基于DEA的投资组合评价与投资策略优化研究

There are several researches on applying DEA approach to portfolio performance evaluation. Among the existing researches, there exist some limitations in the theoretical foundations and practical applications. This project takes the portfolio performance evaluation and investment strategy optimization as the research object. The input-output processes, stochastic investment possibility sets and their deterministic estimations are studied in the static and dynamic investment situations, respectively. Based on the deterministic estimations of stochastic investment possibility sets, the nonlinear and linear DEA models with certainty and uncertainty parameter are constructed to evaluate portfolio performance, respectively. The relationship among nonlinear and linear DEA frontiers and the real frontier is discussed and the convergence of the DEA frontiers is proved. An iterative algorithm is designed for the continuous improvement of DEA frontier and investment strategy. In order to connect the financial theory and empirical evidence more closely, an out-of-sample test is designed for testing the sustainability of the investment strategy. This project is expected to provide theoretical and methodological support for applying DEA methods to portfolio performance evaluation and optimization. The study presents a novel idea for optimizing investment strategies, and can provide decision supports to investors, portfolio managers and financial market regulation authorities.

现有的基于DEA的投资组合评价研究在理论基础和实际应用中存在诸多不足。本项目以投资组合评价和优化为研究对象，在静态和动态两种情形下，分别研究投资组合的投入-产出过程、随机投资可能集及其确定性估计等问题。在参数确定和不确定两种情形下，分别构建非线性和线性投资组合DEA评价模型，研究非线性和线性DEA前沿面与真实前沿面之间的关系，从理论上证明DEA前沿面的收敛性，为DEA应用于投资组合评价奠定理论基础。通过设计迭代算法对DEA前沿面与投资策略进行持续改进，设计样本外检验方法对投资策略绩效的可持续性进行评价，以弥补投资组合评价中“金融理论与实证证据”相脱离的缺陷。本项目为投资组合评价和优化提供了一种新的思路，为DEA方法在投资组合评价和优化中的应用提供系统的理论基础与方法支持，相关成果可以为投资者、金融产品管理者和金融监管部门提供决策支持。

针对现有基于DEA方法的投资组合评价研究大多基于历史数据，以风险-期望收益的投入-产出关系构建评价模型，基本不考虑DEA方法应用于投资组合评价的理论基础，普遍假定资产收益参数估计不存在误差等问题。本项目以投资组合评价与投资策略优化为研究对象，分析实际投资过程中投资组合的投入-产出过程，在静态和动态两种情形下构建随机投资可能集，通过对随机投资可能集的确定性估计来建立相应的DEA评价模型，进而讨论投资组合的绩效。并以DEA评价模型为基础，在资产收益参数确定和不确定两种情形下分别构建可实现的静态、动态投资策略，设计样本外评价方法，检验评价结果和投资策略标杆的有效性。实证研究中，基于我国以及欧美发达市场的金融产品数据对上述评价模型、算法以及投资组合策略进行应用分析，为个体投资者和机构投资者在实际投资中提供决策建议。本项目从新的研究视角进一步完善了现有的投资组合评价和优化研究，对促进DEA方法在投资组合评价和投资策略优化中的应用具有重要的理论和实际意义。