基于拟范数正则化的稀疏投资组合选择

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英文标题：
《Sparse Portfolio Selection via Quasi-Norm Regularization》
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作者：
Caihua Chen, Xindan Li, Caleb Tolman, Suyang Wang, Yinyu Ye
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最新提交年份：
2013
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英文摘要：
  In this paper, we propose $\\ell_p$-norm regularized models to seek near-optimal sparse portfolios. These sparse solutions reduce the complexity of portfolio implementation and management. Theoretical results are established to guarantee the sparsity of the second-order KKT points of the $\\ell_p$-norm regularized models. More interestingly, we present a theory that relates sparsity of the KKT points with Projected correlation and Projected Sharpe ratio. We also design an interior point algorithm to obtain an approximate second-order KKT solution of the $\\ell_p$-norm models in polynomial time with a fixed error tolerance, and then test our $\\ell_p$-norm modes on S&P 500 (2008-2012) data and international market data.\\ The computational results illustrate that the $\\ell_p$-norm regularized models can generate portfolios of any desired sparsity with portfolio variance and portfolio return comparable to those of the unregularized Markowitz model with cardinality constraint. Our analysis of a combined model lead us to conclude that sparsity is not directly related to overfitting at all. Instead, we find that sparsity moderates overfitting only indirectly. A combined $\\ell_1$-$\\ell_p$ model shows that the proper choose of leverage, which is the amount of additional buying-power generated by selling short can mitigate overfitting; A combined $\\ell_2$-$\\ell_p$ model is able to produce extremely high performing portfolios that exceeded the 1/N strategy and all $\\ell_1$ and $\\ell_2$ regularized portfolios.
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中文摘要：
在本文中，我们提出了$\\ ell\\u p$-范数正则化模型来寻求接近最优的稀疏投资组合。这些稀疏的解决方案降低了项目组合实施和管理的复杂性。建立了保证$\\ ell\\u p$-范数正则化模型二阶KKT点稀疏性的理论结果。更有趣的是，我们提出了一个理论，将KKT点的稀疏性和投影相关性和投影夏普比联系起来。我们还设计了一个内点算法，以获得多项式时间内具有固定误差容限的$\\ell\\u p$-范数模型的近似二阶KKT解，然后在标准普尔500（2008-2012）数据和国际市场数据上测试我们的$\\ell\\u p$-范数模型。\\计算结果表明$\\ ell\\u p$-范数正则化模型可以生成任意稀疏度的投资组合，其投资组合方差和投资组合收益与基数约束下的非正则化Markowitz模型相当。通过对组合模型的分析，我们得出结论，稀疏性与过度拟合没有直接关系。相反，我们发现稀疏性只是间接地缓和了过度拟合。组合的$\\ellu 1$-$\\ellu p$模型表明，适当选择杠杆率，即卖空产生的额外购买力，可以缓解过度拟合；组合的$\\ellu 2$-$\\ellu p$模型能够产生超过1/N策略的极高绩效投资组合，以及所有$\\ellu 1$和$\\ellu 2$正规化投资组合。
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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：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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关键词：投资组合选择 投资组合 正则化 Optimization Quantitative