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七七 · 2024年07月14日

Resampling为什么会导致riskier资产over-diversified

NO.PZ2022122801000026

问题如下:

Remington and Montgomery discuss with Winfeld some alternative asset allocation models that she may wish to consider, including resampled mean–variance optimization (resampling). Remington explains that resampling combines mean–variance optimization (MVO) with Monte Carlo simulation, leading to more diversified asset allocations. Montgomery comments that resampling, like other asset allocation models, is subject to criticisms, including that risker asset allocations tend to be under-diversified and the asset allocations inherit the estimation errors in the original inputs.

In Remington and Montgomery’s discussion with Winfeld on resampling, Montgomery’s comment is most likely:

选项:

A.

correct.

B.

incorrect regarding estimation errors.

C.

incorrect regarding diversification of asset allocations.

解释:

Montgomery’s comment about the criticisms of resampling is incorrect regarding diversification of asset allocations. Risker asset allocations are over-diversified, not under-diversified. The comment is correct with regard to estimation errors because the asset allocations do inherit the estimation errors in the original inputs.

Resampling为什么会导致riskier资产over-diversified?

一般MVO在包含alternative资产时,可能存在使用appraisal data的情况,会使得riskier资产看起来收益高风险低,进而over allocate另类资产的情况,那不就是under-diversified的了么

1 个答案

Lucky_品职助教 · 2024年07月15日

嗨,努力学习的PZer你好:


同学你好:


over-diversified 过度分散化是Resampling的缺点之一。框架图P16有总结到这一句,在Criticisms的(2)

说到底Resampling是一种统计学的方法,他是通过Monte Carlo Simulation扩大的数据规模,然后画出来了很多条有效前沿(simulated frontiers),最后在很多条有效前沿里取均值。但是某些有效前沿虽然统计学上成立,却不具有经济学的意义,也就是Criticisms中提到的(1)concave “bumps”。

因为正常情况下,有效前沿是向上倾斜的一条曲线,虽然表现为concave,但是风险增加,收益是增加的。而concave bump 指的是风险增加,收益反而减小了,体现在图中就是曲线弯过头了,下图中蓝色部分。长的跟肿块一样,所以比较形象地称为 bumps problem 。

Criticisms中的(1)(2)都是Resampling统计方法造成的结果。因为重复抽样、重复统计的次数太多了,为了充分分散化甚至重复画了很多次有效前沿,但导致的结果反而没有经济学意义。


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