Quantitative Models and Factor Construction Multi-Horizon Factor - **Factor Name**: Multi-Horizon Factor - **Construction Idea**: This factor captures short-term reversal, medium-term momentum, and long-term reversal effects by analyzing moving average (MA) data across multiple time horizons [2][14][21] - **Construction Process**: - Calculate moving averages for different time horizons \( L = [3, 5, 10, 20, 30, 60, 90, 120, 180, 240, 270, 300] \) using the formula: \[ A_{j t,L} = \frac{P_{j,\,d-L+1}^{t} + \cdots + P_{j,d}^{t}}{L} \] where \( P_{j,d}^t \) represents the price of stock \( j \) at time \( t \) [21] - Standardize the moving average factor: \[ \tilde{A}_{j t,\,L} = \frac{A_{j t,\,L}}{P_{j}^{t}} \] [22] - Perform cross-sectional regression of stock returns on lagged standardized moving average factors: \[ r_{j,t} = \beta_{0,t} + \Sigma_{i}\beta_{i,t}\tilde{A}_{j t-1,L_{i}} + \epsilon_{j,t} \] [23] - Predict next-period regression coefficients by averaging the past 25 weeks' coefficients: \[ E\left[\beta_{i,\,t+1}\right] = \frac{1}{25}\,\sum_{m=1}^{25}\,\beta_{i,t+1-m} \] [24] - Use predicted coefficients and new factor values to estimate next-period returns: \[ E\left[r_{j,t+1}\right] = \Sigma_{i}\,E\left[\beta_{i,\,t+1}\right]\tilde{A}_{j t,\,L_{i}} \] [25] - Rank stocks by predicted returns and construct long-short portfolios [26] - **Evaluation**: The factor demonstrates strong predictive power for stock returns across different market segments, with positive IC values dominating [30][32] LLT Trend Factor - **Factor Name**: LLT Trend Factor - **Construction Idea**: To address the lagging sensitivity of MA, the LLT (Low-Lag Trendline) indicator is used as a replacement. LLT reduces delay and better captures momentum and reversal effects [14][76] - **Construction Process**: - LLT is calculated using a second-order linear filter with the recursive formula: \[ LLT = \begin{cases} P(T), & T=1,2 \\ (2-2\alpha)LLT(T-1) - (1-\alpha)^2LLT(T-2) + \left(\alpha-\frac{\alpha^2}{4}\right)P(T) \\ + \left(\frac{\alpha^2}{2}\right)P(T-1) - \left(\alpha-\frac{3}{4}\alpha^2\right)P(T-2), & \text{else} \end{cases} \] where \( \alpha = \frac{2}{1+N} \) and \( N \) is the smoothing parameter [76] - Replace MA with LLT in the multi-horizon factor construction process [76] - **Evaluation**: LLT-based factors outperform MA-based factors in terms of IC mean, positive IC ratio, and predictive power for asset returns [82][84] --- Backtesting Results Multi-Horizon Factor - **Annualized Return**: 25.40% [3][48] - **Annualized Volatility**: 14.12% [48] - **Maximum Drawdown**: 13.31% [48] - **IR**: 1.81 [48] LLT Trend Factor - **Annualized Return**: 29.58% [4][103] - **Annualized Volatility**: 10.46% [103] - **Maximum Drawdown**: 11.57% [103] - **IR**: 2.51 [103]