Paper: arXiv 2402.15588

Abstract

The paper provides a mathematical model and a tool for the focused investing strategy as advocated by Buffett, Munger, and others from this investment community. The approach presented here assumes that the investor’s role is to think about probabilities of different outcomes for a set of businesses. Based on these assumptions, the tool calculates the optimal allocation of capital for each of the investment candidates. The model is based on a generalized Kelly Criterion with options to provide constraints that ensure: no shorting, limited use of leverage, providing a maximum limit to the risk of permanent loss of capital, and maximum individual allocation. The software is applied to an example portfolio from which certain observations about excessive diversification are obtained. In addition, the software is made available for public use.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a generalized Kelly Criterion with a non-linear system of equations derived from probability-weighted scenarios, showing significant mathematical density. However, it lacks any backtesting, datasets, or statistical metrics, and the empirical application is limited to a single example portfolio without performance data.

Research Flowchart

  flowchart TD
  A["Research Goal:<br>Focused Portfolio Sizing"] --> B{"Key Methodology"}
  B --> C["Data/Inputs:<br>Est. Return &<br>Probability of Outcomes"]
  C --> D["Computational Process:<br>Generalized Kelly<br>with Constraints"]
  D --> E["Outputs:<br>Optimal Capital<br>Allocation"]
  E --> F["Key Findings:<br>Excessive Diversification<br>Reduced Risk"]

Cited References (19)

  1. Thinking, Fast and Slow (2011)
  2. Influence: The Psychology of Persuasion (2006)
  3. Poor Charlie’s Almanack: The Wit and Wisdom of Charles T. Munger (2005)
  4. The Intelligent Investor (2003)
  5. A New Interpretation of Information Rate (1956)
  6. Generalized framework for applying the Kelly criterion to stock markets (2018)
  7. Actuarial Life Table (2023)
  8. Maximizing Portfolio Predictability with Machine Learning — → 2311.01985
and 11 more
  1. Kelly Criterion: From a Simple Random Walk To L' e vy Processes (2020) — link
  2. On the Benefit of Nonlinear Control for Robust Logarithmic Growth:Coin Flipping Games as a Demonstration Case (2023) — link
  3. Sports Betting: An Application of Neural Networks and Modern Portfolio Theory to the English Premier League (2023) — link
  4. James, N. and Menzies, M. (2023) — link
  5. Sparse spanning portfolios and under-diversification with second-order stochastic dominance — → 2402.01951
  6. A quantum double-or-nothing game: The Kelly Criterion for Spins (2023) — link
  7. Gambling the World Away: Myopic Investors (2023) — link
  8. Berkshire Hathaway Shareholder Letters (2023)
  9. Nomad Investment Partnership Letters to Investors (2021)
  10. Li Lu’s Lecture at Professor Greenwald’s 2006 Class. (2023)
  11. What I Learned About Investing from Darwin (2023)

2 of 19 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.