SHANXI SECURITIES(SZ:002500) Shanxi Securities·2025-06-17 15:09Quantitative Models and Construction Methods - Model Name: JumpModel Construction Idea: JumpModel extends the traditional Hidden Markov Model (HMM) by introducing jump processes to better capture abrupt market state changes, addressing the limitations of smooth state transitions in HMM[13][14][15] Construction Process: 1. In HMM, the state transition probability is defined as: $ P(S_{t}|S_{t-1})=P_{i j},\quad S_{t},S_{t-1}\in{1,2,...,K} $ Here, $ P_{ij} $ represents the transition probability from state $ i $ to state $ j $[13] 2. JumpModel introduces a jump process to account for abrupt changes: $ P(S_{t}|S_{t-1},J_{t})=(1-\lambda)P_{i j}+\lambda Q_{i j} $ Where $ \lambda $ controls the probability of jump events, and $ Q_{ij} $ represents the transition probability under jump conditions[14][15] 3. Observed variables in JumpModel are modeled with higher variance to capture extreme events: $ Y_{t}|S_{t},J_{t}\sim{\mathcal{N}}{\big(}\mu_{S_{t}}+J_{t},\sigma_{S_{t}}^{2}+\sigma_{J}^{2}{\big)} $ This allows the model to better respond to market shocks and tail risks[16][17][19] Evaluation: JumpModel improves responsiveness to market volatility and extreme events, making it more adaptive during rapid market changes compared to HMM[19] - Model Name: XGBoost Construction Idea: XGBoost leverages ensemble learning to enhance prediction accuracy, particularly in high-dimensional and multi-feature datasets[4][31] Construction Process: 1. Features used for training include asset-specific return characteristics (e.g., EMA, Sortino ratio) and macroeconomic indicators (e.g., VIX index, bond yield curve)[32] 2. Preprocessing techniques such as exponential moving averages and log differences are applied to stabilize data and extract key signals[31][32] 3. Default parameters are used to avoid overfitting and ensure generalization across different market environments[34] Evaluation: XGBoost demonstrates robust predictive performance, balancing complexity and reliability without requiring extensive parameter tuning[34] - Model Name: Mean-Variance Optimization Construction Idea: This model dynamically adjusts portfolio weights based on predicted market states to optimize the trade-off between risk and return[5][42] Construction Process: 1. Objective function: $ \text{max } \mu - \text{risk} - \alpha \times |w - w_{\text{pre}}|1 $ Where $ \mu $ represents expected returns, $ \text{risk} $ denotes systematic risk exposure, and $ \alpha |w - w{\text{pre}}|1 $ accounts for transaction costs[43] 2. Constraints: $ 0 \leq w \leq w{\text{max}} $ 3. Covariance matrix is used to model risk transmission and asset interdependencies[43] 4. Rolling window approach is applied for iterative training and validation, ensuring adaptability to market changes[30][43] Evaluation: The model effectively balances risk and return, dynamically reallocating weights based on market predictions[45] --- Model Backtesting Results - JumpModel: - Annualized return: 6.37%[5] - Information ratio (IR): 0.58[5] - XGBoost: - Performance in Shanghai-Shenzhen 300 Index: Successfully avoided major downturns and captured upward trends during backtesting from 2018 to 2025[35][37] - Performance in CSI 500 Index: Higher trading frequency observed due to increased volatility, leading to potential higher transaction costs[39][41] - Performance in long-term bond index: Lower trading frequency due to stable bull market conditions, effectively capturing upward trends[41][44] - Mean-Variance Optimization: - Annualized return: 6.37%[49] - Information ratio (IR): 0.58[49] - Sharpe ratio: 1.50 (2022)[55] - Maximum drawdown: 13.9% (2021)[55] - Volatility: 12.9% (2020)[55] --- Quantitative Factors and Construction Methods - Factor Name: Jump Intensity Parameter ($ \lambda $) Construction Idea: $ \lambda $ determines the sensitivity of JumpModel to market state transitions, balancing responsiveness and stability[20] Construction Process: 1. High $ \lambda $ values suppress frequent state transitions, enhancing stability in low-volatility environments[20] 2. Low $ \lambda $ values increase responsiveness to abrupt market changes, suitable for trend reversal scenarios[20] 3. Rolling window cross-validation is used to optimize $ \lambda $ based on Sharpe ratio maximization[30] Evaluation: Proper tuning of $ \lambda $ ensures adaptability to varying market conditions, reducing false signals while capturing key transitions[30] --- Factor Backtesting Results - Jump Intensity Parameter ($ \lambda $): - Performance in Shanghai-Shenzhen 300 Index: - $ \lambda = 10 $: Frequent short-term signal generation[22] - $ \lambda = 30 $: Balanced responsiveness and stability[25] - $ \lambda = 50 $: Focused on long-term trends, reduced noise sensitivity[28]