学海拾珠系列之二百三十四：利用强化学习和文本网络改进相关矩阵估计

Quantitative Models and Construction Methods - Model Name: RL-TBN; Model Construction Idea: Combines reinforcement learning (RL) with text-based networks (TBN) to optimize covariance matrix shrinkage and global minimum variance (GMV) portfolio[2][3][19] - Model Construction Process: 1. Covariance Matrix Shrinkage: The covariance matrix is decomposed into a diagonal matrix of volatilities and a correlation matrix. Shrinkage is applied to the correlation matrix using the formula: $ \widetilde{\mathbf{R}}{t}=(1-\alpha)\widehat{\mathbf{R}}{t}+\alpha\mathbf{\widetilde{R}}{t} $ Here, $\alpha$ represents the shrinkage intensity, and $\mathbf{\widetilde{R}}{t}$ is the shrinkage target[33][34]. 2. Text-Based Networks (TBN): TBN is constructed by analyzing product descriptions in companies' 10-K filings. Unique nouns are extracted and vectorized, and cosine similarity is calculated to form the TBN matrix: $ B_{t}={\frac{M_{t}M_{t}^{\mathsf{T}}}{|M_{t}|{F}^{2}}} $ where $M{t}$ is the normalized matrix of product descriptions[37][38]. 3. Reinforcement Learning (RL): RL optimizes shrinkage intensity $\alpha$ using the Proximal Policy Optimization (PPO) algorithm. The reward function is based on exponential utility: $ r_{p,t+\frac{i}{252}}(\alpha_{t}(m))={\bf x}(\alpha_{t}(m))^{\sf T}{\bf Y}_{t+\frac{i}{252}} $ RL agents are trained using rolling windows to dynamically adjust shrinkage intensity[48][53][55]. - Model Evaluation: RL-TBN demonstrates adaptability to macroeconomic uncertainty and effectively reduces estimation errors, outperforming traditional methods in stability and risk-adjusted returns[5][19][80]. Model Backtesting Results - RL-TBN: - Volatility: 0.088 - Sharpe Ratio: 1.351 - VaR: 0.129[4][79][80] Quantitative Factors and Construction Methods - Factor Name: Text-Based Networks (TBN); Factor Construction Idea: Measures product similarity between companies using textual analysis of 10-K filings[19][37][38] - Factor Construction Process: 1. Extract unique nouns from product descriptions in 10-K filings, excluding common words and stop words. 2. Vectorize product descriptions into binary vectors and normalize them. 3. Calculate cosine similarity between vectors to form the TBN matrix[37][38]. - Factor Evaluation: TBN provides a fundamental perspective on stock correlations, capturing industry structure and reducing estimation variance[23][99][102]. Factor Backtesting Results - TBN: - Volatility: Lower than sample correlation matrices - Frobenius Norm Stability: Demonstrates reduced variance compared to traditional methods[101][119][120] Additional Insights - Mechanism Analysis: - TBN predicts future stock correlation changes, with higher product similarity leading to lower future correlations[25][104][108]. - RL dynamically adjusts shrinkage intensity based on macroeconomic indicators, such as investor sentiment and uncertainty[94][95][96]. - Variance Reduction: TBN-based RL strategies achieve superior performance by reducing variance, particularly in low-variance groups[118][124][125].