Optimal Arbitrage Allocation for Mean-Reverting Spreads Under OU Dynamics
Summary
The document explains a stochastic-control model for an arbitrageur trading a mean-reverting spread, such as an equity pairs position. It models mispricing with an Ornstein–Uhlenbeck process, allowing convergence timing to be uncertain and the spread to diverge before reverting. A cointegrating regression can be used to construct spread weights from total-return indices. The investor allocates between the spread and a riskless asset under either finite-horizon CRRA utility over terminal wealth or an Epstein–Zin preference specification that can represent ongoing fee income.
The model’s allocation depends on spread level, wealth, risk aversion, and time remaining. It can imply a threshold beyond which further divergence leads the arbitrageur to reduce exposure: worsening losses and a nearer evaluation date can outweigh the more attractive entry opportunity. The framework is analytical, not empirical evidence of profitability. It assumes continuous frictionless trading without transaction costs or margin constraints, and its results depend on the OU and preference assumptions; real markets may violate these conditions.
Key ideas
- The model represents spread mispricing with an Ornstein–Uhlenbeck process that can diverge before reverting.
- Spread weights may be estimated using cointegration on total-return indices.
- Optimal allocation changes with wealth, mispricing, investor preferences, and time to the horizon.
- Severe divergence can lead a rational arbitrageur to cut exposure as losses and horizon risk reduce risk-bearing capacity.
- The analysis assumes frictionless continuous trading without transaction costs or margin constraints.
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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.