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.
The Center for New Economics' newsletter post, "The World Grid and New Geographies of Cooperation," elaborates on the concept of a "world grid" – a multifaceted framework representing the interconnectedness of global systems, particularly emphasizing the interwoven nature of energy infrastructure, data networks, and logistical pathways. The authors posit that understanding this intricate web is crucial for navigating the complexities of the 21st century and fostering effective international cooperation.
The piece argues that traditional geopolitical analyses, often focused on nation-states and their individual interests, are inadequate for addressing contemporary challenges. Instead, it advocates for a perspective that recognizes the increasing importance of transboundary flows of energy, information, and goods. These flows, facilitated by the world grid, are reshaping the global landscape and creating new opportunities for collaboration, while simultaneously presenting novel risks and vulnerabilities.
The newsletter delves into the historical evolution of interconnectedness, tracing it from early trade routes and telegraph lines to the contemporary internet and sprawling energy grids. This historical context underscores the ongoing process of integration and highlights the ever-increasing complexity of the world grid. The authors argue that this increasing complexity demands a shift in how we understand and manage global systems, moving away from fragmented national approaches towards more integrated and cooperative strategies.
The post explores the potential of the world grid to facilitate the transition to renewable energy sources. It suggests that interconnected energy grids can enable more efficient distribution of renewable energy, overcoming the intermittency challenges associated with solar and wind power by leveraging resources across different geographical regions. This collaborative approach to energy production and distribution could be instrumental in mitigating climate change and promoting sustainable development.
Furthermore, the newsletter examines the implications of the world grid for global governance. It suggests that the increasing interconnectedness necessitates new forms of international cooperation and regulatory frameworks. These frameworks must address issues such as cybersecurity, data privacy, and equitable access to the benefits of the world grid, ensuring that the interconnectedness fostered by the grid does not exacerbate existing inequalities or create new forms of digital divide.
Finally, the piece concludes with a call for a more nuanced and holistic understanding of the world grid. It emphasizes the need for further research and analysis to fully grasp the implications of this complex system and to develop effective strategies for leveraging its potential while mitigating its risks. This understanding, the authors argue, is essential for navigating the challenges and opportunities of the 21st century and building a more sustainable and cooperative future. They suggest that recognizing the interconnected nature of global systems, as represented by the world grid, is not merely a descriptive exercise but a crucial step towards building a more resilient and equitable world order.
The Hacker News post titled "The World Grid and New Geographies of Cooperation" has generated a modest number of comments, sparking a discussion around the feasibility, benefits, and challenges of a global energy grid. While not a highly active thread, several commenters engage with the core idea proposed in the linked article.
A recurring theme is the complexity of such a massive undertaking. One commenter highlights the political hurdles involved in coordinating across different nations, suggesting that differing national interests and regulatory frameworks would pose significant obstacles to implementation. This sentiment is echoed by another user who points to the challenges of even establishing smaller-scale interconnected grids within individual countries or regions, using the example of the difficulty of integrating Texas's power grid with the rest of the United States.
The potential benefits of a global grid are also acknowledged. One commenter suggests that a globally interconnected grid could facilitate the efficient distribution of renewable energy, allowing regions with excess solar or wind power to export to areas with deficits. This is further emphasized by another commenter who points out that such a system could effectively harness the continuous sunlight available somewhere on the Earth at any given time.
However, some commenters express skepticism about the technical feasibility of transmitting power over such vast distances. They raise concerns about transmission losses and the efficiency of long-distance power lines. One user specifically mentions the significant power loss associated with high-voltage direct current (HVDC) lines, questioning the overall viability of the concept.
Furthermore, the discussion touches upon the security implications of a global grid. One commenter raises the concern that a highly interconnected system could be more vulnerable to large-scale blackouts if a critical node were to fail. This potential vulnerability is contrasted with the relative resilience of more localized grids.
Finally, a few comments offer alternative solutions or additions to the global grid concept. One user suggests the use of pumped hydro storage as a means of storing excess renewable energy, while another mentions the potential of hydrogen as an energy carrier.
In summary, the comments on Hacker News present a mixed perspective on the idea of a world grid. While acknowledging the potential advantages of efficient renewable energy distribution, many commenters express significant concerns about the political, technical, and security challenges associated with such a project. The discussion highlights the complexity of the undertaking and the need for further consideration of both the benefits and risks involved.
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.