This work introduces a novel methodology for portfolio optimization that is the first to integrate support vector machines (SVMs) with cardinality-constrained mean–variance optimization. We propose augmenting cardinality-constrained mean–variance optimization with a preference for portfolios with the property that a low-dimensional hyperplane can separate assets eligible for investment from those ineligible. We present convex mixed-integer quadratic programming models that jointly select a portfolio and a separating hyperplane. This joint selection optimizes a tradeoff between risk-adjusted returns, hyperplane margin, and classification errors made by the hyperplane. The models are amenable to standard commercial branch-and-bound solvers, requiring no custom implementation. We discuss the properties of the proposed optimization models and draw connections between existing portfolio optimization and SVM approaches. We develop a parameter selection strategy to address the selection of big-Ms and provide a financial interpretation of the proposed approach’s parameters. The parameter strategy yields valid big-M values, ensures the risk of the resulting portfolio is within a factor of the lowest possible risk, and produces informative hyperplanes for practitioners. The mathematical programming models and the associated parameter selection strategy are amenable to financial backtesting. The models are evaluated in-sample and out-of-sample on two distinct datasets in a rolling horizon backtesting framework. The portfolios resulting from the proposed approach display improved out-of-sample risk-adjusted returns compared to cardinality-constrained mean–variance optimization.

中文翻译：

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集成支持向量机和均值-方差优化以进行资本配置


这项工作介绍了一种新的投资组合优化方法，这是第一个将支持向量机 （SVM） 与基数约束的均值-方差优化集成在一起的方法。我们建议增强基数约束的均值方差优化，优先选择具有低维超平面可以将符合投资条件的资产与不符合投资条件的资产分开的投资组合。我们提出了凸混合整数二次规划模型，这些模型共同选择投资组合和分离超平面。这种联合选择优化了风险调整后回报、超平面利润率和超平面分类误差之间的权衡。这些模型适用于标准的商业 branch-and-bound 求解器，不需要自定义实现。我们讨论了所提出的优化模型的属性，并在现有的投资组合优化和 SVM 方法之间建立联系。我们开发了一个参数选择策略来解决 big-M 的选择问题，并提供了对所提出方法参数的财务解释。参数策略产生有效的 big-M 值，确保最终投资组合的风险在尽可能低的风险系数内，并为从业者提供信息丰富的超平面。数学规划模型和相关的参数选择策略适用于财务回溯测试。在滚动水平回溯测试框架中的两个不同数据集上对模型进行样本内和样本外评估。与基数约束的均值方差优化相比，所提出的方法产生的投资组合显示出更高的样本外风险调整后回报。