Quantitative Models and Construction Methods Model Name: Black Swan Index - **Construction Idea**: Measure the extremity of market transactions based on the deviation of style factor returns[24][25] - **Construction Process**: 1. Calculate the daily return deviation of style factors: $$ \sigma_{s,t}=\frac{\bar{r}_{s,t}-\bar{r}_{s}}{\sigma_{s}} $$ where $\bar{r}_{s,t}$ is the daily return of style factor $s$ on day $t$, $\bar{r}_{s}$ is the average daily return of style factor $s$ over the entire sample period, and $\sigma_{s}$ is the standard deviation of daily returns of style factor $s$ over the entire sample period[25] 2. Calculate the Black Swan Index: $$ BlackSwan_{t}=\frac{1}{N}\times\sum_{s\in S}\left|\sigma_{s,t}\right| $$ where $BlackSwan_{t}$ is the Black Swan Index on day $t$, $S$ is the set of all style factors, and $N$ is the number of style factors[25] - **Evaluation**: The Black Swan Index effectively captures the extremity of market transactions, indicating higher probabilities of extreme tail risks[24][25] Model Name: Heuristic Style Classification for Cognitive Risk Control - **Construction Idea**: Address the discrepancy between individual and collective cognition in style classification to control cognitive risk[80][81] - **Construction Process**: 1. Calculate the value and growth factors for each stock based on predefined metrics[85] 2. Construct value and growth portfolios by selecting the top 10% and bottom 10% stocks based on factor scores[82] 3. Perform time-series regression to classify stocks into value, growth, or balanced styles: $$ r_{t,t}\sim\beta_{\mathit{Value}}\cdot r_{\mathit{Value},t}+\beta_{\mathit{Growth}}\cdot r_{\mathit{Growth},t}+\varepsilon_{t} $$ subject to $0\leq\beta_{\mathit{Value}}\leq1$, $0\leq\beta_{\mathit{Growth}}\leq1$, and $\beta_{\mathit{Value}}+\beta_{\mathit{Growth}}=1$[97] 4. Use weighted least squares (WLS) to estimate regression coefficients based on the most differentiated trading days[98] - **Evaluation**: The heuristic style classification method captures market consensus more accurately than traditional factor scoring methods, reducing cognitive risk[80][81] Model Name: Louvain Community Detection for Hidden Risk Control - **Construction Idea**: Cluster stocks based on excess return correlations to identify hidden risks[116][117] - **Construction Process**: 1. Calculate weighted correlation of excess returns between stocks: $$ Corr_{w}(X,Y)=\frac{Cov_{w}(X,Y)}{\sigma_{w,X}\cdot\sigma_{w,Y}}=\frac{\sum_{i=1}^{n}w_{i}(x_{i}-\overline{X_{w}})(y_{i}-\overline{Y_{w}})}{\sqrt{\sum_{i=1}^{n}w_{i}(x_{i}-\overline{X_{w}})^{2}}\cdot\sqrt{\sum_{i=1}^{n}w_{i}(y_{i}-\overline{Y_{w}})^{2}}} $$ where $w_{i}$ is the weight for day $i$, reflecting market volatility[118] 2. Use Louvain algorithm to cluster stocks based on weighted correlation matrix[117] 3. Ensure clusters have at least 20 stocks and remove clusters with fewer stocks[121] - **Evaluation**: The Louvain community detection method effectively identifies hidden risks by clustering stocks with similar return patterns, which traditional risk models may overlook[116][117] Model Name: Dynamic Style Factor Control - **Construction Idea**: Control style factors dynamically based on their volatility clustering effect[128][129] - **Construction Process**: 1. Identify style factors with high volatility or significant volatility increase: $$ \text{High volatility: Rolling 3-month volatility in top 3} $$ $$ \text{Volatility increase: Rolling 3-month volatility > historical mean + 1 standard deviation} $$ 2. Set the exposure of these style factors to zero in the portfolio[136] - **Evaluation**: Dynamic style factor control captures major market risks without significantly affecting portfolio returns, leveraging the predictability of volatility clustering[128][129] Model Name: Adaptive Stock Deviation Control under Target Tracking Error - **Construction Idea**: Adjust stock deviation based on tracking error to control portfolio risk[146][147] - **Construction Process**: 1. Calculate rolling 3-month tracking error for different stock deviation levels[153] 2. Set the maximum stock deviation that keeps tracking error within the target range[153] - **Evaluation**: Adaptive stock deviation control effectively reduces tracking error during high market volatility, maintaining portfolio stability[146][147] Model Backtest Results Traditional CSI 500 Enhanced Index - **Annualized Excess Return**: 18.77%[5][162] - **Maximum Drawdown**: 9.68%[5][162] - **Information Ratio (IR)**: 3.56[5][162] - **Return-to-Drawdown Ratio**: 1.94[5][162] - **Annualized Tracking Error**: 4.88%[5][162] CSI 500 Enhanced Index with Full-Process Risk Control - **Annualized Excess Return**: 16.51%[5][169] - **Maximum Drawdown**: 4.90%[5][169] - **Information Ratio (IR)**: 3.94[5][169] - **Return-to-Drawdown Ratio**: 3.37[5][169] - **Annualized Tracking Error**: 3.98%[5][169]