Chapter 28: Hidden Markov Models — Regime-Switching Trading Strategy

Chapter 28: Hidden Markov Models — Regime-Switching Trading Strategy

Overview

Финансовые рынки функционируют в различных режимах (bull, bear, sideways), каждый со своими статистическими характеристиками. Hidden Markov Models (HMM) позволяют автоматически определять текущий режим и вероятности перехода между режимами. В этой главе мы строим стратегию, которая адаптирует свое поведение к текущему рыночному режиму.

Trading Strategy

Суть стратегии: HMM определяет 3 режима рынка. Для каждого режима — своя подстратегия:

• Bull regime: Aggressive momentum, high equity allocation
• Bear regime: Defensive, low equity / high bonds / hedges
• Sideways regime: Mean-reversion, pairs trading

Сигнал на переключение: Когда posterior probability нового режима превышает порог (например, 70%)

Position Sizing: Зависит от confidence в текущем режиме и волатильности режима

Technical Specification

Notebooks to Create

#	Notebook	Description
1	01_data_preparation.ipynb	Загрузка S&P 500, VIX, yields, macro данных
2	02_hmm_theory.ipynb	Теория HMM: forward-backward, Viterbi, Baum-Welch
3	03_regime_features.ipynb	Feature engineering для определения режимов
4	04_gaussian_hmm.ipynb	Обучение Gaussian HMM с hmmlearn
5	05_regime_interpretation.ipynb	Интерпретация режимов, визуализация
6	06_regime_characteristics.ipynb	Статистика каждого режима (return, vol, duration)
7	07_substrategy_bull.ipynb	Momentum стратегия для bull режима
8	08_substrategy_bear.ipynb	Defensive стратегия для bear режима
9	09_substrategy_sideways.ipynb	Mean-reversion для sideways режима
10	10_strategy_switching.ipynb	Логика переключения между стратегиями
11	11_backtesting.ipynb	Full backtest с transaction costs
12	12_robustness_analysis.ipynb	Sensitivity analysis, out-of-sample

Data Requirements

Market Data:
├── S&P 500 index daily (20+ лет для разных режимов)
├── VIX index
├── US Treasury yields (2Y, 10Y)
├── Credit spreads (BAA-AAA)
└── Gold, USD index

Macro Indicators:
├── NBER recession dates (ground truth)
├── Leading Economic Index (LEI)
├── Yield curve slope
└── Unemployment rate

HMM Configuration

from hmmlearn import hmm

# 3-state Gaussian HMM
model = hmm.GaussianHMM(
    n_components=3,           # Bull, Bear, Sideways
    covariance_type="full",   # Full covariance matrix
    n_iter=1000,
    random_state=42
)

# Features for regime detection
features = [
    'return_20d',      # 20-day return
    'volatility_20d',  # 20-day realized vol
    'vix_level',       # VIX
    'yield_slope',     # 10Y - 2Y
    'credit_spread'    # BAA - AAA
]

Regime Characteristics (Expected)

Regime	Avg Return	Volatility	Avg Duration	Typical Indicators
Bull	+15% ann.	12%	24 months	Low VIX, steep yield curve
Bear	-20% ann.	25%	8 months	High VIX, inverted curve
Sideways	+5% ann.	15%	12 months	Mid VIX, flat curve

Sub-strategies per Regime

Bull Regime Strategy:
├── Long equity (100% allocation)
├── Momentum factor tilt
├── Small cap overweight
└── No hedges

Bear Regime Strategy:
├── Reduced equity (30% allocation)
├── Long-term treasuries (40%)
├── Gold allocation (20%)
├── Cash buffer (10%)
└── Optional: VIX calls hedge

Sideways Regime Strategy:
├── Market neutral (50% equity)
├── Pairs trading overlay
├── Sector rotation (momentum within)
└── Enhanced yield strategies

Transition Matrix Example

         To Bull  To Bear  To Sideways
From Bull    0.92    0.03       0.05
From Bear    0.08    0.85       0.07
From Sideways 0.10   0.08       0.82

Key Metrics

• Regime Detection: Accuracy vs NBER, Average regime duration, False switches
• Strategy: Sharpe Ratio, Max Drawdown, Calmar Ratio
• Comparison: vs Buy&Hold, vs 60/40, vs static momentum

Dependencies

hmmlearn>=0.3.0
pomegranate>=1.0.0  # Alternative HMM library
pandas>=1.5.0
numpy>=1.23.0
matplotlib>=3.6.0
seaborn>=0.12.0
scipy>=1.10.0
yfinance>=0.2.0

Expected Outcomes

1. 3-state HMM с интерпретируемыми режимами (bull/bear/sideways)
2. Visualization режимов на историческом графике S&P 500
3. Статистика режимов — duration, returns, volatility per regime
4. 3 подстратегии оптимизированные для каждого режима
5. Switching logic с учетом transaction costs и whipsaws
6. Backtest results с улучшением risk-adjusted returns vs buy&hold

References

• Regime Switching Models for Financial Time Series
• Hidden Markov Models for Time Series
• hmmlearn Documentation
• Market Regime Detection Using Machine Learning

Difficulty Level

⭐⭐⭐☆☆ (Intermediate)

Требуется понимание: HMM theory, Time series analysis, Portfolio construction