贝叶斯均值方差分析：最优投资组合选择

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英文标题：
《Bayesian mean-variance analysis: Optimal portfolio selection under
  parameter uncertainty》
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作者：
David Bauder, Taras Bodnar, Nestor Parolya, Wolfgang Schmid
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最新提交年份：
2018
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英文摘要：
  The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, like the mean vector and the covariance matrix are unknown and have to be estimated by using historical data of the asset returns. The new approach employs the Bayesian posterior predictive distribution which is the distribution of the future realization of the asset returns given the observable sample. The parameters of the posterior predictive distributions are functions of the observed data values and, consequently, the solution of the optimization problem is expressed in terms of data only and does not depend on unknown quantities. In contrast, the optimization problem of the traditional approach is based on unknown quantities which are estimated in the second step leading to a suboptimal solution. We also derive a very useful stochastic representation of the posterior predictive distribution whose application leads not only to the solution of the considered optimization problem, but provides the posterior predictive distribution of the optimal portfolio return used to construct a prediction interval. A Bayesian efficient frontier, a set of optimal portfolios obtained by employing the posterior predictive distribution, is constructed as well. Theoretically and using real data we show that the Bayesian efficient frontier outperforms the sample efficient frontier, a common estimator of the set of optimal portfolios known to be overoptimistic.
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中文摘要：
本文解决了当资产收益率分布的均值向量和协方差矩阵等参数未知且必须利用资产收益率的历史数据进行估计时的最优投资组合选择问题。新方法采用贝叶斯后验预测分布，即给定可观测样本的资产收益未来实现的分布。后验预测分布的参数是观测数据值的函数，因此，优化问题的解仅用数据表示，不依赖于未知量。相比之下，传统方法的优化问题是基于未知量的，这些未知量在第二步进行估计，从而得到次优解。我们还推导了后验预测分布的一个非常有用的随机表示，其应用不仅可以解决所考虑的优化问题，而且可以提供用于构建预测区间的最优投资组合回报的后验预测分布。构造了贝叶斯有效前沿，即采用后验预测分布得到的一组最优投资组合。从理论上并使用实际数据，我们表明贝叶斯有效边界优于样本有效边界，样本有效边界是最优投资组合集合的一种常见估计量，被认为过于乐观。
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分类信息：

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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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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关键词：投资组合选择 均值方差 投资组合 方差分析 贝叶斯