Systematic Investor Rob Carver: Choosing Strategies Using Left-Tail Percentiles, More Conservative Than Kelly Optimal
In a blog post, Rob Carver proposes that when choosing between multiple trading strategies or leverage levels, one is essentially selecting among N distributions of outcomes. He compares three methods—optimizing the median (equivalent to Kelly optimal), optimizing the right tail (the gambler's approach), and optimizing the left tail (a conservative approach)—and argues that optimizing for the 10th or 25th percentile of the left tail is a reasonable practical compromise, while acknowledging that historical backtesting cannot predict true extreme outcomes.
What is the real question when a systematic investor faces N trading strategies or N leverage levels? Rob Carver provides a clear reframing in his blog: whether bootstrapping historical returns to obtain a distribution of final Compound Annual Growth Rate (CAGR), or bootstrapping different leverage levels to generate a series of discrete possible outcomes, both are fundamentally about choosing which of N outcome distributions you prefer. You are not selecting the average performance of a specific strategy, but rather which complete outcome distribution you favor.
Carver distinguishes three selection methods. The first is the strict expectation method: selecting the distribution with the best median value, i.e., the best 50th percentile. As he has previously argued, this is mathematically equivalent to Kelly optimal, which maximizes long-term compound growth. The second is the gambler's method: selecting the distribution with the best right tail, such as the option with the most favorable 1% right-tail point. This corresponds to high-leverage, cryptocurrency, or short-gamma strategies—paths that do not blow up in the best possible alternative histories generated by the bootstrap. Carver's assessment is that nobody should be a gambler, except occasionally. The third is the conservative method he favors: selecting the distribution with the best left tail, i.e., the option with the most favorable 1st, 10th, or 25th percentile point, meaning the option that yields the best outcome if bad things happen.