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Covers Rebalancing Option With Discrete Hindsight Optimization

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Document pages: 34 pages

Abstract: We study T. Cover s rebalancing option (Ordentlich and Cover 1998) underdiscrete hindsight optimization in continuous time. The payoff in question isequal to the final wealth that would have accrued to a $ $1$ deposit into thebest of some finite set of (perhaps levered) rebalancing rules determined inhindsight. A rebalancing rule (or fixed-fraction betting scheme) amounts tofixing an asset allocation (i.e. $200 $ stocks and $-100 $ bonds) and thencontinuously 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 thefinal wealth of the best unlevered rebalancing rule of any kind in hindsight.Our approach lets practitioners express an a priori view that one of thefavored asset allocations ( "bets ") $b in {b 1,...,b n }$ will turn out to haveperformed spectacularly well in hindsight. In limiting our robustness to somediscrete set of asset allocations (rather than all possible asset allocations)we reduce the price of the rebalancing option and guarantee to achieve acorrespondingly higher percentage of the hindsight-optimized wealth at the endof the planning period. A practitioner who lives to delta-hedge this variant ofCover s rebalancing option through several decades is guaranteed to see the daythat his realized compound-annual capital growth rate is very close to that ofthe best $b i$ in hindsight. Hence the point of the rock-bottom option price.

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