高维稀疏低秩的多目标矩阵回归模型及其组合管理策略

本文通过双因子随机过程表征资产价格的长短期运行趋势，选择具有重要影响力的市场指数构建有效市场组合，采用稀疏低秩的多目标回归方法深度挖掘市场特征，并自适应地捕捉市场趋势，最终利用预配权稀疏分散再优化方法获得矩阵回归的最优投资策略.研究发现高维稀疏低秩策略不仅可以实现全局和局部降维、低秩和稀疏约减的统一，还可以选择性地降低高维资产数目，更好地捕捉资产的非线性特性，更容易抓住资产间的关联关系.多目标稀疏分散回归策略具有集中配置资源、稀疏分散风险和稳定提高投资组合整体绩效的能力，组合管理成本更低，优越性更明显.实证结论对量化投资组合管理、资产配置优化及投资分析具有重要指导意义.

High-dimensional sparse low-rank multi-objective matrix regression model and its portfolio management strategy

This paper uses a two-factor stochastic process to characterize the long-term and short-term operating trends of asset prices, selects market indexes with important influences to build an effective market portfolio, uses sparse low-rank multi-objective regression methods to deeply explore market characteristics, and adaptively captures market trends. Finally, the optimal investment strategy for matrix regression is obtained by using the sparse decentralized re-optimization method of pre-assignment weights. The study found that the high-dimensional sparse low-rank strategy can not only achieve the unity of global and local dimensionality reduction, but also selectively discard high-dimensional assets, better capture the nonlinear characteristics of assets, and make it easier to grasp the relationship between assets. The multi-objective sparse and decentralized regression strategy has the ability to centrally allocate resources, sparsely disperse risks, and steadily improve the overall performance of the portfolio. The portfolio management cost is lower and the advantages are more obvious. The empirical conclusions have important guiding significance for quantitative portfolio management, asset allocation optimization and investment analysis.