Nassim Nicholas Taleb: To Prevail in an Uncertain World, Get Convex

Investment professionals know the value of a convex bond – it gains more from falling rates than it loses from rising ones. According to Nassim Nicholas Taleb, people and institutions can and should position themselves to be convex. Indeed, they should be antifragile – ready to gain from disorder or uncertainty.

That is the theme of the provocative, sometimes playful and often infuriating book, Antifragile: Things That Gain From Disorder, by Taleb, a philosopher and businessman.

Say that a shock to the environment causes you to have an equal probability of moving left or right along the x-axis in Figure 1 below. Your well-being is on the y-axis. You stand to gain more from a move to the right than you stand to lose from an equal move to the left, so you’re better off with the shock than without it.

You’re convex.

You’re not just “not fragile” — that would be a straight line in the diagram. You’re antifragile.

Figure 1: Why it’s good to be convex

-	Figure 1: Why it’s good to be convex

Source: Taleb, Nassim. 2012. Antifragile: Things that Gain from Disorder. New York: Random House, p. 273.

Convexity refers to the shape of the curve in Figure 1. A convex curve bends away from the origin, the point where the x and y axes cross. A curve that bends the other way is concave. Things that are convex benefit from uncertainty, while things that are concave are hurt by it. The book argues that in a world in which predictions are mostly useless, we want to be convex.

Instead of using the term “convexity” throughout, Taleb renamed this principle antifragility. He didn’t think convexity would resonate with most readers, who are not investment professionals. Moreover, antifragility is not just robustness. Antifragility is as distant from robustness as robustness is from fragility. Unlike a robust person or system, an antifragile one is actually made better off by stress or disorder.

The rest of Taleb’s weighty book is an elaboration of this neat idea, filled in with characters familiar from the author’s previous works: Fat Tony, an unlettered but wise securities trader; Nero Tulip, a ringer for Taleb himself; and the very real Robert Merton. Taleb regards Merton, who developed an option pricing formula, as the worst of a large crowd of Nobel-decorated charlatans. Taleb calls these people “fragilistas” and argues that their theories and actions have weakened financial institutions. In Taleb’s view, Merton’s option pricing formula, developed with Fischer Black and Myron Scholes, was unoriginal and used “fictional mathematics”. Taleb also criticizes Merton for his role in the 1998 Long-Term Capital Management fiasco.1 The writing of Antifragile seems to have been motivated by Taleb’s anger at the fragilistas, He blames them for creating the conditions that led up to the crash of 2008, in which institutions and firms that were thought to be strong were stress-tested by events and found to be hollow.

Antifragile is the third book in Taleb’s “Incerto” (Italian for uncertain) trilogy. The first two books in the trilogy, Fooled by Randomness and The Black Swan, have made Taleb the “hottest thinker in the world,” according to the London Times. Fooled by Randomness is Taleb’s best book, followed by The Black Swan. The current volume is too long and disjointed to join his earlier ones on my top shelf. But if you can tolerate the pretension of a writer who gives Italian names to collections of his English-language books, Antifragile is a worthy read. It is a valuable extension of Taleb’s earlier work on the themes of randomness and unpredictability.

1. Taleb attributes the option pricing formula to “Louis Bachelier, Ed Thorp, and others” ( The Black Swan, p. 282). I don’t know Thorp’s work very well, but Bachelier’s formula certainly anticipated major aspects of Black-Scholes-Merton, without being identical to it.