Optimal Convergence Trading with Utility-Based Portfolio Weights

Summary

This document explains a stochastic-control approach to trading two cointegrated assets whose log-price spread is modeled as a stationary process. A mean-reverting spread represents relative mispricing, while a market index and a risk-free asset capture broader market exposure. The investor chooses portfolio weights to maximize expected power utility of terminal wealth, balancing expected return, risk, and diversification rather than simply holding equal and opposite positions in the pair.

For recurring convergence opportunities, the source gives closed-form weights for both unconstrained portfolios and a delta-neutral version. It also distinguishes recurring spreads from one-time mispricing that disappears permanently at convergence, for which the optimal weights differ. The model assumes specified price dynamics and parameters, and its demonstrations use a Royal Dutch–Shell pair; the displayed portfolio and wealth plots are illustrations rather than general evidence of performance. The document describes fitting model parameters on training data and applying the resulting weights to evaluation data, but does not establish that the assumptions or estimates will hold in other markets or out of sample.

Key ideas

• The optimal convergence portfolio accounts for risk and diversification as well as relative mispricing.

Tags

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