Quantitative Models and Factor Construction Quantitative Models and Construction Methods 1. **Model Name**: Nonlinear Multi-Factor Alpha Model **Model Construction Idea**: This model addresses the nonlinear relationship between factors and stock returns by transforming nonlinear factors into a linear form through polynomial functions[3][23]. **Model Construction Process**: - The model uses a third-degree polynomial transformation for factors with nonlinear characteristics. - The polynomial function is expressed as: $ r_{i}=aF^{3}+bF^{2}+cF+d $ where $a$, $b$, $c$, and $d$ are coefficients determined through least squares fitting[24][25]. **Model Evaluation**: This method is simple and intuitive but relies heavily on historical data and lacks rigorous economic logic[23][99]. 2. **Model Name**: Alpha Model with Additional Factors **Model Construction Idea**: This model introduces auxiliary factors to explain the nonlinear characteristics of primary factors, improving their predictive power[4][75]. **Model Construction Process**: - Identify auxiliary factors that interact with primary factors. For example, market capitalization is used as an auxiliary factor for turnover rate. - Construct a dummy variable $d_{high\_cap}$, which takes values of 0 or 1 depending on whether the stock belongs to a high or low market capitalization group. - The adjusted model is expressed as: $ r_{i}=v_{i0}+v_{i1}F_{i}+v_{i2}d_{i}F_{i}+\varepsilon_{i} $ where $d_{i}$ represents the dummy variable[78][79]. **Model Evaluation**: This method provides a more reasonable economic explanation and achieves significant improvements in factor effectiveness. However, it requires extensive pairwise comparisons and is labor-intensive[5][99]. Model Backtesting Results 1. **Nonlinear Multi-Factor Alpha Model**: - **Annualized Return**: 19.36% (in-sample), 19.19% (out-of-sample) - **Annualized Volatility**: 13.07% (in-sample), 8.97% (out-of-sample) - **IR**: 1.48 (in-sample), 2.14 (out-of-sample) - **Maximum Drawdown**: 15.33% (in-sample), 2.26% (out-of-sample)[63][67][76] 2. **Alpha Model with Additional Factors**: - **Annualized Return**: 30.90% (in-sample), 17.20% (out-of-sample) - **Annualized Volatility**: 15.43% (in-sample), 11.01% (out-of-sample) - **IR**: 2.00 (in-sample), 1.56 (out-of-sample) - **Maximum Drawdown**: 8.23% (in-sample), 1.70% (out-of-sample)[96][97][98] --- Quantitative Factors and Construction Methods 1. **Factor Name**: Debt-to-Asset Ratio **Factor Construction Idea**: This factor exhibits a nonlinear relationship with stock returns, where both high and low values are suboptimal[27]. **Factor Construction Process**: - Transform the factor using a third-degree polynomial function. - Compare cumulative returns before and after transformation. - Annualized return improved from -0.5% to 3% after transformation[27][28]. 2. **Factor Name**: Turnover Rate **Factor Construction Idea**: The factor shows a nonlinear characteristic at low turnover levels[30]. **Factor Construction Process**: - Apply a polynomial transformation to enhance linearity. - Annualized return increased from 21.7% to 28.4% after transformation[30][36]. 3. **Factor Name**: Earnings-to-Price Ratio (EP) **Factor Construction Idea**: The factor demonstrates nonlinear behavior at low EP levels[34]. **Factor Construction Process**: - Use a polynomial transformation to improve linearity. - Annualized return increased from 11% to 13.5% after transformation[34][40]. 4. **Factor Name**: Total Assets **Factor Construction Idea**: The factor is generally linear but shows nonlinear characteristics at low asset levels[38]. **Factor Construction Process**: - Apply a polynomial transformation. - Annualized return improved from 8.1% to 10% after transformation[38][44]. 5. **Factor Name**: Fixed Ratio **Factor Construction Idea**: The factor exhibits a "middle is better" nonlinear pattern[42]. **Factor Construction Process**: - Transform the factor using a polynomial function. - Annualized return increased from 2.75% to 6.57% after transformation[42][48]. 6. **Factor Name**: Current Ratio **Factor Construction Idea**: Similar to the fixed ratio, this factor also shows a "middle is better" pattern[46]. **Factor Construction Process**: - Apply a polynomial transformation. - Annualized return improved from 3.76% to 5.32% after transformation[46][52]. Factor Backtesting Results 1. **Debt-to-Asset Ratio**: Annualized return improved from -0.5% to 3%[27][28] 2. **Turnover Rate**: Annualized return improved from 21.7% to 28.4%[30][36] 3. **Earnings-to-Price Ratio (EP)**: Annualized return improved from 11% to 13.5%[34][40] 4. **Total Assets**: Annualized return improved from 8.1% to 10%[38][44] 5. **Fixed Ratio**: Annualized return improved from 2.75% to 6.57%[42][48] 6. **Current Ratio**: Annualized return improved from 3.76% to 5.32%[46][52]