Quantitative Models and Construction Methods 1. Model Name: Industry Investment Radar - **Model Construction Idea**: The model identifies four states of industry trends (volume increase with price rise, volume increase with price drop, volume decrease with price drop, and volume decrease with price rise) based on the direction of price and trading volume changes. These states are visualized in a polar coordinate system to locate investment opportunities when industries move into specific regions of the radar[7][8][11] - **Model Construction Process**: 1. **State Classification in Cartesian Coordinates**: - Price and trading volume changes are categorized into four states: - Volume increase with price rise (Quadrant 1) - Volume increase with price drop (Quadrant 2) - Volume decrease with price drop (Quadrant 3) - Volume decrease with price rise (Quadrant 4)[11] 2. **Polar Coordinate Transformation**: - **Polar Angle**: Calculated using the arctangent function to represent the ratio of trading volume change to price change $ \theta = \arctan2(\text{Volume Change}, \text{Price Change}) $[14][18] - **Polar Radius**: Calculated using the Mahalanobis distance to measure the distance between the current and historical price-volume data $ \rho = \sqrt{(x-y)^T \cdot \Sigma^{-1} \cdot (x-y)} $ where $x$ is the current price-volume vector, $y$ is the historical price-volume vector, and $\Sigma$ is the covariance matrix[13][14] 3. **State Mapping in Polar Coordinates**: - Quadrants are mapped to specific polar angle ranges: - 0°-90°: Volume increase with price rise - 90°-180°: Volume increase with price drop - 180°-270°: Volume decrease with price drop - 270°-360°: Volume decrease with price rise[17][18] - **Model Evaluation**: The model provides a clear and interpretable framework for identifying industry rotation opportunities, leveraging historical price-volume relationships to predict future performance[8][18] 2. Model Name: Position Parameter Table - **Model Construction Idea**: This model establishes a mapping between historical price-volume states and future returns by dividing the polar coordinate space into regions and calculating the average future returns for each region[29][38] - **Model Construction Process**: 1. **Region Division**: - The polar radius is divided into five equal segments, and the polar angle is divided into 16 equal regions, resulting in 80 distinct regions[29] 2. **Return Mapping**: - For each region, the average future 20-day return is calculated based on historical data[29][38] 3. **Multi-Dimensional Expansion**: - **Dimension 1**: Multiple historical periods are analyzed for their relationship with future 20-day returns[47] - **Dimension 2**: Multiple historical dates are aggregated to identify stable investment regions[45] - **Model Evaluation**: The position parameter table enhances the model's robustness by incorporating multi-period and multi-date data, providing a more comprehensive mapping of historical states to future returns[47][50] --- Model Backtesting Results 1. Industry Investment Radar - **Weekly Rebalancing Portfolio**: - Cumulative Return: 369.06% - Benchmark Return: 80.97% - Excess Return: 288.09%[56] - **Monthly Rebalancing Portfolio**: - Cumulative Return: 388.85% - Benchmark Return: 80.97% - Excess Return: 307.88%[59] - **Semi-Annual Rebalancing Portfolio**: - Cumulative Return: 279.77% - Benchmark Return: 80.97% - Excess Return: 198.80%[60] 2. Position Parameter Table - **Future 20-Day Return Mapping**: - Example Regions: - Polar Radius (1/5, 2/5), Polar Angle (4π/8, 5π/8): 5.55% - Polar Radius (0, 1/5), Polar Angle (-5π/8, -4π/8): 4.64% - Polar Radius (1/5, 2/5), Polar Angle (-6π/8, -5π/8): 4.09%[42][44] --- Quantitative Factors and Construction Methods 1. Factor Name: Price-Volume State Factor - **Factor Construction Idea**: This factor captures the relationship between price and trading volume changes to classify industry states and predict future returns[7][8][11] - **Factor Construction Process**: - Derived from the polar coordinate transformation of price and volume data, incorporating both polar radius and polar angle as key metrics[13][14][18] - **Factor Evaluation**: The factor is intuitive and interpretable, effectively linking historical price-volume dynamics to future performance[8][18] 2. Factor Name: Regional Return Factor - **Factor Construction Idea**: This factor quantifies the average future returns of industries based on their historical positions in the polar coordinate system[29][38] - **Factor Construction Process**: - Calculated as the average future 20-day return for each region in the position parameter table[29][38] - **Factor Evaluation**: The factor provides a systematic approach to identifying high-return regions, leveraging historical data to enhance predictive accuracy[45][47] --- Factor Backtesting Results 1. Price-Volume State Factor - **Future 20-Day Return Examples**: - Polar Radius (2/5, 3/5), Polar Angle (5π/8, 6π/8): 3.51% - Polar Radius (0, 1/5), Polar Angle (4π/8, 5π/8): 2.49%[42][44] 2. Regional Return Factor - **Future 20-Day Return Examples**: - Polar Radius (3/5, 4/5), Polar Angle (6π/8, 7π/8): -3.06% - Polar Radius (0, 1/5), Polar Angle (3π/8, 4π/8): -3.95%[42][44]