Systematic and discretionary investment strategies alike are game plans, which should perform under risk, i.e. quantifiable outcomes of “known unknowns”, and under uncertainty, i.e. unquantifiable “unknown unknowns”. Investment strategies must capitalize on actionable new information while tolerating information noise and market volatility. In this short article, I review some foremost insights about risk, uncertainty, and strategies’ edge from wonderful books by Ed Thorp, Aaron Brown, and Michael Mauboussin.

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In a new book “A Man for All Markets”, Ed Thorp describes his successful and exciting adventures in gambling and markets. His general strategy is always to look for edge (excess return) and to leverage this edge optimally according to geometric-growth Kelly strategy. Kelly strategy* prescribes the asset allocation (i.e. leverage) to be the ratio of excess premium and variance (a measure of risk). Thorp succeeded in all markets and games (blackjack, roulette, and multiple financial markets) but not as much in the academic recognition, which he does not regret. Thorp is a spectacular master of finding clear-cut markets inefficiencies and quantifiying and exploiting them through skillful leverage. Another practical insight from Thorp’s strategies is to neutralise uncertainty in various strategies (for instance, market neutral strategy) in order to exploit (fractional) Kelly strategy confidently (one of the results of my recent paper is that uncertainty makes Kelly criterion fractional and fragile ).


Uncertainty, due to incomplete information and behaviour of other players, is one of the most important driving forces of the markets and some games like poker (as opposed to blackjack, which is a so called perfect information game). Uncertainty, being different from risk as stressed by , is the “unknown unknown” where neither probability nor the nature and impact of some events can be perceived. In “The Poker Face of Wall Street”, Aaron Brown embraces uncertainty representing strategic challenge and opportunity. Brown highlights the creative nature of competitive and incomplete markets and encourages taking multiple, reasonably sized, strategic and opportunistic bets in markets, poker and life. Uncertainty requires adaptive and flexible strategy and risk management. He describes many stories in the games of poker and markets, and this is perhaps the best thing to do in the absence of a “unified grand theory” of games, evolution, information and optionality. The impossibility of such a grand unified theory is arguable on the similar grounds in my opinion as impossibility of unified theory of physics due to emerging complexity and structures at each level of knowledge.

Michael Mauboussin untangles skill and luck in business, sports and investing in his book “The Success Equation”. In the imperfect information games, hardly separable combination of luck and skill makes the winners. To make the connections between Thorp’s and Mauboussin’s key concepts, skill is the same as advantage and edge, while luck (in the sense of the future) is inverse of risk and uncertainty. Mauboussin advises that, under uncertainty in particular, skill is best expressed in good decision making. Being long-term oriented in order to ignore noise and randomness, finding easy (or easier) games to keep the edge, awareness of the factors that distort judgement are the strategies advised by Mauboussin. “The inventor” – Ed Thorp – have had not only great skill in the sense of finding certain excess returns but also have followed his “arc of skill” on the border of exploration and exploitation, which is another recipe by Mauboussin.

In summary, how investment strategies can exploit their advantage - not crowded information edge - and leverage and deal with risk and uncertainty is what can be learned from many insightful books and articles by Ed Thorp, Aaron Brown, and Michael Mauboussin. Practical application of information theory and game theory is very useful in understanding and succeeding in markets. I will discuss the above ideas and their technical expression in my talk “Information, Games, and Investment Strategies” at Global Derivatives and Risk Management Conference in May 2017.

Learn more about Mihail and Global Derivatives here.

  1. Thorp, “A Man for All Markets” (2017)
  2. Turlakov, “Leverage and Uncertainty”, preprint is available at arXiv and SSRN (2017)
  3. Knight, “Risk, Uncertainty, and Profit” (1964)
  4. Brown, “The Poker Face of Wall Street” (2006)
  5. Mauboussin, “The Success Equation: Untangling Skill and Luck in Business, Sports and Investing” (2012)

*Several qualitative interpretations of Kelly fraction underscore its general and multidisciplinary importance. From information theory perspective, which is, in fact, the origin of the Kelly-Thorp theory, Kelly fraction is the ratio of (the bandwidth of) useful information to (the bandwidth of) information noise. From skill and luck perspective, Kelly fraction is simply a product of (the level and probabilities of) skill and luck in the game, where you strive to develop skill and to reduce risk and uncertainty by skilful decision process and risk management. Thus, Kelly fraction of allocating into promising investments can be large when useful information exceeds noise or when good luck (reduced risk) and skill are present. Yet from physics perspective, Kelly ratio is the ratio of the signal diffusion time and the signal propagation time. When Kelly ratio is large (the signal propagation time is much shorter than the diffusion time), the signal is not suppressed and can be exploited handsomely.

Written by Mihail Turlakov, is a head of CVA/XVA trading desk at Sberbank CIB and will be speaking at Global Derivatives this May in Barcelona.