Cover's Rebalancing Option With Discrete Hindsight Optimization

33 Pages Posted: 26 Mar 2019

See all articles by Alex Garivaltis

Alex Garivaltis

Northern Illinois University - Department of Economics

Date Written: March 2, 2019


We study T. Cover’s rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to a $1 deposit into the best of some finite set of (perhaps levered) rebalancing rules determined in hindsight. A rebalancing rule (or fixed-fraction betting scheme) amounts to fixing an asset allocation (i.e. 200% stocks and -100% bonds) and then continuously executing rebalancing trades to counteract allocation drift. Restricting the hindsight optimization to a small number of rebalancing rules (i.e. 2) has some advantages over the pioneering approach taken by Cover & Company in their brilliant theory of universal portfolios (1986, 1991, 1996, 1998), where one’s on-line trading performance is benchmarked relative to the final wealth of the best unlevered rebalancing rule of any kind in hindsight. Our approach lets practitioners express an a priori view that one of the favored asset allocations (“bets”) b ∈ {b1,...,bn} will turn out to have performed spectacularly well in hindsight. In limiting our robustness to some discrete set of asset allocations (rather than all possible asset allocations) we reduce the price of the rebalancing option and guarantee to achieve a correspondingly higher percentage of the hindsight-optimized wealth at the end of the planning period. A practitioner who lives to delta-hedge this variant of Cover’s rebalancing option through several decades is guaranteed to see the day that his realized compound-annual capital growth rate is very close to that of the best of the discrete set of rebalancing rules in hindsight. Hence the point of the rock-bottom option price.

Keywords: Continuously-Rebalanced Portfolios, Adaptive Asset Allocation, Kelly Criterion, Universal Portfolios, Lookback Options, Exchange Options, Rainbow Options, On-Line Portfolio Selection, Robust Procedures

JEL Classification: C44, D80, D81, G11

Suggested Citation

Garivaltis, Alex, Cover's Rebalancing Option With Discrete Hindsight Optimization (March 2, 2019). Available at SSRN: or

Alex Garivaltis (Contact Author)

Northern Illinois University - Department of Economics ( email )

DeKalb, IL 60115
United States


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