Optimal Convergence Trading with Flexible Portfolio Weights

Summary

The article explains a stochastic control framework for convergence trades between cointegrated assets. Earlier approaches constrain positions to be delta-neutral and fix the relative stock weights; the generalized approach allows individual asset weights to vary. It models log-price differences as a mean-reverting error-correction process, separating short-term absolute mispricing from longer-term relative mispricing. The investor chooses positions to maximize expected power utility of terminal wealth, with separate treatments for recurring cointegration and a stopped process in which the spread remains zero after convergence.

For recurring opportunities, the framework yields closed-form optimal weights; the stopped case requires numerical methods based on the Hamilton–Jacobi–Bellman equation. The article’s Shell–Royal Dutch illustrations show that unconstrained and delta-neutral allocations can behave similarly when estimated mispricing parameters are close, while larger spreads can favor unconstrained weights in expected wealth comparisons. These are model-based results, not a full live-trading assessment. The approach assumes daily rebalancing, which may generate substantial transaction costs, and the article calls for comparisons that account for market frictions.

Key ideas

• Delta-neutral convergence positions can be suboptimal because they restrict how the trader exploits mispricing and diversification.
• A mean-reverting error-correction process represents the relative mispricing of cointegrated assets.
• The unconstrained strategy optimizes individual asset weights against terminal wealth utility.
• Recurring cointegration allows closed-form weights, while a spread that stops at zero requires numerical optimization.
• Daily rebalancing can create high transaction costs that weaken the model’s practical performance.

Tags

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