AI 中文总结
本文针对投资组合复制的不适定问题，提出熵因子模型，通过两阶段熵方法优化权重，在多类实验中较OLS表现更优，且在市场极端压力下具鲁棒性。
AI 中文摘要
投资组合复制即构建可交易资产篮子以匹配目标基准的风险收益特征，本质是不适定逆问题。当限定于部分可用资产时，经典方差最小化模型常产生不稳定、过度杠杆化的投资组合，极易受市场冲击影响。本文提出一种基于信息论的统一两阶段方法以实现鲁棒投资组合复制：第一阶段，将成分资产收益建模为目标因子，通过熵最小化原理在数据驱动的经验边界内估计参数；第二阶段，采用相同熵方法确定最优复制权重。两种阶段均使用直接定义于逆问题约束集上的费米-狄拉克型熵函数。本文在五项数值实验（含标准股票跟踪、多资产合成及极端压力测试场景）中，将该熵因子模型（EFM）与普通最小二乘法（OLS）对比验证。实证结果显示，EFM在年化换手率和税后收益方面始终优于OLS；尤为关键的是，在COVID-19市场崩盘及严重的特质性数据损坏情况下，该熵框架可作为概率型“断路器”，主动降低对受损资产的资本配置，为广义投资组合复制提供高度鲁棒、风险规避的解决方案。
英文摘要
Portfolio replication, or the construction of a tradable basket of assets to match the risk-return profile of a target benchmark, is fundamentally an ill-posed inverse problem. When restricted to a subset of available assets, classical variance-minimizing models often yield unstable, over-leveraged portfolios highly vulnerable to market shocks. We propose a unified, two-stage methodology rooted in information theory to achieve robust portfolio replication. First, we model the constituent asset returns against target factors, estimating parameters within data-driven empirical bounds via an entropy minimization principle. Second, using the same entropic approach, we determine the optimal weight replication. In both cases we use an entropy function of the Fermi-Dirac type defined directly on sets of constraints of the inverse problem. We validate this Entropic Factor Model (EFM) against standard Ordinary Least Squares (OLS) across five numerical experiments, including standard equity tracking, multi-asset synthesis, and severe stress-test scenarios. Empirical results demonstrate that the EFM consistently outperforms OLS in terms of annualized turnover and net-of-fees returns. Crucially, during the COVID-19 market crash and under severe idiosyncratic data corruption, the entropic framework acts as a probabilistic ``circuit breaker", defensively reducing capital allocation to compromised assets and providing a highly robust, risk-averse solution for generalized portfolio replication.
Comments20 pages, 1 figure
