英文标题：
《Asymptotic distribution of the Markowitz portfolio》
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作者：
Steven E. Pav
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最新提交年份：
2020
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英文摘要：
The asymptotic distribution of the Markowitz portfolio is derived, for the general case (assuming fourth moments of returns exist), and for the case of multivariate normal returns. The derivation allows for inference which is robust to heteroskedasticity and autocorrelation of moments up to order four. As a side effect, one can estimate the proportion of error in the Markowitz portfolio due to mis-estimation of the covariance matrix. A likelihood ratio test is given which generalizes Dempster\'s Covariance Selection test to allow inference on linear combinations of the precision matrix and the Markowitz portfolio. Extensions of the main method to deal with hedged portfolios, conditional heteroskedasticity, conditional expectation, and constrained estimation are given. It is shown that the Hotelling-Lawley statistic generalizes the (squared) Sharpe ratio under the conditional expectation model. Asymptotic distributions of all four of the common `MGLH\' statistics are found, assuming random covariates. Examples are given demonstrating the possible uses of these results.
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中文摘要：
对于一般情况（假设存在收益的四阶矩），以及多元正态收益的情况，导出了马科维茨投资组合的渐近分布。该推导允许对高达四阶矩的异方差和自相关具有鲁棒性的推理。作为一种副作用，人们可以估计由于协方差矩阵估计错误而导致的马科维茨投资组合中的误差比例。给出了一个似然比检验，它推广了邓普斯特的协方差选择检验，允许对精度矩阵和马科维茨投资组合的线性组合进行推断。给出了处理套期保值投资组合、条件异方差性、条件期望和约束估计的主要方法的扩展。结果表明，Hotelling-Lawley统计量推广了条件期望模型下的（平方）Sharpe比率。在假设随机协变量的情况下，找到了所有四种常见“MGLH”统计量的渐近分布。举例说明了这些结果的可能用途。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Portfolio Management 项目组合管理
分类描述：Security selection and optimization, capital allocation, investment strategies and performance measurement
证券选择与优化、资本配置、投资策略与绩效评价
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一级分类：Quantitative Finance 数量金融学
二级分类：Statistical Finance 统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
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