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Why Taleb Is Wrong About Markets And Uncertainty

 November 26, 2012 01:12 PM

Once you cut through the layers of purple prose and elective neologism, Nassim Nicholas Taleb's central thesis is not hard to understand: people often know less than they think that they do, and some human affairs are arranged so that they are negatively, neutrally, or positively affected by surprising events. His prior work has focused on large, unlikely risks – cases where agents who think they are neutrally oriented or robust to surprises are actually fragile when the unexpected happens. Antifragile, his most recent effort, covers the last set of cases – arrangements that profit from volatility.

If you understand optionality, you already understand anti-fragility. And you probably also understand why Taleb's efforts to valorize anti-fragile institutions fall flat: given the infrequency of high-impact events, even the very low but frequent costs of betting on or insuring against them tend to outrun the costs of the events themselves. Here are some examples.

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Startup companies are anti-fragile when they move quickly to profit from unexpected customer feedback. "We all hate your current product, but we would love to see this other version of that product," is information that a nimble startup can profit from. Lumbering, legacy corporations might struggle to accommodate the same information, much less use it as a driver of profitability. Despite these virtues, most startups fail, and failure imposes real costs, even for founders who go on to find later success. Recent studies of the performance of venture capital funds are not encouraging on this front. 

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Insurance companies are the very essence of fragility: they collect policy premiums and hope that the world stays exactly as it is. A natural disaster, epidemic, or outbreak of mass hysteria could ruin an insurer. But in the real world, we see insurance companies surviving easily enough after disruptions. The premiums collected in quiet periods are typically more than enough to offset risks, and companies even use recent events to justify charging higher premiums to newly risk-averse customers. Historically, betting on the fragility of insurance companies – especially immediately after a natural disaster – has been a losing strategy.

A more literal case of anti-fragility is an investor who buys an option straddle, consisting of a put and a call on the same security with the same strike price and time to expiration. The more volatile the underlying asset is, the more profit accrues to the straddle buyer, and because the position consists of both puts and calls, the investor is indifferent to the direction of price movement. A breath-taking rally is just as advantageous as a market crash.* The risk to a straddle buyer is that the options will be worthless at expiration: if the underlying asset is priced at the strike price of the straddle at expiry, all of the premium paid for those options will be lost.

In spite of their epistemically virtuous behavior (as Taleb would have it), option buyers tend to lose more than they win: not just more often, but more money, too. VCs are long gamma, too, and have on average delivered sub-par returns in spite of the anti-fragility of the companies they fund. Somehow, short-gamma insurance companies survive.

This is the fact that should make sympathetic readers of Taleb pause: we have had at least two major global crises in recent years – the financial crisis in 2007-08 and the European banking crisis in 2011 – and yet the payoff to option buyers from those events has not even covered the carrying costs of the strategy in the last several years, much less the costs incurred from buying anti-fragility (option gamma) during the prior decade. It's not just that options are not underpriced in light of "black swan" risks: they're dramatically overpriced.

Fig. 1 – S&P 500 1-month historical and implied volatility (upper) and volatility risk premium (lower). Source: Yahoo!, Condor Options

The orange line in the upper panel of fig. 1 shows the one month strike-weighted implied volatility of S&P 500 index options (VIX); the blue line shows the one month trailing volatility using daily closing prices. The lower panel plots the lagged difference between them, between the actual market volatility over the past month and the forward-looking option volatility estimate from one month ago: this estimate of the volatility risk premium tells us how cheap or expensive options are relative to what actually occurs in the market.

The volatility risk premium is negative. Notice how the line in the lower panel spends almost all of its time below zero. The median value there is -0.049; if we let the spikes in 2008 and 2011 exert their full weight and use the mean, we still get a value of -0.044.

Fig. 2 – S&P 500 1-month cumulative volatility risk premium. Source: Yahoo!, Condor Options

Fig. 2 shows what it would look like to incur these costs regularly over time. The tail risk events barely make a dent. For the sake of rigor, we can make some analytical tweaks to try to narrow the implied/realized volatility gap – to make the situation easier for Taleb and harder for us.** But various combinations of these changes all yielded results that were only trivially different from the original – the risk premium in options was still large, and had the wrong sign.

Remember that a key part of his argument against contemporary economists and investment professionals was that market returns do not follow a Gaussian, normal distribution. Perhaps this actually was news to some people, somewhere. The critique of Modern Portfolio Theory and of the intellectual laziness of so many economists may all be entirely right, but those criticisms do not touch the empirical evidence from options markets. Options traders in general not only do not assume a normal distribution; they assume that market crashes are around every corner. And the volatility risk premium is not unique to developed markets or to equities, either: it is a persistent feature of every major asset class around the world. (I wrote a short survey of some of the literature on this topic.)

I take it that Taleb is not unaware of the data shown above. During an exchange on Twitter, he suggested to me that just because anti-fragility (gamma) in at the money options is overpriced does not mean that it is cumulatively a problem, and that he always sells at the money straddles. I'll suspend judgment and wait for the forthcoming paper he mentions, but this response was a surprise. Option gamma is greatest in at the money strikes, and options are the most overpriced at far out of the money strikes, so I would expect someone with Taleb's views to be a net buyer of at the money straddles and perhaps a seller of the tails.

The other question I have is about the significance of this empirical rebuttal. As a public figure, he has pushed for changes in things like government regulation of banking and in attitudes about which sorts of jobs are desirable for individuals. He endorsed Ron Paul in the 2012 election. But his views about big-picture topics really all depend, I think, on how his core thesis relates to financial markets. There is a story that circulates among Austrian economists, some old-school Marxists, and some others about how economics really took a bad turn in the 1940s and 50s when Paul Samuelson et al. led everyone down the path of formalization. Journal articles before this period are recognizably about what our economy should be like; contemporary economics journal articles have large middle sections that are entirely mathematical. This isn't the place to argue for or against academic economics, but one conclusion of arguments like Taleb's is that economists and regulators should stop trying to worry about precise measurements and start looking for helpful rules of thumb instead. We should stop trying to get a quantitative understanding of the world and do something else. (Dissolve the public ‘we' into a Paulist collection of risk-taking ‘I's? Buy gold? It isn't clear.) My point is that if Taleb has been getting the case against financial markets wrong, then even if Modern Portfolio Theory is unworkable and many economists are too self-satisfied, the best answer might not be eccentric, vague heuristics but rather more quantification.

My academic work is in philosophy, so I appreciate Taleb's engagement with philosophers, but I wish he would take the literature in contemporary epistemology as seriously as he does the texts of classical and literary figures. Sometimes a carefully constructed argument is better than a hundred anecdotes, and modern theories of knowledge and skepticism have long been running on wheels that Taleb seems to be reinventing from ancient wood.

There is one easy rejoinder to everything above, which is that the irreducibility of uncertainty means skeptics need never change their views. Frank Knight made a famous distinction between risk, which we can measure and manage, and uncertainty, which we can't. Think of the difference between a series of bets on a coin toss – which is risky, but has fixed and known parameters – and a series of bets about the favorite band of the next hundred people you meet – who could've known that girl #38 would like pre-Geffen Jawbreaker more than any other band in the world? Asset returns, the response goes, are irreducibly uncertain, so no matter how expensive options look now, and no matter how expensive they look in the future, it will always be the case that possibly, at the end of history, there will have been enough negative tail risks to justify the premiums paid. Who knows? Maybe the soi-disant bubble in Treasury bonds will burst tomorrow, too.

Appealing to irreducible uncertainty isn't an argument for or against any policy, it can never be proven wrong, and it wastes the time of everyone under its sway. You can reason from uncertainty to, apparently, a desire for smaller government, wilder markets, and maximal risk borne by every individual. Some people think that the reality of uncertainty is just as good an argument for a social safety net and well-run health and education systems, since reducing some of the big tail risks by pooling public resources frees entrepreneurs and innovators to get on with their real work. Either way, we'll never know which systems and regulations and methods work until we try them. In this respect, the Taleb who writes technical papers is more interesting and thoughtful than both his Hayekian fans and the blustery, performance artist persona of his popular books.

The other problem with this line of argument is that, much of the time, uncertainty actually is reducible.*** By finding out more about the world, we can expand the zone of cases that are merely risky and no longer uncertain, where we still have questions but where we also know what a good answer would look like. Quantifying things that used to be wooly and mysterious serves a valuable purpose. Medicine saves lives. Engineering gives us shelter. Science and philosophy bring information and clarity to our superstitious minds. Wagging the finger of uncertainty at everyone does not.


* Because option implied volatility tends to rise as stock prices fall, the payoff prior to option expiration is still asymmetric, but this is a feature of the natural long bias of most participants in stock markets; it does not hold in some commodities and other assets.

** Details on the tweaks: 1) We can use a Yang-Zhang estimate of historical volatility, which typically gives a higher reading than a close-close measure because it accounts for opening price jumps. 2) We can use a 10-day estimate of historical volatility: this means we're comparing implied apples to historical oranges, but again the ‘error' should be in Taleb's favor and it is an intuitive enough change, since traders feel realized volatility on shorter timeframes even if their options have longer horizons. 3) We can use VXO implied volatility data, which takes out the effects of out of the money implied volatility skew. Skew is a major part of the volatility risk premium, but an at the money straddle buyer would normally be paying something closer to the rates given by VXO rather than VIX.

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