Kelly Betting Can Be Too Conservative
Chung-Han Hsieh, B. Ross Barmish, and John A. Gubner

TL;DR
This paper challenges the common view that Kelly betting is overly aggressive, showing instead that it can be overly conservative when based on theoretical models versus empirical data, leading to missed opportunities.
Contribution
The paper introduces the Restricted Betting Theorem, demonstrating situations where theoretical Kelly bets are more conservative than empirical ones, highlighting potential pitfalls of relying solely on theory.
Findings
Theoretical Kelly bets can be smaller than empirical bets, missing profitable opportunities.
Empirical data can reveal 'golden' bets that theoretical models reject.
In cases with unbounded support, Kelly betting may suggest no bets at all.
Abstract
Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes arguments that the theory often leads to bets which are "too aggressive" with respect to various risk metrics. To remedy this problem, many papers include prescriptions for scaling down the bet size. Such schemes are referred to as Fractional Kelly Betting. In this paper, we take the opposite tack. That is, we show that in many cases, the theoretical Kelly-based results may lead to bets which are "too conservative" rather than too aggressive. To make this argument, we consider a random vector X with its assumed probability distribution and draw m samples to obtain an empirically-derived counterpart Xhat. Subsequently, we derive and compare the resulting…
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Taxonomy
TopicsConsumer Market Behavior and Pricing · Advanced Bandit Algorithms Research
