Stochastic Control for Mean-Reverting Pairs Portfolios
Summary
This article explains how stochastic control models can set dynamic positions in a mean-reverting spread. It outlines two investor preference models: constant relative risk aversion over terminal wealth, and Epstein–Zin recursive utility, which can account for intertemporal substitution and fee income. The spread is constructed as a weighted combination of total return indices, with weights estimated through cointegration. Its dynamics are modeled with an Ornstein–Uhlenbeck process, whose parameters are estimated from training data. The discussion frames horizon risk and divergence risk as central challenges: convergence timing is uncertain, and a spread may move farther from its mean before reverting.
The article describes examples using gold and mining-related exchange-traded funds and presents a second stochastic control approach alongside the Jurek model. It explains that the resulting portfolio allocations vary with prices and time remaining. The examples illustrate estimated parameters, portfolio weights, and wealth paths, but do not establish that the results generalize. The models omit transaction costs, borrowing costs, margin constraints, and other institutional frictions, so the reported gains are an optimistic upper bound.
Key ideas
- Pairs trading takes offsetting positions in related assets when their spread diverges, anticipating convergence.
- An Ornstein–Uhlenbeck process models spread reversion while representing uncertainty in convergence timing and interim divergence.
- Stochastic control uses investor preferences and wealth dynamics to determine time-varying spread allocations.
- Cointegration can supply fixed hedge weights for a spread built from asset total return indices.
- The examples omit important trading frictions, limiting their use as estimates of attainable returns.
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- Strategies Gold Miners vs Gold Beta-Hedged Residual Reversion: fade a >=2-sigma 10-session GDX-vs-GLD idiosyncratic move, dollar/beta-neutral long-short, 15-session time stop (USEQ 1-DAY)
- Hypotheses Gold Miners vs Gold Beta-Hedged Residual Reversion: fade a >=2-sigma 10-session GDX-vs-GLD idiosyncratic move, dollar/beta-neutral long-short, 15-session time stop (USEQ 1-DAY)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.