Nassim Nicholas Taleb. Seven rules of antifragility (convexity) in research. 2012. 원문보기

I outline the rules. In parentheses are fancier words that link the idea to option theory.

1) Convexity is easier to attain than knowledge (in the technical jargon, the “long-gamma” property): As we saw in Figure 2, under some level of uncertainty, we benefit more from improving the payoff function than from knowledge about what exactly we are looking for. Convexity can be increased by lowering costs per unit of trial (to improve the downside).


Figure 2 The Antifragility Edge (Convexity Bias). A random simulation shows the difference between a) the process with convex trial and error (antifragile) b) a process of pure knowledge devoid of convex tinkering (knowledge based), c) the process of nonconvex trial and error; where errors are equal in harm and gains (pure chance). As we can see there are domains in which rational and convex tinkering dwarfs the effect of pure knowledge iv.

2) A “1/N” strategy is almost always best with convex strategies (the dispersion property): following point (1) and reducing the costs per attempt, compensate by multiplying the number of trials and allocating 1/N of the potential investment across N investments, and make N as large as possible. This allows us to minimize the probability of missing rather than maximize profits should one have a win, as the latter teleological strategy lowers the probability of a win. A large exposure to a single trial has lower expected return than a portfolio of small trials.

Further, research payoffs have “fat tails”, with results in the “tails” of the distribution dominating the properties; the bulk of the gains come from the rare event, “Black Swan”: 1 in 1000 trials can lead to 50% of the total contributions—similar to size of companies (50% of capitalization often comes from 1 in 1000 companies), bestsellers (think Harry Potter), or wealth. And critically we don’t know the winner ahead of time.


Figure 3-Fat Tails: Small Probability, High Impact Payoffs: The horizontal line can be the payoff over time, or cross-sectional over many simultaneous trials.

3) Serial optionality (the cliquet property). A rigid business plan gets one locked into a preset invariant policy, like a highway without exits —hence devoid of optionality. One needs the ability to change opportunistically and “reset” the option for a new option, by ratcheting up, and getting locked up in a higher state. To translate into practical terms, plans need to 1) stay flexible with frequent ways out, and, counter to intuition 2) be very short term, in order to properly capture the long term. Mathematically, five sequential one-year options are vastly more valuable than a single five-year option.

This explains why matters such as strategic planning have never born fruit in empirical reality: planning has a side effect to restrict optionality. It also explains why top-down centralized decisions tend to fail.

4) Nonnarrative Research (the optionality property). Technologists in California “harvesting Black Swans” tend to invest with agents rather than plans and narratives that look good on paper, and agents who know how to use the option by opportunistically switching and ratcheting up —typically people try six or seven technological ventures before getting to destination. Note the failure in “strategic planning” to compete with convexity.

5) Theory is born from (convex) practice more often than the reverse (the nonteleological property). Textbooks tend to show technology flowing from science, when it is more often the opposite case, dubbed the “lecturing birds on how to fly” effect v vi.In such developments as the industrial revolution (and more generally outside linear domains such as physics), there is very little historical evidence for the contribution of fundamental research compared to that of tinkering by hobbyists. vii Figure 2 shows, more technically how in a random process characterized by “skills” and “luck”, and some opacity, antifragility —the convexity bias— can be shown to severely outperform “skills”. And convexity is missed in histories of technologies, replaced with ex post narratives.

6) Premium for simplicity (the less-is-more property). It took at least five millennia between the invention of the wheel and the innovation of putting wheels under suitcases. It is sometimes the simplest technologies that are ignored. In practice there is no premium for complexification; in academia there is. Looking for rationalizations, narratives and theories invites for complexity. In an opaque operation to figure out ex ante what knowledge is required to navigate is impossible.

7) Better cataloguing of negative results (the via negativa property). Optionality works by negative information, reducing the space of what we do by knowledge of what does not work. For that we need to pay for negative results.

Some of the critics of these ideas —over the past two decades— have been countering that this proposal resembles buying “lottery tickets”. Lottery tickets are patently overpriced, reflecting the “long shot bias” by which agents, according to economists, overpay for long odds. This comparison, it turns out is fallacious, as the effect of the long shot bias is limited to artificial setups: lotteries are sterilized randomness, constructed and sold by humans, and have a known upper bound. This author calls such a problem the “ludic fallacy”. Research has explosive payoffs, with unknown upper bound —a “free option”, literally. And we have evidence (from the performance of banks) that in the real world, betting against long shots does not pay, which makes research a form of reverse-bankingviii .

iii Jensen, J.L.W.V., 1906, “Sur les fonctions convexes et les inégalités entre les valeurs moyennes.” Acta Mathematica 30.
iv Take F[x] = Max[x,0], where x is the outcome of trial and error and F is the payoff. ∫ F(x) p(x) dx ≥ F(∫ x p(x)) , by Jensen’s inequality. The difference between the two sides is the convexity bias, which increases with uncertainty.
v Taleb, N., and Douady, R., 2013, “Mathematical Definition and Mapping of (Anti)Fragility”,f.. Quantitative Finance
vi Mokyr, Joel, 2002, The Gifts of Athena: Historical Origins of the Knowledge Economy. Princeton, N.J.: Princeton University Press.
vii Kealey, T., 1996, The Economic Laws of Scientific Research. London: Macmillan.
viii Briys, E., Nock,R. ,& Magdalou, B., 2012, Convexity and Conflation Biases as Bregman Divergences: A note on Taleb’s Antifragile.

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