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我爱荷包蛋 · 2024年04月23日

Reverse-optimization方法如何得到implied return?

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NO.PZ201803130100000401

问题如下:

Contrast, using the information provided above, the results of a reverse optimization approach with that of the MVO approach for each of the following:
i. The asset allocation mix. Justify your response.

选项:

解释:

■ The asset allocation weights for the reverse optimization method are inputs into the optimization and are determined by the market capitalization weights of the global market portfolio.

■ The asset allocation weights for the MVO method are outputs of the optimization with the expected returns, covariances, and a risk aversion coefficient used as inputs.

■ The two methods result in significantly different asset allocation mixes.

■ In contrast to MVO, the reverse optimization method results in a higher percentage point allocation to global bonds, US bonds, and global equities as well as a lower percentage point allocation to cash and US equities.

The reverse optimization method takes the asset allocation weights as its inputs that are assumed to be optimal. These weights are calculated as the market capitalization weights of a global market portfolio. In contrast, the outputs of an MVO are the asset allocation weights, which are based on (1) expected returns and covariances that are forecasted using historical data and (2) a risk aversion coefficient. The two methods result in significantly different asset allocation mixes. In contrast to MVO, the reverse optimization method results in a 4.9, 5.5, and 10.1 higher percentage point allocation to US bonds, global equities, and global bonds, respectively, and a 6.1 and 14.4 lower percentage point allocation to cash and US equities, respectively.
The asset allocation under the two methods is as follows:



第一题的第二小问为什么使用CAPM来求资产大类的implied return?

课程中何老师是说用资产大类的市值权重来求?

1 个答案

Lucky_品职助教 · 2024年04月23日

嗨,从没放弃的小努力你好:


Reverse-optimization 是用来解决MVO方法中,用历史数据估计expected return不靠谱的问题。

MVO正向最优化,是通过已知的expected return,SD,correlation来求出最优的一组权重。而Reverse-optimization反向最优,则是先假定一组最优的权重,然后通过已知的SD和correlation,来求出expected return,这里的最优的权重一般都是使用资产大类的市值权重,最后求得的expected return,我们把它叫做implied return。


资本资产定价模型CAPM主要研究证券市场中均衡价格是怎样形成的,以此来寻找证券市场中被错误定价的证券。将现行的实际证券市场价格与均衡状态下的证券价格进行比较,若两者不等,说明市场价格被错误定价,误定的市场价格应该能够回归到均衡价格。利用这一点便可获得超正常收益,当现实的市场价格低于均衡价格时,说明该证券被低估了,应该购买;反之,如果现实的市场价格高于均衡价格, 说明该证券被高估了,则应该卖出该证券。


CAPM的关键假设是,所有投资者都会用一系列的投入组合来绘制包含了所有风险资产的有效边界,从而通过绘出有效边界的切线资产配置线(CAL)确定一个有效风险组合 P。因为市场组合是所有风险组合的加总, 市场组合内的资产比例也是投资者的持有比例。所以如果所有投资者选择相同的风险资产组合, 这个组合一定是市场组合, 即可投资集中所有资产以市值加权平均得到的组合。所以,通过CAPM计算出的是某个证券在给定的风险水平下,能够获得的必要报酬率或是基准收益率,也称之为implied return。










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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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