HJB-Optimized Statistical Arbitrage for Cointegrated Stocks

Summary

The article develops statistical arbitrage portfolios for multiple cointegrated stocks, using eigenportfolios as factors. It formulates portfolio choice as a stochastic control problem and determines optimal weights by solving a Hamilton-Jacobi-Bellman equation. The analysis considers both unconstrained portfolios and portfolios required to remain market neutral, and gives parameter conditions intended to ensure long-term stability of the solutions and portfolio growth rates.

Historical backtests on S&P 500 constituents from 2000 through 2021 suggest the model can identify many cointegrated stocks over long horizons. The reported strategies performed better during periods of higher overall market volatility, but their results were sensitive to parameter estimates. These findings indicate that estimation quality and market regime may matter substantially in implementation. The document does not specify transaction costs, benchmark comparisons, or out-of-sample safeguards, so the backtests alone do not establish that the strategies would remain profitable in live trading.

Key ideas

• The framework models multiple cointegrated stocks with eigenportfolios as factors.
• Portfolio weights are derived by solving a Hamilton-Jacobi-Bellman equation.
• The study analyzes both unconstrained and market-neutral portfolio choices.
• Backtests on S&P 500 constituents cover the period from 2000 through 2021.
• Reported profitability is higher in volatile periods, while results are sensitive to parameter estimates.

Tags

# Statistical Arbitrage for Multiple Co-Integrated Stocks


# Statistical Arbitrage for Multiple Co-Integrated Stocks









In this article, we analyse optimal statistical arbitrage strategies from stochastic control and optimisation problems for multiple co-integrated stocks with eigenportfolios being factors. Optimal portfolio weights are found by solving a Hamilton-Jacobi-Bellman (HJB) partial differential equation, which we solve for both an unconstrained portfolio and a portfolio constrained to be market neutral. Our analyses demonstrate sufficient conditions on the model parameters to ensure long-term stability of the HJB solutions and stable growth rates for the optimal portfolios. To gauge how these optimal portfolios behave in practice, we perform backtests on historical stock prices of the S&P 500 constituents from year 2000 through year 2021. These backtests suggest three key conclusions: that the proposed co-integrated model with eigenportfolios being factors can generate a large number of co-integrated stocks over a long time horizon, that the optimal portfolios are sensitive to parameter estimation, and that the statistical arbitrage strategies are more profitable in periods when overall market volatilities are high.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.