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风险因子及风险控制系列之二:共同风险、特质风险的计算及应用
Xinda Securities·2025-08-14 10:04

Quantitative Models and Construction Methods Factor Covariance Matrix and Specific Volatility - Model Name: Factor Covariance Matrix - Construction Idea: The factor covariance matrix is used to capture the dynamic co-variation relationships between factors, providing a systematic framework for understanding market risk transmission mechanisms[3][18] - Construction Process: 1. EM Algorithm: Used to fill missing values in factor returns. The E-step estimates the conditional expectation of missing values, while the M-step re-estimates parameters iteratively until convergence Formula: $E[f_{mis}|f_{obs}]=\mu_{mis}+\Sigma_{mis,obs}\Sigma_{obs,obs}^{-1}(f_{obs}-\mu_{obs})$[21] Log-likelihood function: $L(\mu,\Sigma)=-\frac{T}{2}\big(D ln(2\pi)+\ln\big(\operatorname*{det}(\Sigma)\big)\big)-\frac{1}{2}\sum_{t=1}^{T}(f_{t}-\mu)^{\prime}\Sigma^{-1}(f_{t}-\mu)$[22] 2. Half-life Weighted Adjustment: Assigns exponentially decaying weights to historical data, emphasizing recent data[26] 3. Newey-West Adjustment: Corrects for heteroskedasticity and autocorrelation in time series data Formula: $\Sigma_{NW}=\Sigma_{0}+\sum_{i=1}^{L}w_{i}(\Sigma_{i}+\Sigma_{i}^{\prime})$[28] 4. Eigenfactor Adjustment: Addresses systematic underestimation of low-risk factor combinations using Monte Carlo simulations[35][38] 5. Volatility Regime Adjustment (VRA): Adjusts factor volatilities to account for cross-sectional biases Formula: $\lambda_{F}=\sqrt{\sum_{t}(B_{t}^{F})^{2}w_{t}}$ $\tilde{\sigma}{k}=\lambda{F}\sigma_{k}$[53][54] - Evaluation: The factor covariance matrix effectively captures market co-variation relationships and provides reliable inputs for portfolio optimization[18][85] - Model Name: Specific Volatility - Construction Idea: Specific volatility focuses on predicting idiosyncratic risks at the stock level, addressing missing values and data anomalies[60] - Construction Process: 1. Half-life Weighted Adjustment and Newey-West Adjustment: Similar to the factor covariance matrix, but with different half-life settings for covariance and autocovariance matrices[61] 2. Structured Model: Adjusts for missing and anomalous data based on the relationship between specific volatility and factor exposures Formula: $\ln(\sigma_{n}^{TS})=\sum_{k}x_{nk}b_{k}+\epsilon_{n}$[67] 3. Bayesian Shrinkage: Reduces mean-reversion bias by shrinking estimates toward group averages Formula: $\sigma_{n}^{SH}=v_{n}\bar{\sigma}(g_{n})+(1-v_{n})\hat{\sigma}{n}$[72] 4. Volatility Regime Adjustment (VRA): Similar to factor volatility adjustment, but incorporates market-cap-weighted cross-sectional biases Formula: $\lambda{S}=\sqrt{\sum_{t}(B_{t}^{S})^{2}w_{t}}$ $\tilde{\sigma}{n}=\lambda{S}\sigma_{n}^{SH}$[79][80] - Evaluation: Specific volatility adjustments improve the accuracy of idiosyncratic risk predictions, particularly for stocks with high data quality[60][73] --- Model Backtesting Results Factor Covariance Matrix - Bias Statistic: - Random portfolios: 1.05-1.06 - CSI 300: 1.15-1.19 - CSI 1000: 1.10-1.16[91] - Q Statistic: - Random portfolios: 2.73 - CSI 300: 2.95-2.97 - CSI 1000: 2.72-2.83[91] Specific Volatility - Bias Statistic: - Random portfolios: 1.06-1.07 - CSI 300: 1.19 - CSI 1000: 1.10[93] - Q Statistic: - Random portfolios: 2.73 - CSI 300: 2.97 - CSI 1000: 2.72[93] --- Quantitative Factors and Construction Methods Composite Fundamental-Price Factor - Factor Name: Composite Fundamental-Price Factor - Construction Idea: Combines low-frequency and high-frequency price-volume factors with fundamental factors to predict stock returns[128] - Construction Process: 1. Lasso Model: Uses a penalty coefficient of 0.001 to select features and predict market-neutralized stock returns[128] 2. Factor Evaluation: - RankIC: 7.43% - ICIR: 0.72 - Annualized long-short excess return: 61.15%[131] - Evaluation: The factor demonstrates strong predictive power but exhibits periodic underperformance during unfavorable market conditions[130] --- Factor Backtesting Results Composite Fundamental-Price Factor - RankIC: 7.43% - ICIR: 0.72 - Annualized Long-Short Excess Return: 61.15% - Annualized Long-Only Excess Return: 18.74%[131] 800 Index Enhancement Strategy - Annualized Returns: - Portfolio 1 (only stock deviation control): 18.28% - Portfolio 2 (stock/industry/style deviation control): 16.26% - Portfolio 3 (stock deviation + tracking error control): 17.81%[135][144] - Tracking Error: - Portfolio 1: 9.14% - Portfolio 2: 4.73% - Portfolio 3: 4.99%[135] --- Evaluation and Insights - The factor covariance matrix and specific volatility models provide robust risk predictions, enabling effective portfolio optimization and risk decomposition[85][152] - The composite fundamental-price factor demonstrates strong predictive ability but requires careful management of style and industry constraints to maintain alpha generation[130][136]