Quantitative Models and Construction Methods 1. **Model Name**: Amihud Illiquidity Indicator - **Model Construction Idea**: Measures the price impact of trading volume to assess the liquidity level of an asset. A higher value indicates lower liquidity. [11][12][13] - **Model Construction Process**: The formula is: $$ Amihud = \frac{1}{D} \sum_{d=1}^{D} \frac{\left| R_{i,d} \right|}{Vol_{i,d}} $$ Where: - \( D \): Number of trading days in the window - \( R_{i,d} \): Absolute return of security \( i \) on day \( d \) - \( Vol_{i,d} \): Trading volume of security \( i \) on day \( d \) This indicator reflects the sensitivity of price to trading volume. A higher value indicates that smaller trading volumes cause larger price changes, implying lower liquidity. [12][13] 2. **Model Name**: Pastor-Stambaugh Liquidity Indicator - **Model Construction Idea**: Based on the reversal of asset returns to measure liquidity. Assets with lower liquidity tend to exhibit higher return reversals. [14] - **Model Construction Process**: The formula is: $$ r_{i,d+1}^{e} = \alpha + \beta_{i} r_{i,d} + \gamma_{i} sign(r_{i,d}^{e}) \cdot v_{i,d} + \epsilon_{i,d+1} $$ Where: - \( r_{i,d+1}^{e} \): Excess return of security \( i \) on day \( d+1 \) - \( r_{i,d} \): Return of security \( i \) on day \( d \) - \( v_{i,d} \): Trading volume of security \( i \) on day \( d \) - \( \gamma_{i} \): Liquidity indicator, with a significantly negative value indicating poor liquidity. [14] 3. **Model Name**: Turnover Rate Indicator - **Model Construction Idea**: Reflects the trading activity of an asset by measuring the frequency of its turnover. Higher values indicate higher market liquidity. [15] - **Model Construction Process**: The turnover rate is calculated as: $$ Turnover\ Rate = \frac{Trading\ Volume}{Market\ Capitalization} $$ Where: - \( Trading\ Volume \): Total trading volume of the asset - \( Market\ Capitalization \): Total market value of the asset. [15] 4. **Model Name**: Component Stock Diffusion Indicator - **Model Construction Idea**: Measures the consistency of trends among individual stocks within an industry to assess crowding. Higher values indicate a more crowded market. [16] - **Model Construction Process**: The indicator is calculated as the proportion of stocks in an industry that exhibit a bullish trend, defined as the closing price being above the short-term, medium-term, and long-term moving averages. [16] 5. **Model Name**: Component Stock Pairwise Correlation Indicator - **Model Construction Idea**: Quantifies the homogeneity of stock movements within an industry to evaluate crowding. Higher values indicate stronger synchronization and higher crowding. [17] - **Model Construction Process**: The indicator is the average of pairwise correlation coefficients of returns among all component stocks in an industry over a given window. [17] 6. **Model Name**: Component Stock Return Kurtosis Indicator - **Model Construction Idea**: Captures the extremity of trading by analyzing the tail characteristics of return distributions. Higher kurtosis indicates more extreme returns, suggesting heightened market crowding. [18] - **Model Construction Process**: The indicator is the average kurtosis of daily cross-sectional returns within a window. Kurtosis measures the "peakedness" or "flatness" of a distribution, with higher values indicating fatter tails. [18] 7. **Model Name**: Heat Indicator - **Model Construction Idea**: Uses principal component analysis (PCA) to measure the contribution of a single industry to systemic market risk, reflecting its trading heat. [21][22] - **Model Construction Process**: The formula is: $$ AR_{m} = \frac{\sigma_{m}^{2}}{\sum_{j=1}^{N} \sigma_{j}^{2}} $$ $$ C_{i} = \frac{\sum_{j=1}^{n} AR_{j} \cdot \frac{\left| EV_{i}^{j} \right|}{\sum_{k=1}^{N} \left| EV_{k}^{i} \right|}}{\sum_{j=1}^{n} AR_{j}} $$ Where: - \( N \): Total number of industries - \( n \): Number of principal components - \( \sigma_{m}^{2} \): Variance of the \( m \)-th principal component - \( \sigma_{j}^{2} \): Variance of the \( j \)-th industry return - \( EV_{i}^{j} \): Exposure of the \( j \)-th principal component to the \( i \)-th industry. A higher value indicates that the industry contributes more to systemic market risk, suggesting higher trading heat. [21][22] 8. **Model Name**: Herding Effect Indicator - **Model Construction Idea**: Captures the consistency of market participants' behavior. A significant negative value indicates strong herding behavior, often signaling extreme market sentiment and crowded trading. [23][24] - **Model Construction Process**: The formula is: $$ CSAD_{t} = \gamma_{0} + \gamma_{1} \left| R_{m,t} \right| + \gamma_{2} R_{m,t}^{2} + \mathcal{E}_{t} $$ Where: - \( CSAD_{t} \): Cross-sectional absolute deviation of returns on day \( t \) - \( R_{m,t} \): Market return on day \( t \) - \( \gamma_{2} \): Herding effect indicator. [23][24] 9. **Model Name**: Closing Price-Trading Volume Correlation Indicator - **Model Construction Idea**: Analyzes the stability of the relationship between price and trading volume to predict potential trend reversals. Persistent negative correlation often signals overtrading and potential reversals. [25] - **Model Construction Process**: The indicator is the correlation coefficient between the series of closing prices and trading volumes of an index. [25] 10. **Model Name**: Trading Volume Share Indicator - **Model Construction Idea**: Reflects the concentration of trading in a specific sector or industry. Higher values indicate higher trading concentration and potential overheating. [26] - **Model Construction Process**: The indicator is calculated as the daily trading volume of a sector or industry divided by the total market trading volume. [26] Model Backtesting Results 1. **Amihud Illiquidity Indicator**: No specific backtesting results provided 2. **Pastor-Stambaugh Liquidity Indicator**: No specific backtesting results provided 3. **Turnover Rate Indicator**: No specific backtesting results provided 4. **Component Stock Diffusion Indicator**: No specific backtesting results provided 5. **Component Stock Pairwise Correlation Indicator**: No specific backtesting results provided 6. **Component Stock Return Kurtosis Indicator**: No specific backtesting results provided 7. **Heat Indicator**: No specific backtesting results provided 8. **Herding Effect Indicator**: No specific backtesting results provided 9. **Closing Price-Trading Volume Correlation Indicator**: No specific backtesting results provided 10. **Trading Volume Share Indicator**: No specific backtesting results provided Historical Similarity Analysis Results - Using the Wind Satellite Index (866125.WI) as an example, historical similar segments were identified based on metrics such as component stock count, trading volume share, and market capitalization. - For the next 60 trading days: - **Average maximum return**: 12.79% - **Average time to peak**: 33 days - **Average peak trading volume share**: 4.48% [42][46][49]