关于Cov(Ri,Rp)最小的一个疑问

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：

less than 25%.

equal to 25%.

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)=$\frac1n\sigma_p^2$

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.

考点：risk parity

解析：risk parity的宗旨是组合中每种资产对总风险的贡献度相同，即ACTR1=ACTR2=...ACTRn。题目中的这个组合总共有4种资产，所以n=4，每一种资产对总风险的贡献度应当为25%。由于 expected return of the domestic bond asset class is the lowest of the asset classes，国内债券的收益率是4种资产中最低的，所以风险也是最低的，那么为了达到对总风险的贡献度为25%，这种资产类型的权重应当比其他资产更大，因此大于25%。