Case Study: A Post-Mortem of an HMM-Based Pairs Trading Strategy

The Strategy: An HMM-Based Pairs Trading Model

This case study examines a pairs trading strategy that uses a Hidden Markov Model (HMM) to identify different regimes in the spread between two cointegrated stocks: Coca-Cola (KO) and PepsiCo (PEP). The strategy is based on the idea that the spread between these two stocks will be mean-reverting in some regimes and trending in others. The HMM is used to identify these regimes, and the trading signals are generated accordingly.

Development and Backtesting

The strategy was developed and backtested on historical data from 2010 to 2020. A two-state HMM was fitted to the log spread between KO and PEP. The HMM identified a mean-reverting regime and a trending regime. The trading rules were as follows:

• In the mean-reverting regime, the strategy would buy the spread when it was two standard deviations below its mean and sell it when it was two standard deviations above its mean.
• In the trending regime, the strategy would not trade.

The backtest showed promising results. The strategy generated a consistent stream of profits with a Sharpe ratio of 1.5. The drawdown was also relatively low, at 15%.

Simulated Execution and the Real World

The strategy was then simulated in a live trading environment from 2021 to 2023. The results were not as good as the backtest. The Sharpe ratio dropped to 0.5, and the drawdown increased to 25%. What went wrong?

Post-Mortem: What We Learned

A post-mortem analysis revealed several reasons for the discrepancy between the backtest and the live simulation:

• Regime change: The relationship between KO and PEP changed in the live trading period. The spread became less mean-reverting and more trending. The HMM was able to identify this change, but the strategy was not designed to profit from a trending regime.
• Transaction costs: The backtest did not fully account for transaction costs, such as commissions and slippage. In the live simulation, these costs ate into the profits of the strategy.
• Overfitting: It is possible that the model was overfitted to the historical data. The two-standard-deviation entry and exit thresholds may have been optimal for the backtesting period but not for the live trading period.

Lessons for the Future

This case study provides several important lessons for quantitative traders:

• Backtests can be misleading: A good backtest is no guarantee of future success. It is important to be aware of the limitations of backtesting and to be prepared for the possibility that a strategy will not perform as well in the real world.
• Models need to be adaptive: Financial markets are constantly changing. A model that worked well in the past may not work well in the future. It is important to build models that are adaptive and can adjust to changing market conditions.
• Risk management is key: Even the best trading strategy will have losing periods. It is important to have a solid risk management plan in place to protect your capital.

By learning from our mistakes, we can become better traders. This case study is a valuable reminder of the challenges and pitfalls of quantitative trading, but also of the importance of continuous learning and improvement.