Social and Behavioral Sciences Commons^™

Exact Replication Of The Best Rebalancing Rule In Hindsight, Alex Garivaltis

Faculty Peer-Reviewed Publications

This paper prices and replicates the financial derivative whose payoff at T is the wealth that would have accrued to a $1 deposit into the best continuously-rebalanced portfolio (or fixed-fraction betting scheme) determined in hindsight. For the single-stock Black-Scholes market, Ordentlich and Cover (1998) only priced this derivative at time-0, giving C0=1+s*sqrt[T/(2*p)]. Of course, the general time-t price is not equal to 1+s*sqrt[T/(2p)]. I complete the Ordentlich-Cover (1998) analysis by deriving the price at any time t. By contrast, I also study the more natural case of the best levered rebalancing rule in hindsight. This yields C(S,t)=sqrt(T/t)*exp[r*t+s^2*b(S,t)^2*t/2], where b(S,t) is …