The blog post "Kelly Can't Fail," authored by John Mount and published on the Win-Vector LLC website, delves into the oft-misunderstood concept of the Kelly criterion, a formula used to determine optimal bet sizing in scenarios with known probabilities and payoffs. The author meticulously dismantles the common misconception that the Kelly criterion guarantees success, emphasizing that its proper application merely optimizes the long-run growth rate of capital, not its absolute preservation. He accomplishes this by rigorously demonstrating, through mathematical derivation and illustrative simulations coded in R, that even when the Kelly criterion is correctly applied, the possibility of experiencing substantial drawdowns, or losses, remains inherent.
Mount begins by meticulously establishing the mathematical foundations of the Kelly criterion, illustrating how it maximizes the expected logarithmic growth rate of wealth. He then proceeds to construct a series of simulations involving a biased coin flip game with favorable odds. These simulations vividly depict the stochastic nature of Kelly betting, showcasing how even with a statistically advantageous scenario, significant capital fluctuations are not only possible but also probable. The simulations graphically illustrate the wide range of potential outcomes, including scenarios where the wealth trajectory exhibits substantial declines before eventually recovering and growing, emphasizing the volatility inherent in the strategy.
The core argument of the post revolves around the distinction between maximizing expected logarithmic growth and guaranteeing absolute profits. While the Kelly criterion excels at the former, it offers no safeguards against the latter. This vulnerability to large drawdowns, Mount argues, stems from the criterion's inherent reliance on leveraging favorable odds, which, while statistically advantageous in the long run, exposes the bettor to the risk of significant short-term losses. He further underscores this point by contrasting Kelly betting with a more conservative fractional Kelly strategy, demonstrating how reducing the bet size, while potentially slowing the growth rate, can significantly mitigate the severity of drawdowns.
In conclusion, Mount's post provides a nuanced and technically robust explanation of the Kelly criterion, dispelling the myth of its infallibility. He meticulously illustrates, using both mathematical proofs and computational simulations, that while the Kelly criterion provides a powerful tool for optimizing long-term growth, it offers no guarantees against substantial, and potentially psychologically challenging, temporary losses. This clarification serves as a crucial reminder that even statistically sound betting strategies are subject to the inherent volatility of probabilistic outcomes and require careful consideration of risk tolerance alongside potential reward.
Summary of Comments ( 120 )
https://news.ycombinator.com/item?id=42466676
The Hacker News comments discuss the limitations and practical challenges of applying the Kelly criterion. Several commenters point out that the Kelly criterion assumes perfect knowledge of the probability distribution of outcomes, which is rarely the case in real-world scenarios. Others emphasize the difficulty of estimating the "edge" accurately, and how even small errors can lead to substantial drawdowns. The emotional toll of large swings, even if theoretically optimal, is also discussed, with some suggesting fractional Kelly strategies as a more palatable approach. Finally, the computational complexity of Kelly for portfolios of correlated assets is brought up, making its implementation challenging beyond simple examples. A few commenters defend Kelly, arguing that its supposed failures often stem from misapplication or overlooking its long-term nature.
The Hacker News post "Kelly Can't Fail" (linking to a Win-Vector blog post about the Kelly Criterion) generated several comments discussing the nuances and practical applications of the Kelly Criterion.
One commenter highlighted the importance of understanding the difference between "fraction of wealth" and "fraction of bankroll," particularly in situations involving leveraged bets. They emphasize that Kelly Criterion calculations should be based on the total amount at risk (bankroll), not just the portion of wealth allocated to a specific betting or investment strategy. Ignoring leverage can lead to overbetting and potential ruin, even if the Kelly formula is applied correctly to the initial capital.
Another commenter raised concerns about the practical challenges of estimating the parameters needed for the Kelly Criterion (specifically, the probabilities of winning and losing). They argued that inaccuracies in these estimates can drastically affect the Kelly fraction, leading to suboptimal or even dangerous betting sizes. This commenter advocates for a more conservative approach, suggesting reducing the calculated Kelly fraction to mitigate the impact of estimation errors.
Another point of discussion revolves around the emotional difficulty of adhering to the Kelly Criterion. Even when correctly applied, Kelly can lead to significant drawdowns, which can be psychologically challenging for investors. One commenter notes that the discomfort associated with these drawdowns can lead people to deviate from the strategy, thus negating the long-term benefits of Kelly.
A further comment thread delves into the application of Kelly to a broader investment context, specifically index funds. Commenters discuss the difficulties in estimating the parameters needed to apply Kelly in such a scenario, given the complexities of market behavior and the long time horizons involved. They also debate the appropriateness of using Kelly for investments with correlated returns.
Finally, several commenters share additional resources for learning more about the Kelly Criterion, including links to academic papers, books, and online simulations. This suggests a general interest among the commenters in understanding the concept more deeply and exploring its practical implications.