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Statistical Arbitrage for Multiple Co-integrated Stocks.

Thomas Nanfeng Li1, Andrew Papanicolaou2

  • 1Department of Mathematics, New York University, 251 Mercer Street, New York, 10012 NY USA.

Applied Mathematics and Optimization
|June 13, 2022
PubMed
Summary
This summary is machine-generated.

This study introduces optimal statistical arbitrage strategies using stochastic control for co-integrated stocks. Strategies are more profitable during high market volatility periods and show stable growth rates.

Keywords:
Co-integrated stocksEigenportfolioFactor modelMarket-neutral portfolioMatrix Riccati equationOptimisationStatistical arbitrageStochastic control

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Area of Science:

  • Quantitative Finance
  • Econometrics
  • Financial Mathematics

Background:

  • Statistical arbitrage relies on identifying and exploiting temporary mispricings between related assets.
  • Co-integrated assets exhibit a long-term statistical relationship, making them suitable for arbitrage strategies.

Purpose of the Study:

  • To develop and analyze optimal statistical arbitrage strategies for multiple co-integrated stocks.
  • To investigate the stability and growth rates of these optimal portfolios.
  • To assess the practical performance of these strategies through historical backtesting.

Main Methods:

  • Stochastic control and optimization problems were used to model statistical arbitrage.
  • A Hamilton-Jacobi-Bellman (HJB) partial differential equation was solved to find optimal portfolio weights.
  • Backtesting was performed on historical S&P 500 constituent stock prices from 2000-2021.

Main Results:

  • The co-integrated model with eigenportfolios as factors can identify numerous co-integrated stocks over extended periods.
  • Optimal portfolio performance is sensitive to parameter estimation accuracy.
  • Statistical arbitrage strategies demonstrated higher profitability during periods of elevated market volatility.

Conclusions:

  • The proposed model provides a robust framework for statistical arbitrage in co-integrated markets.
  • Parameter estimation accuracy is crucial for the success of these strategies.
  • Market volatility presents opportunities for enhanced profitability in statistical arbitrage.