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Lulu1214 · 2020年10月01日

问一道题:NO.PZ2018011501000007 [ CFA III ]

问题如下:

Müller uses a risk parity asset allocation approach with a client’s four–asset class portfolio. The expected return of the domestic bond asset class is the lowest of the asset classes, and the returns of the domestic bond asset class have the lowest covariance with other asset class returns. Müller estimates the weight that should be placed on domestic bonds.

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)=1nσp2\frac1n\sigma_p^2  

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.

组合的方差是25%?这个怎么来的呢
3 个答案

pzqa015 · 2021年09月28日

嗨,从没放弃的小努力你好:


Risk parity的条件是ACTRi=ACTRj,也即每个资产对portfolio variance贡献应该相同,题目有四个资产,所以每个资产对portfolio variance的贡献应该是portfolio variance的25%。每个资产对portfolio variance的贡献用wi*Cov(Ri,Rp)表示。

这道题说: the returns of the domestic bond asset class have the lowest co-variance with other asset class returns,若假设domestic bond asset class是资产i,这句话意思就是在四个资产中,Cov(Ri,Rp)最小,既然wi*Cov(Ri,Rp)要达到portfolio variance的25%,Cov(Ri,Rp)小,所以,wi要大于25%。

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加油吧,让我们一起遇见更好的自己!

Shimin_CPA税法主讲、CFA教研 · 2021年03月07日

嗨,努力学习的PZer你好:


@ mino酱是个小破货,可以这么理解。加油!

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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!

Olive_品职助教 · 2020年10月03日

嗨,从没放弃的小努力你好:


题目说了是four–asset class portfolio,说明组合中一共有四种资产,所以n=4,1/4=25%


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努力的时光都是限量版,加油!


mino酱是个小破货 · 2021年03月07日

补充下不知道这个思路可否行,因为cov(r,P)小于cov(p,p)即平凡,所以为公式相等wi要大于1/n

Louis · 2021年09月23日

老师没看懂这里,25%到底是假设的还是算出来的?题目里没有方差的信息呀