# A Game of Convexity

## There are rules

Having loosely followed the writings of the author Nassim Taleb for a while, I’d like to offer a brief review of his latest work, Skin in the Game, in the form of a contrast to the preceding work in the Incerto series, Antifragile. The Incerto series is an accessible multi-book treatise on probability and risk, which also includes the works Fooled By Randomness, The Black Swan, and The Bed of Procrustes (along with a technical companion for the series in mathematical prose pending release). Part of what I hope to contribute in this discussion is to illustrate some of the ways these two latest works are related by way of an exploration of their respective themes, as they share some interesting contrasts. Please note that this essay isn’t meant to be a comprehensive discussion of these works — part of the appeal of the author’s writings is the kind of density of prose that resists summary; themes in these works are often woven in multiple layers ranging from the wisdom of the ancients, illustrative character studies, to the trappings of modernity — often moving from one to the other rather quickly, so I’ve found that the best reviews of these works serve as highlights or takeaways of interest rather than some attempt to extract a comprehensive summary. That is not to say that these works are without overriding themes, for each certainly explores central and distinct questions related to risk and probability (along with a few tangents). Given the author’s background as a professional trader, I have sometimes seen the misconception from the uninitiated that his writings are primarily meant to apply to markets and financials. While the influence of this arena on the work is certainly prevalent, the intent of the thesis is to transcend simple financial considerations and extend these lessons of probability, risks, and exposures thereto to all kind of playing fields.

## Antifragile

The principle of antifragility is summarized quite succinctly in the subtitle of the book: things that gain from disorder. Antifragility has a comparable mathematical attribute whose term can be used interchangeably: convexity, which describes exposures f(x) with second order derivatives d2f/dx2>0, such that variations of some condition x that venture deeper into the tail (the outliers of a probability distribution) result in a nonlinearly positive contribution to the benefit function f(x), as could be demonstrated by Jensen’s inequality. Thus antifragile systems enjoy outsized gains from high variations in conditions and therefore gain from disorder. This antifragile property is one of the work’s defined triad of exposure categories, with a fragile exposure having some non-ergodic properties (non-ergodic meaning the presence of an exit barrier with some variation in conditions x, such as a brittle teacup that can stand being dropped from small distances x up until the point it shatters), a robust exposure having the ability to withstand high variance in x if not outsized benefit, and antifragile exposures as already described being the preferred of the three. Given enough time there will always be potential for black swans to shift the playing field in unexpected directions, so rather than trying to predict some precise future state of x an antifragile tactic is to instead assume that x is unknown but it’s potential for change is not, an especially appropriate tactic when the conditions of x are determined to have probability distributions with less tractable fat-tailed characteristics (a common error of risk managers being the propensity to approximate a distribution as Gaussian (normal) or some other thin tailed variant even when not appropriate). A reader looking to apply the lessons of this work should walk away with a better idea of what kinds of risks he should be taking and perhaps more importantly what kind of risks he should avoid to ensure survival and thrive under the unknown conditions of which the passages of time and randomness are sure to present.

## Skin in the Game

The final chapter in the Incerto series narrows further the types of risk that are appropriate or acceptable in the context of a collective by taking into account principles of both ethics and governance. The theme is meant to address a shortcoming of broad scale adoption of antifragile risk-taking which derives from a kind of tragedy of the commons, for as each agent seeks to offload his tail exposure to harm the risk tends to flow downhill to non-participants, causing an asymmetry between those who experience gain or harm from disorder. This type of risk transfer could happen on the small scale, say a hypothetical home builder who cuts corners on storm reinforcement to reduce costs and exposing the homeowner to catastrophic losses in the event of a hurricane, or on the large scale when too big to fail banks take risks that result in high probability short term gains but with exposure to possibility of catastrophic losses leading to taxpayer bailouts. The principle of skin in the game is more than just giving participants exposure to variations in outcome, such as an executive’s stock options — more importantly the risk sharing should serve as a kind of filter, with potential to remove from the game players who cause harm to others, for just as evolution requires a survival of the fittest (and corresponding trimming of the weakest), a system that doesn’t remove bad participants will stagnate to bad practice. Incentives matter, and positive reinforcement is not sufficient when players’ rewards are funneled through the equivalent of a check valve with one way flow. Skin in the game transitions from a consideration of governance to one of honor when you consider those with soul in the game, a different kind of asymmetry such that participants take on risks to themselves for the benefits of the collective. This idea of the collective turns out to have a kind of hierarchy of tribes, with the ergodicity of an individual less important than that of his family, congregation, nation, or collective humanity. This principle of ergodicity is an important part of the book. Ergodicity is a mathematical principle that describes a system’s symmetry with long term exposures, while a non-ergodic system has exposure to an exit barrier which given enough time or variability will prevent experiencing all possible states. The idea of time as a test for ergodicity is a useful heuristic, and can be extended to the Lindy Effect to derive an estimate of life-expectancy of some non-perishable idea or technology.

## Green Lumber

A anecdote that comes up in both these works involves the story of two traders active in an obscure commodity, green lumber, which I will embellish here in this telling. Green lumber is a term used to describe freshly cut lumber, whose futures are traded in the commodity markets. Trader A, let’s call her Alice, went to an ivy league school and wrote her thesis on the subject of forestry practices. Trader B, let’s call him Bob, went to a public school and doesn’t know the meaning of green lumber — he assumes it is wood that has been painted green. The irony of these two traders is that it is Bob who survives and makes a living trading the commodity over the long term, while Alice ends up going bankrupt. The reason for this outcome is that while Alice was surely knowledgeable about forestry and could talk at length about preservation practices, grades of lumber ratings, or what beetles are encroaching in which region, this ability to create narratives is not what drives the price of the commodity, there are different forces at play that are less tractable but more influential, forces that Bob was more in tune with. Alice knew the wrong tings. The lesson of this anecdote, which Taleb dubs the green lumber fallacy, is that it is easy to misattribute influence to that which we can describe or narrate, while there may be more fundamental forces at play that although more abstract are nonetheless more important. The Incerto’s core themes of probability and risk taking are the very kind of forces that can be easily overlooked by those succumbing to the green lumber fallacy. Every time we misattribute some outcome to that which is easy to narrate or measure, every time we make a decision based on a precise forecast of some variable as opposed to second order exposure from a variable’s range, every time we allow misaligned incentives to subvert our institutions, we lose sight of fundamental and universal forces at play. We’re paying attention to the wrong tings.

Books that were referenced here or otherwise inspired this post:

## Skin in the Game — Nassim Taleb

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Albums that were referenced here or otherwise inspired this post:

## Horowitz In Moscow — Vladimir Horowitz

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