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yan · 2025年01月06日

能否解释一下,为什么高协方差会导致低active risk

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NO.PZ202207040100000405

问题如下:

From Exhibit 3, the replacement candidate fund that, if included, will most likely minimize the active risk of the final Amity equity fund is:

选项:

A.Ash.

B.Blue.

C.March.

解释:

Solution

A is correct. Active risk is a measure of the volatility of portfolio returns relative to the volatility of benchmark returns. The Ash fund will most likely minimize the active risk when combined in the final Amity equity portfolio because of its high covariance with the present fund. The low-covariance funds may reduce overall portfolio volatility but not active risk.

B is incorrect. The low covariance with the Amity portfolio will lower the overall volatility of the fund but not the active risk, because active risk measures the volatility of portfolio returns relative to that of the benchmark: This will be achieved through the substitution of a high-covariance fund.

C is incorrect. The low covariance with the Amity portfolio will lower the overall volatility of the fund but not the active risk, because active risk measures the volatility of portfolio returns relative to that of the benchmark: This will be achieved through the substitution of a high covariance fund.

中文解析:

本题考查的是主动风险。这道题目要求根据给出的数据选择一个能够最有效降低整体投资组合(Amity基金)主动风险的基金。主动风险是指投资组合回报与基准回报之间的波动差异,题目要求从三个基金中选择一个能够最小化这一差异的基金。

选项AAsh基金。 Ash基金与Amity基金的协方差较高,这意味着该基金的收益波动率与Amity基金的收益波动率相似。当两个基金的收益波动率相似时,它们可以在组合中相互对冲,从而减少整体的主动风险。尽管Ash基金的主动风险较高,但与Amity基金的高协方差意味着它在组合中的贡献将最有效地降低整体的主动风险。因此,正确答案是A

选项B不正确。Blue基金与Amity基金的协方差较低,虽然这可以降低组合的整体波动性,但它不会减少主动风险。主动风险衡量的是投资组合相对于基准的波动性,低协方差的基金会减少整体波动性,但无法有效降低主动风险。

选项C也不正确。尽管March基金与Amity基金的协方差也较低,且其年化主动风险最小,但它不能有效降低主动风险,因为其收益波动率与Amity基金的收益波动率差异较大,低协方差的基金对于降低主动风险的效果有限。

能否解释一下,为什么高协方差会导致低active risk

1 个答案

笛子_品职助教 · 2025年01月06日

嗨,爱思考的PZer你好:


能否解释一下,为什么高协方差会导致低active risk

Hello,亲爱的同学~

这里需补充一个已知条件:原来的基金是amity,这个原来的amity基金是风险有效的(risk efficiency)。


结合本题:

Amity基金是risk efficiency的

现在要把amity基金中的20%,替换成其他的基金,新基金是80% 的amity + 20% 的其他基金,要让新基金依然风险有效(risk efficiency)


因为原来的基金已经risk efficiency了,所以我们替换的这部分,要与原来的基金相关性高,协方差高。

这样组合起来的新基金才不会改变老基金risk efficiency的特征。


例如:A同学确认要参加数学竞赛,A同学满分100分的试卷可以考98分。

现在,竞赛必须2人参加,因此,需要在B、C两名同学中,选择1名同学,和A同学一起参加竞赛。

B同学可以考95分,C同学可以考85分。

那么我们选择B同学,因为B同学的95分,与A同学的98分,更像,协方差更高。

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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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