# Statistical Arbitrage for Multiple Co-Integrated Stocks

## TL;DR

This paper develops optimal statistical arbitrage strategies for multiple co-integrated stocks using stochastic control, solving HJB equations, and validates them through backtests on S&P 500 data, revealing insights on stability and profitability.

## Contribution

It introduces a novel approach to optimize portfolios of co-integrated stocks via HJB equations and analyzes their long-term stability and practical performance.

## Key findings

- Optimal portfolios are sensitive to parameter estimation.
- Strategies perform better during high market volatility.
- Model can generate many co-integrated stocks over time.

## Abstract

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.

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Source: https://tomesphere.com/paper/1908.02164