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yan · 2024年09月23日

1.文中只说了收益最小，没说风险最小，如何得出风险最小？2.如何从公式理解这道题？

  1. CFA III
  2. Asset Allocation

* 问题详情，请 查看题干

NO.PZ201803130100000107

问题如下：

In the risk parity asset allocation approach that Müller uses, the weight that Müller places on domestic bonds should be:

选项：

A.

less than 25%.

B.

equal to 25%.

C.

greater than 25%.

解释：

C is correct.

A risk parity asset allocation is based on the notion that each asset class should contribute equally to the total risk of the portfolio. Bonds have the lowest risk level and must contribute 25% of the portfolio’s total risk, so bonds must be overweighted (greater than 25%). The equal contribution of each asset class is calculated as:

wi* Cov(ri,rp)=1nδρ2

where

wi = weight of asset i

Cov(ri,rp) = covariance of asset i with the portfolio

n = number of assets

σ2= variance of the portfolio

In this example, there are four asset classes, and the variance of the total portfolio is assumed to be 25%; therefore, using a risk parity approach, the allocation to each asset class is expected to contribute (1/4 × 25%) = 6.25% of the total variance. Because bonds have the lowest covariance, they must have a higher relative weight to achieve the same contribution to risk as the other asset classes.

1.文中只说了收益最小，没说风险最小，如何得出风险最小？2.如何从公式理解这道题？


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已采纳答案

Lucky_品职助教 · 2024年09月23日

嗨，从没放弃的小努力你好：


同学你好：


严谨一点讲，这道题的结论是通过这个公式推导出来的，而不是计算出来的。


这个公式的左边，是每一个资产的权重乘以它和组合的Cov, 右边是组合variance的四分之一，无论组合variance是多少，风险平价在资产配置里的观念是，每个资产类别对投资组合的总风险的贡献应该相等，也就是每个资产的公式右侧都是相等的，在这个例子中，有四个资产类别，如果平均来看，每个资产应该贡献总风险的25%。那既然等式的右侧都是相同的，而左侧中 domestic bond的Cov是最低的，所以如果想要让domestic bond贡献出和其他资产相同的风险，那就需要domestic bond的配置权重必须大于平均的25%，因此它们必须具有较高的相对权重才能实现与其他资产类别相同的风险贡献。




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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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