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Optimal Convergence Portfolios for Cointegrated Asset Pairs

Code Stratmill research code

Summary

This implementation describes convergence trading for two cointegrated assets as a portfolio optimization problem. It estimates error-correction speeds and other model parameters from price data, then computes portfolio weights under both unconstrained and delta-neutral approaches. The unconstrained solution can take positions in the same direction in both assets, while the constrained approach keeps the pair weights offsetting. A market portfolio allocation is also included.

The model treats recurring opportunities with continuing cointegrated processes and includes calculations for nonrecurring, stopped processes, as well as an estimate of the wealth advantage of unconstrained trading over delta neutrality. Its motivation is to balance convergence opportunities with market risk and diversification. The document provides implementation details and references a published study, but offers no independent empirical validation. Parameter estimates depend on the supplied data and assumptions; the code warns that negative residual variance estimates signal poor fit and may require a longer sample or a more suitable pair.

Key ideas

  • The method frames convergence trading as a portfolio optimization problem.
  • Model parameters are estimated from the price history of two assets.
  • Unconstrained optimal weights can hold both pair assets in the same direction.
  • A delta-neutral version forces the two pair weights to sum to zero.
  • The model's reliability depends on the data and its cointegration assumptions.

Tags

Pairs tradingArbitragePortfolio constructionStatisticsRisk management

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