Quantitative Models and Construction Methods 1. Model Name: Maximized Factor Exposure Portfolio (MFE) - **Model Construction Idea**: The MFE portfolio is designed to maximize the exposure of a single factor while controlling for various constraints such as industry exposure, style exposure, stock weight deviation, and turnover rate[64][65] - **Model Construction Process**: - The optimization model is formulated as follows: $$ \begin{array}{ll} \max & f^{T}w \\ \text{s.t.} & s_{l} \leq X(w-w_{b}) \leq s_{h} \\ & h_{l} \leq H(w-w_{b}) \leq h_{h} \\ & w_{l} \leq w-w_{b} \leq w_{h} \\ & b_{l} \leq B_{b}w \leq b_{h} \\ & 0 \leq w \leq l \\ & 1^{T}w = 1 \\ & \Sigma|w-w_{0}| \leq to_{h} \end{array} $$ - **Explanation of Parameters**: - \( f^{T}w \): Weighted exposure of the portfolio to the factor - \( w \): Portfolio weight vector - \( w_{b} \): Benchmark weight vector - \( X, H, B_{b} \): Matrices representing factor, industry, and benchmark exposures - \( s_{l}, s_{h}, h_{l}, h_{h}, w_{l}, w_{h}, b_{l}, b_{h}, to_{h} \): Constraints on factor exposure, industry exposure, stock weight deviation, and turnover rate - Constraints include: - Limiting style and industry deviations relative to the benchmark - Controlling stock weight deviations and turnover rates - Ensuring full investment (weights sum to 1) and no short selling[64][65][67] - The portfolio is rebalanced monthly, and historical returns are calculated after deducting transaction costs to evaluate factor effectiveness[68] - **Model Evaluation**: The MFE model effectively isolates the impact of individual factors while adhering to practical constraints, making it a robust tool for factor evaluation[64][65] --- Quantitative Factors and Construction Methods 1. Factor Name: Trend - **Factor Construction Idea**: Captures the momentum of stock price trends over different time horizons[16] - **Factor Construction Process**: - Two variations: - **Trend_120**: \( \text{EWMA}(\text{halflife}=20) / \text{EWMA}(\text{halflife}=120) \) - **Trend_240**: \( \text{EWMA}(\text{halflife}=20) / \text{EWMA}(\text{halflife}=240) \) - \( \text{EWMA} \): Exponentially Weighted Moving Average[16] - **Factor Evaluation**: Demonstrates strong performance in capturing price continuation patterns, particularly in volatile markets[11][13] 2. Factor Name: Volatility - **Factor Construction Idea**: Measures the variability of stock returns over a specified period[16] - **Factor Construction Process**: - Variants include: - **Stdvol**: Standard deviation of daily returns over the past 243 days - **Ivff**: Fama-French 3-factor idiosyncratic volatility over the past 243 days - **Range**: \( \text{High Price}/\text{Low Price} - 1 \) over the past 243 days - **MaxRet_6**: Average of the six highest daily returns over the past 243 days - **MinRet_6**: Average of the six lowest daily returns over the past 243 days[16] - **Factor Evaluation**: Effective in identifying high-risk stocks, though performance may vary across market conditions[11][13] 3. Factor Name: BP (Book-to-Price Ratio) - **Factor Construction Idea**: Represents the valuation of a stock relative to its book value[20] - **Factor Construction Process**: - Formula: \( \text{BP} = \text{Net Assets} / \text{Market Capitalization} \)[20] - **Factor Evaluation**: Consistently performs well in value-oriented strategies, particularly in markets favoring undervalued stocks[42][43] 4. Factor Name: Three-Month Institutional Coverage - **Factor Construction Idea**: Measures the level of analyst coverage over the past three months[20] - **Factor Construction Process**: - Formula: Count of research reports published by institutions over the past three months[20] - **Factor Evaluation**: Strongly correlated with market sentiment and stock visibility, often leading to positive price momentum[8][46] --- Factor Backtesting Results 1. Trend Factor - **Recent Weekly Return**: 2.39% - **Recent Monthly Return**: 5.57% - **Year-to-Date Return**: -0.70% - **Annualized Return (1 Year)**: 24.36% - **Annualized Return (10 Years)**: 14.25%[11][13] 2. Volatility Factor - **Recent Weekly Return**: -1.75% - **Recent Monthly Return**: -3.95% - **Year-to-Date Return**: 4.10% - **Annualized Return (1 Year)**: 24.26% - **Annualized Return (10 Years)**: -13.16%[11][13] 3. BP Factor - **Recent Weekly Return**: 0.68% - **Recent Monthly Return**: 0.06% - **Year-to-Date Return**: -4.33% - **Annualized Return (1 Year)**: -1.51% - **Annualized Return (10 Years)**: -0.61%[42][43] 4. Three-Month Institutional Coverage Factor - **Recent Weekly Return**: 1.70% - **Recent Monthly Return**: 1.29% - **Year-to-Date Return**: 4.96% - **Annualized Return (1 Year)**: 1.66% - **Annualized Return (10 Years)**: 4.39%[46][48]