---
author:
- 'Alex Garivaltis[^1]'
title: '[**Cover’s Rebalancing Option with Discrete Hindsight Optimization**]{}'
---

**JEL Classification:** C44, D80, D81, G11

Introduction
============

The main alternative to the Markowitz (1952) mean-variance theory of portfolio selection was popularized by Kelly (1956) who sought to optimize a gambler’s asymptotic continuously-compounded capital growth rate in repeated bets on horse races in the presence of partial inside information. His reasoning is in fact applicable to all gambling, insurance, and investment problems. Rather than optimize the static reward per unit of risk, the Kelly Criterion (Poundstone 2010) is equivalent to the prescription that one should act each round so as to maximize the expected log of his capital. Breiman (1961) showed that the Kelly Criterion constitutes asymptotically dominant behavior: a Kelly gambler will almost surely beat any other gambler in the long run by an exponential factor, and he has the shortest expected hitting time for a distant wealth goal. With probability approaching 1 as time goes on, the Kelly gambler’s bankroll will (amusingly) overtake that of a mean-variance investor, who has a smooth ride but ultimately cannot “eat his Sharpe ratio.” The books by Cover and Thomas (2006) and Luenberger (1998) are excellent primers of 