随机矩阵理论与基金投资组合优化

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摘要翻译：
对冲基金投资的专有性质意味着，经理人通常只公布最低限度的回报信息。对冲基金投资组合的构建需要一个相关矩阵，该矩阵通常必须使用相对较小的月度收益数据样本来估计，这会产生噪声。本文将随机矩阵理论(RMT)应用于利用对冲基金收益数据构造的互相关矩阵C。分析揭示了许多偏离RMT所建议的谱的特征值。偏离特征向量的组成部分被发现对应于对冲基金经理所应用的不同策略组。反参与比用于量化参与每个特征向量的分量数。最后，通过分离C的噪声部分和非噪声部分来清理相关矩阵。该技术被发现可以大大减小投资组合的预测风险和实现风险之间的差异，从而改善对冲基金基金的风险状况。
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英文标题：
《Random Matrix Theory and Fund of Funds Portfolio Optimisation》
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作者：
Thomas Conlon, Heather J. Ruskin, Martin Crane
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最新提交年份：
2010
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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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一级分类：Quantitative Finance        数量金融学
二级分类：Risk Management        风险管理
分类描述：Measurement and management of financial risks in trading, banking, insurance, corporate and other applications
衡量和管理贸易、银行、保险、企业和其他应用中的金融风险
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英文摘要：
  The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a Fund of Hedge Funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The Inverse Participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.
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PDF链接：
https://arxiv.org/pdf/1005.5021

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关键词：投资组合优化 投资组合 矩阵理论 基金投资 Quantitative hedge Hedge 基金 特征向量 发现