
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已采纳答案

袁园_品职助教 · 2020年03月10日

同学你好！

这道题目的意思是说 Fund 1 的风险可以用四个factor来衡量（market, size, value, momentum），写成方程就是

y=a+1.08*market factor+0.098*size factor-0.401*Value factor+0.034*Momentum factor+E

其中 coefficient就是这个因子的变动程度，也可以理解为是这个因子的weight

题目要我们求的是 market 这个 factor 对总风险的贡献程度

1，market factor 带来的影响 （即解析中的 CVmarket factor ）= market factor 本身的方差 * market factor 系数的平方 + market factor 和其他三个因子之间的协方差乘以各自的系数（例如market和size就用 0.00053*1.08*0.098）

2，总风险就是组合的方差 3.74%的平方

最后相除得到比例。

 

同学我看你报的是经典题Plus，是包含强化班的吧，你可以去听一下 Equity 的 Risk Considerations 那一节视频，李老师在基础班里是详细讲过类似题目的，强化班的那个视频里讲了计算方法，也是很清楚的，如果听完还有问题，可以继续交流！

PEI · 2022年09月19日

但这个题计算器我按出来的CV mkt factor=0.001308，最后得出93%,高于87% 四位小数和6位小数都试过，您能算一下吗？哪里出了问题。我的公式列出的每一项都和答案之前的步骤是一样的，但算出答案不一样。

笛子_品职助教 · 2022年09月20日

嗨，爱思考的PZer你好：


但这个题计算器我按出来的CV mkt factor=0.001308，最后得出93%,高于87% 四位小数和6位小数都试过，您能算一下吗？哪里出了问题。我的公式列出的每一项都和答案之前的步骤是一样的，但算出答案不一样。


Hello，亲爱的同学，根据我的经验，这个问题是不是计算器误触了呀，考试之前指甲要剪短哈。也可能是看错了正负号，后面两个是负号。

老师算一遍，同学看看步骤，核对一下。


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)

=0.001271 + 0.000056 - 0.000095 - 0.000009

= 0.001223

----------------------------------------------
努力的时光都是限量版，加油！

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