摘要翻译：
在这篇简短的报告中，我们讨论了如何使用坐标下降算法来解决组合权重受$l_{q}$范数约束的最小方差组合(MVP)问题，其中$1\leqq\leq2$。权重被这样的规范正则化的投资组合被称为稀疏投资组合（Brodie等人），因为这些约束促进了权重向量的稀疏性（零分量）。我们首先考虑一种情况，当投资组合的权重被加权的$L_{1}$和平方的$L_{2}$范数正则化。然后使用两个基准数据集（Fama和French 48个行业和100个规模和BM比率的投资组合）来检验稀疏投资组合的性能。当样本规模相对于资产数量不是相对较大时，稀疏投资组合往往具有较低的样本外投资组合方差、周转率、活跃资产和卖空头寸，但比非正则化MVP更高的夏普比率。然后我们给出了一些可能的扩展；特别地，我们给出了一个求解允许分组选择资产的MVP问题的有效算法。
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英文标题：
《A Note on Sparse Minimum Variance Portfolios and Coordinate-Wise Descent
  Algorithms》
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作者：
Yu-Min Yen
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最新提交年份：
2013
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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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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
  In this short report, we discuss how coordinate-wise descent algorithms can be used to solve minimum variance portfolio (MVP) problems in which the portfolio weights are constrained by $l_{q}$ norms, where $1\leq q \leq 2$. A portfolio which weights are regularised by such norms is called a sparse portfolio (Brodie et al.), since these constraints facilitate sparsity (zero components) of the weight vector. We first consider a case when the portfolio weights are regularised by a weighted $l_{1}$ and squared $l_{2}$ norm. Then two benchmark data sets (Fama and French 48 industries and 100 size and BM ratio portfolios) are used to examine performances of the sparse portfolios. When the sample size is not relatively large to the number of assets, sparse portfolios tend to have lower out-of-sample portfolio variances, turnover rates, active assets, short-sale positions, but higher Sharpe ratios than the unregularised MVP. We then show some possible extensions; particularly we derive an efficient algorithm for solving an MVP problem in which assets are allowed to be chosen grouply.
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PDF链接：
https://arxiv.org/pdf/1005.5082