Super-Replication of the Best Pairs Trade in Hindsight

TL;DR

This paper introduces a robust online trading algorithm that asymptotically matches the wealth of the best pairs rebalancing rule in hindsight, extending universal portfolio strategies to pairs trading with practical advantages.

Contribution

It develops a computationally feasible, universal pairs trading algorithm that guarantees near-optimal wealth growth compared to the best hindsight pairs rebalancing rule.

Findings

Achieves a polynomial rate of convergence to the best hindsight wealth.

Guarantees asymptotic beating of the market if a profitable pairs rule exists.

Improves upon previous strategies by being practical and reducing the cost of universality.

Abstract

This paper derives a robust on-line equity trading algorithm that achieves the greatest possible percentage of the final wealth of the best pairs rebalancing rule in hindsight. A pairs rebalancing rule chooses some pair of stocks in the market and then perpetually executes rebalancing trades so as to maintain a target fraction of wealth in each of the two. After each discrete market fluctuation, a pairs rebalancing rule will sell a precise amount of the outperforming stock and put the proceeds into the underperforming stock. Under typical conditions, in hindsight one can find pairs rebalancing rules that would have spectacularly beaten the market. Our trading strategy, which extends Ordentlich and Cover's (1998) "max-min universal portfolio," guarantees to achieve an acceptable percentage of the hindsight-optimized wealth, a percentage which tends to zero at a slow (polynomial) rate. This means that on a long enough investment horizon, the trader can enforce a compound-annual growth rate that is arbitrarily close to that of the best pairs rebalancing rule in hindsight. The strategy will "beat the market asymptotically" if there turns out to exist a pairs rebalancing rule that grows capital at a higher asymptotic rate than the market index. The advantages of our algorithm over the Ordentlich and Cover (1998) strategy are twofold. First, their strategy is impossible to compute in practice. Second, in considering the more modest benchmark (instead of the best all-stock rebalancing rule in hindsight), we reduce the "cost of universality" and achieve a higher learning rate.