量化研究专题报告：基于隐马尔可夫模型的行业轮动策略-模式识别之状态匹配

Quantitative Models and Construction Methods - Model Name: Hidden Markov Model (HMM) Model Construction Idea: The model is based on the theory of historical repetition, identifying the current state of industries and matching it with historical states to predict future probabilities of industry price increases[2][9][33] Model Construction Process: 1. Definition of HMM Components: - State set: $Q={q_{1},q_{2},\cdots,q_{N}}$, representing all possible hidden states[17] - Observation set: $V={\nu_{1},\nu_{2},\cdots,\nu_{M}}$, representing all possible observations[17] - State transition matrix: $A=[a_{i,j}]{N\times N}$, where $a{i,j}$ represents the probability of transitioning from state $q_i$ to state $q_j$[19] - Observation probability matrix: $B=[b_{j,k}]{N\times M}$, where $b{j,k}$ represents the probability of observing $\nu_k$ given state $q_j$[20] - Initial state probability vector: $\pi=[\pi_{i}]$, where $\pi_i$ represents the probability of starting in state $q_i$[22] - The HMM is represented as $\lambda=(A,B,\pi)$[23] 2. Industry Rotation Strategy Construction: - Historical data from January 2018 to August 2024 is used to train the model[34] - Monthly rebalancing is applied to the portfolio, considering industry rotation as an asset allocation strategy[35] - Features used for training include daily return, turnover rate, volatility, volatility change, and turnover rate change[35][48] - Features are standardized using Z-Score normalization: $X'={\frac{X-M e a n(X)}{S t d(X)}}$[49][50] - States are generated using HMM, and historical samples are classified into significant upward and downward categories based on future returns thresholds (e.g., 3.5%)[52][64] - Similarity between current states and historical states is calculated using a relaxed matching method: $S_{i}=\begin{cases}1.0&\text{if}\ W_{i}^{\text{Now}}=W_{i}^{\text{Part}}\\ 0.5&\text{if}\ W_{i}^{\text{Now}}=W_{i-1}^{\text{Part}}\ \text{or}\ W_{i}^{\text{Now}}=W_{i+1}^{\text{Part}}\\ 0&\text{otherwise}\end{cases}$ $S=\sum_{i=1}^{K}S_{i}$[54] - The probability of future price increases is defined as: $\frac{S_{U p}}{S_{U p}+S_{D m}}$[35][36] Model Evaluation: The model effectively reduces noise and improves prediction accuracy by extracting abstract states from complex multidimensional features[89] Model Backtesting Results In-Sample Results - Cumulative Excess Return: 2022: 7.02%, 2023: 9.03%[71][73] - Maximum Drawdown: 2022: -3.50%, 2023: -3.40%[71][73] - Monthly Win Rate: 2022: 66.67%, 2023: 91.67%[71][73] - Annualized Volatility: 2022: 5.91%, 2023: 5.33%[71][73] - Monthly Profit-Loss Ratio: 2022: 1.76, 2023: 0.48[71][73] Out-of-Sample Results - Cumulative Excess Return: 2024 (Jan-Aug): 10.75%[74][75] - Maximum Drawdown: 2024 (Jan-Aug): -2.80%[74][75] - Monthly Win Rate: 2024 (Jan-Aug): 75.00%[74][75] - Annualized Volatility: 2024 (Jan-Aug): 6.77%[74][75] - Monthly Profit-Loss Ratio: 2024 (Jan-Aug): 1.91[74][75] Top Industry Selection - 2024 Top Industries: Selected industries include oil & petrochemicals, coal, home appliances, non-bank finance, communication, and comprehensive finance[88][81] - Ranking Performance: - Top 1: Appeared 4 times - Top 3: Appeared 8 times - Top 5: Appeared 13 times - Top 10: Appeared 20 times - Top 15: Appeared 28 times (58% of total samples)[83] - Monthly Turnover Rate: Average turnover rate of 53%, with higher turnover in February, April, and June[83] Quantitative Factors and Construction Methods - Factor Name: Industry State Matching Factor Factor Construction Idea: Predict future industry price increases by matching current states with historical states associated with significant upward or downward trends[33][56] Factor Construction Process: - Historical data is classified into significant upward and downward categories based on future return thresholds[52] - Similarity between current states and historical states is calculated using relaxed matching criteria[54] Factor Evaluation: The factor effectively captures industry trends and improves prediction accuracy[89] Factor Backtesting Results In-Sample Results - Cumulative Excess Return: 2022: 7.02%, 2023: 9.03%[71][73] - Maximum Drawdown: 2022: -3.50%, 2023: -3.40%[71][73] - Monthly Win Rate: 2022: 66.67%, 2023: 91.67%[71][73] - Annualized Volatility: 2022: 5.91%, 2023: 5.33%[71][73] - Monthly Profit-Loss Ratio: 2022: 1.76, 2023: 0.48[71][73] Out-of-Sample Results - Cumulative Excess Return: 2024 (Jan-Aug): 10.75%[74][75] - Maximum Drawdown: 2024 (Jan-Aug): -2.80%[74][75] - Monthly Win Rate: 2024 (Jan-Aug): 75.00%[74][75] - Annualized Volatility: 2024 (Jan-Aug): 6.77%[74][75] - Monthly Profit-Loss Ratio: 2024 (Jan-Aug): 1.91[74][75]