Quantitative Models and Construction Barra Risk Model - **Model Name**: Barra Risk Model (Barra CNE6) - **Model Construction Idea**: The model aims to reduce the dimensionality of asset returns, enabling the calculation of covariance matrices between assets, which are essential for portfolio optimization. It uses constrained weighted least squares (WLS) to address multicollinearity and heteroscedasticity issues, constructing pure factor portfolios that isolate exposure to individual factors [3][9][11] - **Model Construction Process**: 1. The cross-sectional asset returns are modeled using a multi-factor linear regression: $R_{t}=\alpha+\beta\lambda_{t}+\varepsilon_{t}$ Here, $\beta$ represents factor exposures, $\lambda_{t}$ denotes factor returns, and $\varepsilon_{t}$ is the residual [9][10] 2. The covariance matrix of asset returns is derived as: $\Sigma_{R}=\beta\Sigma_{A}\beta^{T}+\Sigma_{E}$ $\Sigma_{A}$ is the covariance matrix of factors, and $\Sigma_{E}$ is the covariance matrix of residuals [11][12] 3. Factor exposures are standardized using market capitalization-weighted normalization: $$\widehat{\boldsymbol{\beta}_{t-1}^{j}}=\frac{{\boldsymbol{\beta}_{t-1}^{j}}-\frac{\sum_{i}^{N}s_{i,t-1}\beta_{i,t-1}^{j}}{\sum_{i}^{N}s_{i,t-1}}}{s t d({\boldsymbol{\beta}_{t-1}^{j}})}$$ Here, $s_{i,t-1}$ represents the market capitalization of stock $i$ at time $t-1$ [18][32] 4. Industry factor returns are constrained to ensure neutrality: $\sum_{i=1}^{P}s_{I_{i}}\lambda_{i}^{I_{i}}=0$ [18][22] 5. Factor returns are estimated using constrained WLS: $$\lambda_{t}=C_{t}(C_{t}\beta_{t-1}W^{-1}\beta_{t-1}C_{t})^{-1}C_{t}\beta_{t-1}W^{-1}R_{t}$$ Here, $W$ is the weight matrix, and $C_{t}$ represents constraints [20][25] - **Model Evaluation**: The model effectively isolates factor exposures, enabling better evaluation of factor returns. However, pure factor portfolios have low investability due to constraints like short-selling limitations [19][21] --- Quantitative Factors and Construction Style Factors - **Factor Names**: Size, Volatility, Liquidity, Momentum, Quality, Value, Growth, Dividend Yield - **Factor Construction Idea**: These factors represent different market characteristics, such as size, volatility, and growth, and are used to explain asset returns and identify systematic risks [3][15][26] - **Factor Construction Process**: 1. **Size**: Logarithm of market capitalization (LNCAP) [114] 2. **Volatility**: Includes Beta, historical sigma, daily standard deviation, and cumulative range [114] 3. **Liquidity**: Calculated using turnover ratios (monthly, quarterly, annual) and annualized traded value ratio [114] 4. **Momentum**: Includes short-term reversal, seasonality, industry momentum, and relative strength [114][115] 5. **Quality**: Includes earnings variability, accruals, profitability metrics, and investment quality [114][116] 6. **Value**: Includes book-to-price ratio, earnings-to-price ratio, and enterprise multiple [114][116] 7. **Growth**: Historical growth rates for earnings per share and sales per share [114][116] 8. **Dividend Yield**: Dividend-to-price ratio [114][116] - **Factor Evaluation**: Single-factor tests show limited stock selection ability, with low significance and effectiveness. However, after constructing pure factor models, the significance of factors improves, especially for Volatility and Momentum [66][78] Residual Factor - **Factor Name**: Residual Factor - **Factor Construction Idea**: Residuals represent the unexplained portion of stock returns after accounting for industry, style, and country factors. They are tested for nonlinear relationships with stock returns [79][82] - **Factor Construction Process**: 1. Residuals are derived from the regression model: $R_{t}=\beta_{t-1}C_{t}\gamma_{t}+\delta_{t}$ Here, $\delta_{t}$ represents residuals [23][79] 2. Residuals are used as stock selection factors and tested using layered backtesting [79][82] - **Factor Evaluation**: Residual factors exhibit strong nonlinear relationships with stock returns, showing robust stock selection ability. Middle-layer groups outperform top and bottom groups significantly [79][82] --- Backtesting Results Pure Factor Model - **Size**: Annualized return -2.75%, annualized volatility 0.026, maximum drawdown 35.53%, Sharpe ratio -1.08 [76][77] - **Volatility**: Annualized return 1.93%, annualized volatility 0.049, maximum drawdown 12.43%, Sharpe ratio 0.39 [76][77] - **Liquidity**: Annualized return -5.90%, annualized volatility 0.033, maximum drawdown 60.88%, Sharpe ratio -1.81 [76][77] - **Momentum**: Annualized return -5.57%, annualized volatility 0.042, maximum drawdown 58.64%, Sharpe ratio -1.32 [76][77] - **Growth**: Annualized return -0.21%, annualized volatility 0.015, maximum drawdown 9.24%, Sharpe ratio -0.15 [76][77] - **Dividend Yield**: Annualized return -0.85%, annualized volatility 0.016, maximum drawdown 17.09%, Sharpe ratio -0.52 [76][77] - **Quality**: Annualized return 0.35%, annualized volatility 0.016, maximum drawdown 8.45%, Sharpe ratio 0.23 [76][77] - **Value**: Annualized return 1.38%, annualized volatility 0.028, maximum drawdown 13.83%, Sharpe ratio 0.49 [76][77] Residual Factor - **Middle Layer (Group 5)**: Annualized return 17.98%, annualized volatility 26.94%, Sharpe ratio 0.68, maximum drawdown 52.50% [82] - **Top vs Bottom Layer (Group 5 vs Group 10)**: Excess annualized return 13.58%, excess Sharpe ratio 1.50 [82] --- Index Attribution Results Positive Excess Return Indices - **Indices**: CSI 500 (3.41%), ChiNext Index (18.23%) - **Key Drivers**: Small-cap, high volatility, low liquidity, high growth, low dividend yield styles; leading sectors include non-ferrous metals, electronics, communication, and new energy [101][110] Negative Excess Return Indices - **Indices**: CSI 1000 (-0.22%), CSI A500 (-1.60%), CSI 300 (-4.30%), SSE 50 (-10.27%) - **Key Drivers**: Large-cap, low volatility, high liquidity, low growth, high dividend yield styles; underperforming sectors include banking, non-bank finance, and food & beverage [101][110]