Quantitative Models and Construction Methods - **Model Name**: Net Index **Model Construction Idea**: The Net Index measures the difference between the number of long anomaly portfolios and short anomaly portfolios a stock belongs to in a given month[16][39][40] **Model Construction Process**: 1. Sort stocks monthly based on 130 anomaly characteristics derived from academic literature[38][39] 2. Define long and short ends of each anomaly strategy as the extreme quintiles from the sorting process[39] 3. Calculate the Net Index as the difference between the number of long anomaly portfolios and short anomaly portfolios a stock belongs to[39] **Formula**: $ Net_{t} = \text{Number of Long Portfolios}_{t} - \text{Number of Short Portfolios}_{t} $[39] **Model Evaluation**: The Net Index demonstrates high persistence across time and captures significant heterogeneity in extreme quintiles[40][41] Model Backtesting Results - **Net Index**: - Mean value: -1.30 - Standard deviation: 8.90 - Extreme quintile difference: 18.8[39][40][41] Quantitative Factors and Construction Methods - **Factor Name**: Retail Trading **Factor Construction Idea**: Retail trading is identified through sub-penny price improvements in transaction prices, reflecting individual investor activity[22][23][24] **Factor Construction Process**: 1. Calculate the fractional part of transaction prices: $ Z_{i t} = 100 \times mod(P_{i t}, 0.01) $ where $ P_{i t} $ is the transaction price[23] 2. Classify trades based on the fractional part and FINRA reporting codes: - Buy orders: $ Z_{i t} \in (0.6, 1) $ - Sell orders: $ Z_{i t} \in (0, 0.4) $[24] 3. Aggregate daily buy and sell proportions normalized by shares outstanding[25] **Factor Evaluation**: Retail trading reflects systematic errors by individual investors, often contrary to expected returns[19][25][27] - **Factor Name**: Short Seller Trading **Factor Construction Idea**: Short seller trading is measured by changes in short interest scaled by shares outstanding[33][34] **Factor Construction Process**: 1. Obtain monthly short interest data from stock exchanges[33] 2. Calculate short seller trading as: $ \text{Short Seller Trading} = \frac{\Delta \text{Short Interest}}{\text{Shares Outstanding}} $ where increases in short interest are negative and decreases are positive[33][34] **Factor Evaluation**: Short sellers are highly skilled in utilizing public information and aligning trades with expected returns[18][34][48] - **Factor Name**: Firm Trading **Factor Construction Idea**: Firm trading is measured by changes in shares outstanding due to issuance or repurchase, scaled by shares outstanding[35][36] **Factor Construction Process**: 1. Calculate monthly changes in shares outstanding adjusted for stock splits and dividends[35] 2. Define firm trading as: $ \text{Firm Trading} = \frac{\text{Issuance} - \text{Repurchase}}{\text{Shares Outstanding}} $ Positive values indicate net issuance, while negative values indicate net repurchase[35][36] **Factor Evaluation**: Firm trading reflects private information and aligns strongly with expected returns[16][35][48] Factor Backtesting Results - **Retail Trading**: - 1-year mean: 0.03% - 3-year mean: 0.05%[27][28] - **Short Seller Trading**: - 1-year mean: -0.18% - 3-year mean: -0.49%[34][44] - **Firm Trading**: - 1-year mean: -3.92% - 3-year mean: -11.40%[35][44] Predictive Results of Factors - **Retail Trading**: Negative correlation with future returns, indicating systematic errors by individual investors[19][66][70] - **Short Seller Trading**: Positive correlation with future returns, reflecting alignment with expected returns[18][66][70] - **Firm Trading**: Positive correlation with future returns, showcasing predictive power based on private information[16][66][70] Residual Analysis - **Retail Trading**: Residual predictive power remains significant for 3-year trading, indicating information orthogonal to anomaly variables[73][75][76] - **Short Seller Trading**: Predictive power largely explained by alignment with anomaly variables[76] - **Firm Trading**: Partial predictive power explained by anomaly alignment, with additional orthogonal information sources[76]