This post has been gathering dust on my hard-drive for a few weeks. I struggled with whether to post it, since I didn't feel there was any driving conclusion. Taleb's Antifragile is more about exploring a general pattern across categories and cultures than it is about finance. Many of the ideas are applicable to economic theory, but not necessarily portfolio theory.
In his new book Antifragile, Nassim Nicholas Taleb defines a whole classification of objects that exceed robust: they are "antifragile" and actually benefit from volatility (at least, to a certain degree). A teacup is fragile; a brick is robust; the human body, which benefits from stressors and variations in environment, diet, and physical activity (to a certain degree) is antifragile.
What we find, however, is that the majority of the book talks about the benefits of convexity, optionality, and randomness for the "whole" and not the individual. While the convex tinkering of Mother Nature in evolution can lead to mutations that are a long-term benefit for the species, they can also lead to short-term losses for the individual. The benefit for the species comes in convexity: there is no real "harm" if a single individual dies prematurely from a mutation so long as the long-term benefit from random mutations allows the species to prosper.
Taleb also cites the field of medicine, which he claims has suffered since it turned from an empirical to a theoretical field. Taleb argues that the majority of breakthroughs do not first come from theory, but rather theory followed evidence. Relying too heavily on theory leads to Taleb's Procrustean bed. Procrustes was a greek bandit from Attica who would either stretch a person or cut off their limbs so that they would fit the size of an iron bed. By defining theory first, we will manipulate our data so that it fits.
It turns out, the snake-oil salesmen, witch-doctors and alchemists may have done more for medicine in their evidence-driven trial-and-error process than modern day theorists. Unfortunately, if stochastic empiricism is the answer, we end up in the same place as evolution: what is good for the field is not great for the individual. That's convexity at play though: the life and health of a single individual (or, perhaps, several), is likely worth less than the benefits to the health of the species of a major breakthrough.
Start-ups are another great example. The small capital outlay required to start a business allows "the economy" (if we personify it) to quickly and rapidly prototype new ideas, letting unsuccessful ones fail and successful ones prosper in a non-linear fashion, therefore justifying the risk of the venture. Again, however, the benefit is to the many and not the individual: the majority of startups fail. Nevertheless, the antifragile nature of startups helps make the economy robust. Taleb would likely smile at Facebook's internal model for engineers: "move fast and break things."
Convexity is the magic that allows something to fail more than 50% of the time and still come out ahead. By all measures, I'd say Taleb would rather be convex than smart -- or ever right.
The question, of course, is "how can we apply this to portfolio management?" I will guess Taleb's suggestions: toss theory and embrace convexity. Taleb says he prefers to rough and fractal nature of empirical evidence to the forced and arbitrary "smoothness" of theory. Theory not only drives us away from antifragile practices, it often takes robustness into the territory of fragility. The danger is academic research without feedback from practice. Since theory is rarely tested by low-probability events, by definition, risks can lurk without our knowledge. Consider the theory and model driven buildings in lower Manhattan, designed to withstand multiple-sigma flood events, and yet were at risk during Hurricane Sandy. Compare them to the significantly older, but empirically driven (and therefore robust) Trinity Church which was simply built atop a hill. Simple heuristics trump complicated models in uncertain environments.
As quantitative modelers, we must fully understand the role non-linearity plays in model errors. Having the right model, but being uncertain about the parameters, is just as bad as having the wrong model, but knowing the parameters perfectly.
So how can we embrace convexity in our portfolios? Taleb would argue that we should take a "barbel" strategy, putting the majority of our wealth in "safe" assets, and a small sliver into antifragile investments, embracing volatility. Traditionally, portfolios are made up of cash + beta + alpha. Taleb proposes cash + convexity. This is the same strategy he has proposed for several years, and it is easier said than done. Again, while convexity is often beneficial for the whole, it is likely damaging for the individual. Should we invest in a handful of startups? A handful of biotechnology firms? The odds are squarely stacked against our success and we'll likely go broke far sooner than we'll get a payoff from a rare event. We may consider buying energy companies with "secure" oil-fields as a play on geopolitical "volatility." We may even construct a portfolio out of many of these convex strategies.
The danger is that the volatility never appears. Consider selling packaged volatility via an at-the-money straddle, a strategy outline in a previous post. While a single-day 1987-esque event would lead to a large return, we may run out of capital long before that event happens. After all, the rare event may be that no rare event happens. What's worse is that we cannot say anything about low-probability events with certainty because we have little to no evidence about them; they are, by definition, rare occurrences. Therefore, any discussion of a data-driven statistical estimate from a fat-tailed distribution is no better than "mere journalistic reporting." Scientific claims should only be made off the true value, not a statistical estimate of it. Designing this portfolio, then, becomes just as much art as science.
For those using the market as a means to grow capital for retirement, this style of investment strategy may not pay off. Removing beta from the cash + beta + alpha equation can leave a portfolio dramatically lagging if the alpha opportunity never materializes. It relies on managing position costs between rare events, as well as presuming that we will have the right position to adequately ride the convex wave of a rare event. Both of these represent big "ifs".
What we can take from Antifragile is the power of convexity, and this may make us take pause and explore how we try to add alpha to our portfolios. Since few funds offer pure alpha solutions, it may make the most sense to look at our beta+ (alpha seeking strategies with significant beta exposure; e.g. most long-only managers) strategies as a beta component and either a betting style that is convex or concave. For example, a momentum strategies are traditionally long volatility; mean-reversion strategies are traditionally short it. Then, by combining multiple beta+ strategies whose alpha components are convex different types of volatility (economic, interest rate, inflation, geopolitical, et cetera), we can have a portfolio whose alpha bets are antifragile.