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jerrywongcn · 2023年02月09日

variance contributed的计算

* 问题详情,请 查看题干

NO.PZ202207040100000805

问题如下:

The proportion of the Herrick Fund’s portfolio variance contributed by Country A is closest to:

选项:

A.20.9%. B.47.5%. C.56.8%.

解释:

Solution

B is correct. The covariance of returns between Country A and the portfolio is provided in Exhibit 2 as 0.0276.

The contribution of Country A to total portfolio variance is calculated as follows:

Weight A × Weight A × cov(A,A) = 0.30 × 0.30 × 0.06250 = 0.005625

Weight A × Weight B × cov(A,B) = 0.03 × 0.50 × 0.15000 = 0.002250

Weight A × Weight C × cov(A,C) = 0.30 × 0.20 × 0.00675 = 0.000405

Country A’s contribution to total portfolio variance = 0.00828

The portfolio variance = (Std. dev.)2 = (0.132)2 = 0.01742.

The proportion of total portfolio variance contributed by Country A is 0.00828 ÷ 0.01742 = 47.5%.

Alternatively, Country A’s contribution to total portfolio variance

= Weight A × cov(A,Pf) = 0.30 × 0.0276 = 0.00828.

A is incorrect. It uses cov(A,Pf) but expresses it as a percentage of std(Pf): 0.0276/0.132 × 100 = 20.9%. The cov(A,Pf) of 0.0276 is calculated above in an alternative presentation.

C is incorrect. It takes Weight A × std(A)/std(Pf) = 0.30 × 25/13.2 × 100 = 56.8%.

请问port variance能否用各country的贡献加总得到:

A: 0.00828;B: 0.004887;C: 0.001499,加总 0.0146655,贡献率变成56.46%




1 个答案

笛子_品职助教 · 2023年02月10日

嗨,努力学习的PZer你好:


请问port variance能否用各country的贡献加总得到:

Hello,亲爱的同学!

不可以这么算哦。教材例题上不是这个算法,这个算法是固定的。

我们的算法:

Weight A × Weight A × cov(A,A) = 0.30 × 0.30 × 0.06250 = 0.005625

Weight A × Weight B × cov(A,B) = 0.03 × 0.50 × 0.15000 = 0.002250

Weight A × Weight C × cov(A,C) = 0.30 × 0.20 × 0.00675 = 0.000405

Country A’s contribution to total portfolio variance = 0.00828

The portfolio variance = (Std. dev.)2 = (0.132)2 = 0.01742.


这样算就好。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!