Quantitative Factors and Models Summary Quantitative Factors and Construction Methods 1. **Factor Name**: Medium-term Momentum Factor **Construction Idea**: The factor is based on the cumulative returns of stocks over a medium-term window (t-12 to t-2 months), excluding the most recent month, to identify "winners" and "losers" for long-short strategies[11][12] **Construction Process**: - Formula: $ MOM_{i,t}^{M} = \prod_{k=t-12}^{t-2}(1 + r_{i,k}) - 1 $ Where $ r_{i,k} $ represents the return of stock $ i $ in month $ k $[12] **Evaluation**: The factor performs poorly in the A-share market, with weak monotonicity in decile grouping and low predictive power[13] 2. **Factor Name**: Short-term Momentum Factor **Construction Idea**: Similar to the medium-term momentum factor but with a shorter calculation window (t-6 to t-2 months), considering the faster style rotation in the A-share market[18] **Construction Process**: - Formula: $ MOM_{i,t}^{s} = \prod_{k=t-6}^{t-2}(1 + r_{i,k}) - 1 $ Where $ r_{i,k} $ represents the return of stock $ i $ in month $ k $[18] **Evaluation**: Shortening the calculation window does not improve the factor's performance, and it remains ineffective in the A-share market[19] 3. **Factor Name**: Directional Momentum (D-MOM) Factor **Construction Idea**: Predicts the "direction" of returns (positive or negative) rather than the magnitude, using a linear probability model (LPM) to enhance robustness and practicality[24][25] **Construction Process**: - Formula: $ r_{i,t}^{+} = \delta_{0} + \delta_{1}V_{i,t-1} + \delta_{2}r_{m,t-1} + \beta_{+}^{m}P_{i,t-1}^{m} + \beta_{+}^{w}P_{i,t-1}^{w} + \beta_{+}^{d}P_{i,t-1}^{d} + \beta_{-}^{m}N_{i,t-1}^{m} + \beta_{-}^{w}N_{i,t-1}^{w} + \beta_{-}^{d}N_{i,t-1}^{d} + u_{i,t} $ Where: - $ r_{i,t}^{+} $: Binary variable indicating positive returns - $ V_{i,t-1} $: Lagged idiosyncratic variance - $ r_{m,t-1} $: Lagged market return - $ P_{i,t-1}^{m}, P_{i,t-1}^{w}, P_{i,t-1}^{d} $: Positive return durations (monthly, weekly, daily) - $ N_{i,t-1}^{m}, N_{i,t-1}^{w}, N_{i,t-1}^{d} $: Negative return durations (monthly, weekly, daily)[25][26] **Evaluation**: The factor demonstrates strong stock selection ability in the A-share market, with better performance and lower risk of "momentum crashes" compared to traditional momentum factors[27][33] 4. **Factor Name**: Enhanced Directional Momentum (D-MOM) Factor **Construction Idea**: Builds on the D-MOM factor by incorporating individual stock's lagged returns as an additional predictor to capture more momentum/reversal characteristics[35] **Construction Process**: - Formula: $ r_{i,t}^{+} = \delta_{0} + \delta_{1}W_{i,t-1} + \delta_{2}r_{m,t-1} + \delta_{3}r_{i,t-1} + \beta_{4}^{m}P_{i,t-1}^{m} + \beta_{4}^{w}P_{i,t-1}^{w} + \beta_{4}^{d}P_{i,t-1}^{d} + \beta_{4}^{m}N_{i,t-1}^{m} + \beta_{2}^{w}N_{i,t-1}^{w} + \beta_{4}^{d}N_{i,t-1}^{d} + u_{i,t} $ Where $ r_{i,t-1} $ represents the lagged return of stock $ i $[35] **Evaluation**: The enhanced factor improves IC values, annualized returns, and decile monotonicity, particularly under market-cap-weighted schemes[36][42] Factor Backtesting Results 1. **Medium-term Momentum Factor**: - IC Mean: 0.019 - Annualized ICIR: 0.30 - IC>0 Probability: 59% - Annualized Long-Short Return: -1.00% - Annualized Long-Only Excess Return: 2.80% - Long-Short Sharpe Ratio: -0.10[13][18] 2. **Short-term Momentum Factor**: - IC Mean: 0.011 - Annualized ICIR: 0.20 - IC>0 Probability: 60% - Annualized Long-Short Return: -10.80% - Annualized Long-Only Excess Return: -3.00% - Long-Short Sharpe Ratio: -0.24[19][24] 3. **Directional Momentum (D-MOM) Factor**: - IC Mean: 0.059 - Annualized ICIR: 1.39 - IC>0 Probability: 86% - Annualized Long-Short Return: 21.40% (equal-weighted), 25.10% (market-cap-weighted) - Annualized Long-Only Excess Return: 11.50% (equal-weighted), 12.30% (market-cap-weighted) - Long-Short Sharpe Ratio: 1.66 (equal-weighted), 1.35 (market-cap-weighted)[33][35] 4. **Enhanced Directional Momentum (D-MOM) Factor**: - IC Mean: 0.064 - Annualized ICIR: 1.40 - IC>0 Probability: 86% - Annualized Long-Short Return: 25.40% (equal-weighted), 26.40% (market-cap-weighted) - Annualized Long-Only Excess Return: 15.10% (equal-weighted), 12.80% (market-cap-weighted) - Long-Short Sharpe Ratio: 1.84 (equal-weighted), 1.58 (market-cap-weighted)[41][42]