Group 1 - The report introduces a quantitative model solution for addressing the value-growth style switching issue, combining investment expectations based on odds and win rates [1][8] - The overall market growth style portfolio achieved a return of 4.58%, while the value style portfolio returned 2.24% in the last week [1][8] Group 2 - The estimated odds for the growth style is 1.08, while for the value style it is 1.12, indicating a negative correlation between relative valuation levels and expected odds [2][14] - The current win rate for the growth style is 63.24%, compared to 36.76% for the value style, based on seven win rate indicators [3][19] Group 3 - The latest investment expectation for the growth style is calculated to be 0.32, while the value style has an investment expectation of -0.22, leading to a recommendation for the growth style [4][21] - Since 2013, the annualized return of the style rotation model based on investment expectations is 27.99%, with a Sharpe ratio of 1.04 [4][22]

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]

Core Insights - The report indicates that high-frequency factors continued to retract, while multi-granularity factors showed some rebound. The AI-enhanced portfolios have sustained a rebound, with the strictly constrained 1000 enhanced portfolio achieving a record high in excess returns [2][5]. Summary by Sections 1. High-Frequency Factors, Deep Learning Factors, and AI Enhanced Portfolio Performance Summary - The report summarizes the historical and 2025 performance of high-frequency stock selection factors, including multi-factor returns and excess returns for October and year-to-date [8]. - The high-frequency skew factor had a multi-directional return of -0.54% for the last week, -2.03% for October, and 20.66% year-to-date [10]. - The deep learning high-frequency factor (improved GRU(50,2)+NN(10)) reported a multi-directional return of 0.62% for the last week, 0.38% for October, and 43.14% year-to-date [12]. 2. Weekly Rebalancing of AI Index Enhanced Portfolios - The weekly rebalancing of the CSI 500 AI enhanced wide constraint portfolio achieved excess returns of 3.51%, 4.71%, and 4.65% for the last week, October, and year-to-date respectively [13]. - The weekly rebalancing of the CSI 1000 AI enhanced strict constraint portfolio achieved excess returns of 2.21%, 3.99%, and 17.63% for the last week, October, and year-to-date respectively [13]. 3. Performance of Specific Factors - The opening buy intention strength factor had a multi-directional return of -0.98% for the last week, -2.72% for October, and 23.09% year-to-date [10]. - The average single outflow amount factor reported a multi-directional return of -0.90% for the last week, -1.90% for October, and -2.44% year-to-date [10]. - The deep learning factor (multi-granularity model - 5-day label) achieved a multi-directional return of 2.04% for the last week, 2.53% for October, and 55.62% year-to-date [12].

Quantitative Models and Construction Methods - **Model Name**: Multi-cycle timing model for domestic interest rate price-volume trends **Model Construction Idea**: The model uses kernel regression algorithms to capture interest rate trend patterns, identifying support and resistance lines based on the shape of interest rate movements across different investment cycles [10][24] **Model Construction Process**: 1. **Data Input**: Utilize 5-year, 10-year, and 30-year government bond YTM data as the basis for analysis [10][24] 2. **Cycle Classification**: Divide the investment horizon into long-term (monthly frequency), medium-term (bi-weekly frequency), and short-term (weekly frequency) cycles [10][24] 3. **Signal Identification**: Detect upward or downward breakthroughs of support and resistance lines for each cycle [10][24] 4. **Composite Scoring**: Aggregate signals across cycles, assigning scores based on the number of consistent breakthroughs (e.g., 2/3 consistent signals lead to a "buy" or "sell" recommendation) [10][24] **Model Evaluation**: The model effectively captures multi-cycle resonance in interest rate trends, providing actionable timing signals for bond trading strategies [10][24] - **Model Name**: Multi-cycle timing model for U.S. interest rate price-volume trends **Model Construction Idea**: Apply the domestic interest rate price-volume timing model to the U.S. Treasury market [21] **Model Construction Process**: 1. **Data Input**: Use 10-year U.S. Treasury YTM data for analysis [21] 2. **Cycle Classification**: Similar to the domestic model, divide the investment horizon into long-term, medium-term, and short-term cycles [21] 3. **Signal Identification**: Detect upward or downward breakthroughs of support and resistance lines for each cycle [21] 4. **Composite Scoring**: Aggregate signals across cycles, assigning scores based on the number of consistent breakthroughs [21] **Model Evaluation**: The model provides a neutral-to-bullish outlook for U.S. Treasury yields, indicating its adaptability to international markets [21] Model Backtesting Results - **Domestic Multi-cycle Timing Model**: - **5-year YTM**: - Long-term annualized return: 5.5% - Maximum drawdown: 2.88% - Return-to-drawdown ratio: 1.91 - Short-term annualized return (since 2024): 1.86% - Maximum drawdown: 0.59% - Return-to-drawdown ratio: 3.16 - Long-term excess return: 1.07% - Short-term excess return: 0.85% [25][27] - **10-year YTM**: - Long-term annualized return: 6.09% - Maximum drawdown: 2.74% - Return-to-drawdown ratio: 2.22 - Short-term annualized return (since 2024): 2.42% - Maximum drawdown: 0.58% - Return-to-drawdown ratio: 4.19 - Long-term excess return: 1.66% - Short-term excess return: 1.55% [28][32] - **30-year YTM**: - Long-term annualized return: 7.38% - Maximum drawdown: 4.27% - Return-to-drawdown ratio: 1.73 - Short-term annualized return (since 2024): 3.11% - Maximum drawdown: 0.92% - Return-to-drawdown ratio: 3.39 - Long-term excess return: 2.42% - Short-term excess return: 2.87% [33][35] - **U.S. Multi-cycle Timing Model**: - **10-year YTM**: - Current signal: Neutral-to-bullish - Long-term annualized return: Not provided - Maximum drawdown: Not provided - Return-to-drawdown ratio: Not provided [21][23] Quantitative Factors and Construction Methods - **Factor Name**: Interest rate structure indicators (level, term, convexity) **Factor Construction Idea**: Transform YTM data into structural indicators to analyze the interest rate market from a mean-reversion perspective [7] **Factor Construction Process**: 1. **Level Structure**: Calculate the average YTM across maturities (1-10 years) 2. **Term Structure**: Measure the slope between short-term and long-term YTM 3. **Convexity Structure**: Assess the curvature of the yield curve [7] **Factor Evaluation**: The indicators effectively capture the current state of the interest rate market, highlighting deviations from historical averages [7] Factor Backtesting Results - **Interest Rate Structure Indicators**: - **Level Structure**: Current reading: 1.64%, historical 10-year percentile: 7% - **Term Structure**: Current reading: 0.38%, historical 10-year percentile: 16% - **Convexity Structure**: Current reading: -0.09%, historical 10-year percentile: 1% [7]

- The report introduces the "Information Distribution Uniformity (UID) factor" as a stock selection factor, which is constructed using minute-level data of individual stocks to calculate daily high-frequency volatility[1][6] - The UID factor significantly outperforms traditional volatility factors in stock selection, even after removing the interference of commonly used market styles and industries, with an annualized ICIR of -3.17[1] - The performance of the UID factor from January 2014 to September 2025 includes an annualized return of 26.48%, annualized volatility of 9.88%, an information ratio (IR) of 2.68, a monthly win rate of 78.72%, and a maximum monthly drawdown of 6.05%[1][7][12] - In September 2025, the 10-group long portfolio of the UID factor in the entire A-share market had a return of 1.84%, the 10-group short portfolio had a return of 0.04%, and the 10-group long-short hedged portfolio had a return of 1.80%[1][11] - The construction process of the UID factor involves using minute-level price data to calculate the high-frequency volatility of individual stocks and then constructing the UID factor based on the uniformity of information distribution[1][6] - The report highlights that the UID factor, despite being a single factor, shows good stock selection ability and can be a valuable addition to the factor library[1][6]

Quantitative Models and Construction Methods - **Model Name**: Multi-cycle timing model for domestic interest rate price-volume trends **Model Construction Idea**: The model uses kernel regression algorithms to capture interest rate trend patterns, identifying support and resistance lines based on different investment cycles. It provides composite timing signals by analyzing the shape of interest rate movements across long, medium, and short cycles[10][24][29] **Model Construction Process**: 1. **Data Input**: Use 5-year, 10-year, and 30-year government bond YTM data as the basis for analysis[10][24][29] 2. **Cycle Definition**: Define long, medium, and short cycles with average switching frequencies of monthly, bi-weekly, and weekly, respectively[10][24][29] 3. **Signal Generation**: - If at least two cycles show downward breakthroughs of the support line and the interest rate trend is not upward, allocate fully to long-duration bonds - If at least two cycles show downward breakthroughs of the support line but the interest rate trend is upward, allocate 50% to medium-duration bonds and 50% to long-duration bonds - If at least two cycles show upward breakthroughs of the resistance line and the interest rate trend is not downward, allocate fully to short-duration bonds - If at least two cycles show upward breakthroughs of the resistance line but the interest rate trend is downward, allocate 50% to medium-duration bonds and 50% to short-duration bonds - In other cases, allocate equally across short, medium, and long durations[24][29][29] **Model Evaluation**: The model demonstrates strong adaptability across different market environments and provides consistent timing signals based on multi-cycle resonance[10][24][29] - **Model Name**: Multi-cycle timing model for U.S. interest rate price-volume trends **Model Construction Idea**: The domestic price-volume timing model is applied to the U.S. interest rate market, analyzing long, medium, and short cycles to generate composite timing signals[21][23][24] **Model Construction Process**: 1. **Data Input**: Use 10-year U.S. Treasury YTM data for analysis[21][23][24] 2. **Cycle Definition**: Define long, medium, and short cycles with average switching frequencies of monthly, bi-weekly, and weekly, respectively[21][23][24] 3. **Signal Generation**: Similar to the domestic model, signals are generated based on the number of cycles showing breakthroughs of support or resistance lines and the direction of interest rate trends[21][23][24] **Model Evaluation**: The model effectively captures U.S. interest rate trends and provides reliable timing signals for investment decisions[21][23][24] Model Backtesting Results - **Domestic Multi-cycle Timing Model** - **5-year YTM**: - Long-term annualized return: 5.5% - Maximum drawdown: 2.88% - Return-to-drawdown ratio: 1.91 - Short-term annualized return (since 2024): 1.86% - Maximum drawdown: 0.59% - Return-to-drawdown ratio: 3.15 - Long-term excess return: 1.07% - Excess return-to-drawdown ratio: 0.62 - Short-term excess return: 0.86% - Excess return-to-drawdown ratio: 2.18[25][27][37] - **10-year YTM**: - Long-term annualized return: 6.09% - Maximum drawdown: 2.74% - Return-to-drawdown ratio: 2.23 - Short-term annualized return (since 2024): 2.35% - Maximum drawdown: 0.58% - Return-to-drawdown ratio: 4.07 - Long-term excess return: 1.66% - Excess return-to-drawdown ratio: 1.16 - Short-term excess return: 1.56% - Excess return-to-drawdown ratio: 3.46[28][32][37] - **30-year YTM**: - Long-term annualized return: 7.38% - Maximum drawdown: 4.27% - Return-to-drawdown ratio: 1.73 - Short-term annualized return (since 2024): 2.98% - Maximum drawdown: 0.92% - Return-to-drawdown ratio: 3.26 - Long-term excess return: 2.42% - Excess return-to-drawdown ratio: 0.87 - Short-term excess return: 2.87% - Excess return-to-drawdown ratio: 3.21[33][35][37] - **U.S. Multi-cycle Timing Model** - **10-year YTM**: - Composite signal: Long cycle upward breakthrough, medium and short cycles downward breakthrough - Final signal: Bullish[21][23][24]

Quantitative Models and Construction Methods - **Model Name**: Excellent Fund Performance Enhancement Portfolio **Construction Idea**: Shift from benchmarking broad-based indices to benchmarking active equity funds, leveraging quantitative methods to enhance fund holdings for optimal selection [4][48][49] **Construction Process**: 1. Benchmark against active equity fund median returns, represented by the biased equity hybrid fund index (885001.WI) [18][48] 2. Select funds based on performance layering, neutralizing return-related factors to mitigate style concentration risks [48] 3. Optimize the portfolio to control deviations in individual stocks, industries, and styles compared to selected fund holdings [49] **Evaluation**: Demonstrates stability and ability to outperform active equity fund medians [49] - **Model Name**: Outperformance Selection Portfolio **Construction Idea**: Focus on stocks with significant earnings surprises, combining fundamental and technical analysis for selection [5][54] **Construction Process**: 1. Identify stocks with earnings surprises based on research titles and analysts' profit revisions [5][54] 2. Conduct dual-layer screening on fundamental and technical dimensions to select stocks with both fundamental support and technical resonance [5][54] **Evaluation**: Consistently ranks in the top 30% of active equity funds annually [55] - **Model Name**: Brokerage Golden Stock Performance Enhancement Portfolio **Construction Idea**: Use brokerage golden stock pools as the stock selection space and constraint benchmark, optimizing the portfolio to control deviations [6][59] **Construction Process**: 1. Benchmark against active equity fund medians, represented by the biased equity hybrid fund index [33][59] 2. Optimize the portfolio to control deviations in individual stocks, industries, and styles compared to the brokerage golden stock pool [6][59] **Evaluation**: Stable performance, consistently ranking in the top 30% of active equity funds annually [60] - **Model Name**: Growth and Stability Portfolio **Construction Idea**: Focus on the time-series release intensity of excess returns for growth stocks, constructing a two-dimensional evaluation system [7][64] **Construction Process**: 1. Use "excess return release maps" to identify the strongest release periods of excess returns around positive events [64] 2. Prioritize stocks closer to financial report disclosure dates, and apply multi-factor scoring to select high-quality stocks when sample size is large [7][64] 3. Introduce mechanisms like weak balance, transition, buffer, and risk avoidance to reduce turnover and mitigate risks [64] **Evaluation**: High efficiency in capturing excess returns during optimal periods, consistently ranking in the top 30% of active equity funds annually [64][65] --- Model Backtesting Results - **Excellent Fund Performance Enhancement Portfolio**: - Annualized return (2012.1.4-2025.6.30): 20.31% - Annualized excess return vs. biased equity hybrid fund index: 11.83% - Most years ranked in the top 30% of active equity funds [50][53] - **Outperformance Selection Portfolio**: - Annualized return (2010.1.4-2025.6.30): 30.55% - Annualized excess return vs. biased equity hybrid fund index: 24.68% - Most years ranked in the top 30% of active equity funds [55][57] - **Brokerage Golden Stock Performance Enhancement Portfolio**: - Annualized return (2018.1.2-2025.6.30): 19.34% - Annualized excess return vs. biased equity hybrid fund index: 14.38% - Most years ranked in the top 30% of active equity funds [60][63] - **Growth and Stability Portfolio**: - Annualized return (2012.1.4-2025.6.30): 35.51% - Annualized excess return vs. biased equity hybrid fund index: 26.88% - Most years ranked in the top 30% of active equity funds [65][68] --- Portfolio Weekly and Yearly Performance - **Excellent Fund Performance Enhancement Portfolio**: - Weekly absolute return: -0.98% - Weekly excess return vs. biased equity hybrid fund index: 0.54% - Yearly absolute return: 29.30% - Yearly excess return vs. biased equity hybrid fund index: -4.01% - Yearly ranking: 54.63% percentile (1895/3469) [2][24][17] - **Outperformance Selection Portfolio**: - Weekly absolute return: 0.22% - Weekly excess return vs. biased equity hybrid fund index: 1.74% - Yearly absolute return: 47.41% - Yearly excess return vs. biased equity hybrid fund index: 14.10% - Yearly ranking: 21.71% percentile (753/3469) [2][32][17] - **Brokerage Golden Stock Performance Enhancement Portfolio**: - Weekly absolute return: -1.51% - Weekly excess return vs. biased equity hybrid fund index: 0.01% - Yearly absolute return: 34.07% - Yearly excess return vs. biased equity hybrid fund index: 0.76% - Yearly ranking: 44.42% percentile (1541/3469) [2][39][17] - **Growth and Stability Portfolio**: - Weekly absolute return: -0.08% - Weekly excess return vs. biased equity hybrid fund index: 1.44% - Yearly absolute return: 54.84% - Yearly excess return vs. biased equity hybrid fund index: 21.53% - Yearly ranking: 13.00% percentile (451/3469) [3][43][17]

- The high-frequency skewness factor showed strong performance with long-short returns of 0.9%, 4.93%, and 22.69% for the past week, September, and 2025, respectively[5][9] - The intraday downside volatility proportion factor had long-short returns of 0.77%, 5.18%, and 18.23% for the past week, September, and 2025, respectively[5][9] - The post-open buying intention proportion factor had long-short returns of 1.11%, 3.65%, and 19.98% for the past week, September, and 2025, respectively[5][9] - The post-open buying intention intensity factor had long-short returns of 1.62%, 3.28%, and 25.81% for the past week, September, and 2025, respectively[5][9] - The post-open large order net buying proportion factor had long-short returns of 0.34%, 1.51%, and 20.7% for the past week, September, and 2025, respectively[5][9] - The post-open large order net buying intensity factor had long-short returns of 0.38%, 1.51%, and 12.86% for the past week, September, and 2025, respectively[5][9] - The intraday return factor had long-short returns of 0.98%, 1.26%, and 20.66% for the past week, September, and 2025, respectively[5][9] - The end-of-day trading proportion factor had long-short returns of 1.25%, 4.18%, and 17.74% for the past week, September, and 2025, respectively[5][9] - The average single outflow amount proportion factor had long-short returns of 0.29%, 0.26%, and -0.54% for the past week, September, and 2025, respectively[5][9] - The large order-driven price increase factor had long-short returns of 0.09%, 2.88%, and 8.88% for the past week, September, and 2025, respectively[5][9] - The GRU(10,2)+NN(10) deep learning factor had long-short returns of 1.33%, 8.73%, and 41.75% for the past week, September, and 2025, respectively, with long-only excess returns of 0.71%, 3.42%, and 8.08%[5][9] - The GRU(50,2)+NN(10) deep learning factor had long-short returns of 1%, 7.98%, and 42.75% for the past week, September, and 2025, respectively, with long-only excess returns of 0.63%, 2.99%, and 7.91%[5][9] - The multi-granularity model (5-day label) factor had long-short returns of 0.99%, 6.15%, and 53.09% for the past week, September, and 2025, respectively, with long-only excess returns of 0.5%, 2.56%, and 19.48%[5][9] - The multi-granularity model (10-day label) factor had long-short returns of 0.81%, 5.2%, and 49.1% for the past week, September, and 2025, respectively, with long-only excess returns of 0.37%, 2.97%, and 20.1%[5][9] - The weekly rebalanced CSI 500 AI enhanced wide constraint portfolio had excess returns of -0.99%, -4.8%, and -0.06% for the past week, September, and 2025, respectively[5][11] - The weekly rebalanced CSI 500 AI enhanced strict constraint portfolio had excess returns of -1%, -2.32%, and 2.66% for the past week, September, and 2025, respectively[5][11] - The weekly rebalanced CSI 1000 AI enhanced wide constraint portfolio had excess returns of -1.48%, -1.06%, and 7.53% for the past week, September, and 2025, respectively[5][11] - The weekly rebalanced CSI 1000 AI enhanced strict constraint portfolio had excess returns of -0.79%, -0.12%, and 13.11% for the past week, September, and 2025, respectively[5][11]

Macro Insights - The macro environment for Q4 is predicted to show signals of inflation, with both credit spreads and term spreads indicating a narrowing trend as of September 2025 [4] - The macro momentum model signals for stocks, bonds, and gold are positive, negative, and positive respectively for October 2025 [5] Semiconductor Industry - The U.S. House of Representatives' "China Semiconductor Strategy" report suggests that the rise of China's semiconductor industry poses a threat to U.S. national security and global technological dominance, recommending measures such as export controls and technology blockades [9] - The report indicates that five major semiconductor equipment companies (AMAT, ASML, KLA, LAM, TEL) hold 80%-85% of the global market share, with an estimated $38 billion to be spent on semiconductor equipment in mainland China in 2024 [9] - Despite existing export controls, there are significant loopholes, and non-U.S. equipment manufacturers are seeing increased revenue from restricted Chinese entities [10] - The report outlines several policy recommendations to strengthen export controls against China, including expanding the entity list and preventing the use of Chinese equipment in global fabs [11] Aviation Industry - The demand for travel during the National Day and Mid-Autumn Festival holidays in 2025 was robust, with a daily average increase of 6% in cross-regional movement compared to the previous year, and domestic air passenger volume expected to grow over 3% [16] - The aviation industry is projected to see profitability growth in Q3 2025, driven by increased passenger load factors and rising ticket prices, with expectations of continued growth compared to Q3 2019 [17] - The recovery of business travel demand is crucial for sustainable profitability in the aviation sector, with signs of recovery observed in April-May 2025 [18] - The Chinese aviation industry is anticipated to enter a "super cycle" if business travel demand continues to recover, with a significant upward shift in profitability expected [19]

- The report proposes an iterative factor selection strategy to compress the "factor zoo" by systematically evaluating the contribution of new factors to the remaining alpha of the factors using the GRS statistic[2][3][4] - The iterative factor selection process starts with the CAPM model and adds one factor at a time that maximally reduces the remaining alpha of the factors, measured by the decrease in the GRS statistic[3][25][26] - The process stops when the added factor no longer makes the remaining alpha of the factors statistically significant from zero[3][25][26] - The study finds that only 10 to 20 carefully selected factors are needed to effectively explain the performance of 153 factors in the US market, indicating high redundancy among factors[4][17][19] - The selected factors come from 8 out of 13 factor style categories, showing the heterogeneity of the factor set[17][19] - The iterative factor model outperforms common academic models by selecting alternative definitions of value, profitability, investment, or momentum factors, or including alternative factor style categories such as seasonality or short-term reversal[17][19] - The study also confirms that equal-weighted factors exhibit stronger and more diverse alpha, requiring more than 30 factors to cover the factor zoo[4][64][69] - The effectiveness of the method is validated using global data, showing similar core factor sets across different regions, but with the global model explaining US factors better than non-US factors[4][71][75] - The iterative factor selection strategy provides a practical framework for investors to streamline their models by focusing on the most relevant factors[2][3][4] Factor Selection Process Results - The iterative factor selection process results in a model that starts with the CAPM model, which leaves 105 significant alphas (t>2) and 86 significant alphas (t>3) with a GRS statistic of 4.36 and a p-value of 0.00[39][40] - Adding the cash-based operating profits-to-book assets (cop_at) factor reduces the GRS statistic to 3.54, leaving 101 significant alphas (t>2) and 78 significant alphas (t>3) with an average absolute alpha of 3.94%[39][40] - The process continues by adding factors such as change in net operating assets (noa_grla), sales growth (saleq_gr1), and intrinsic value-to-market (ival_me), among others, until the remaining significant alphas are reduced to zero[39][40][41] - The final model includes 15 to 18 factors, depending on the significance threshold, effectively explaining the factor zoo[39][42][43] Comparison with Common Academic Models - The iterative factor model leaves fewer significant alphas compared to common academic models such as the Fama and French five-factor and six-factor models, the q-factor model, and the mispricing model[43][44] - The Barillas et al. (2020) revised six-factor model performs better than other academic models but still leaves 33 significant alphas, while the iterative factor model leaves only 10 significant alphas with four factors and 14 significant alphas with five factors[43][44] Global Factor Analysis - The global factor analysis shows that 11 global factors are needed to cover the global factor zoo at the t>3 threshold, and around 20 factors at the t>2 threshold[73][74] - The global factor model explains US factors better than non-US factors, indicating that international factors have higher and more diverse alpha potential[75][76][77] Rolling Window Analysis - The rolling window analysis shows that the number of factors needed to cover the factor zoo decreases over time, with around 8 factors needed in recent years compared to 15 factors in the early sample period[59][60][61] - The most relevant factor styles over time include low volatility, seasonality, investment, and quality, while the relevance of momentum, short-term reversal, and value has decreased in recent years[59][60][61] Robustness to Alternative Weighting Schemes - The robustness analysis shows that equal-weighted factors require more than 30 factors to cover the factor zoo, while cap-weighted and value-weighted factors require 18 and 19 factors, respectively[64][65][69] - The equal-weighted factor model exhibits higher and more diverse alpha potential, indicating the need for more factors to cover the equal-weighted factor zoo[64][65][69]