Why Taleb is Wrong About Markets and Uncertainty

Mon, Nov 26, 2012 | Jared Woodard

Options Myths, Volatility

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.

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. 

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.

*** Thanks to @isomorphisms for discussion on this point.

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13 Comments For This Post

  1. dsquared Says:

    With respect to the global reinsurance industry, one could definitely argue that the phenomenon you identify (the premium cycle, making it the ultimate losing bet to short insurers after a natural disaster) is an excellent example of antifragility!

  2. Jared Woodard Says:

    Good point.

  3. Michael S Says:

    Always enjoy your long form missives Jared. Great stuff. michael

  4. RolandD Says:

    Great, thoughtful article, thank you.

  5. John Clarkson Says:

    Love it. I don’t understand all of what you have written, but I am certainly enjoying the debate. You make some telling points about Taleb’s purplish “pop” writing and his “performance artist persona”. I’m anxiously awaiting my copy of Anti-fragility, and will attack it with a much more critical spirit–thanks to you!!

  6. isomorphismes Says:

    Here is my understanding of robustness, adaptability, fragility, and anti-fragility in analogy to materials.

    • robust — cast iron
    • fragile — glass
    • adaptable — silly putty, water
    • anti-fragile — some kind of weird modern material that’s pliant to gentle bending, but toughens when kicked hard

    Of course if we could design a financial system that automatically lubed the pipes when times were tough, and toughened lending standards during good times, that would be great. However this is not a new point. A central bank that follows the Taylor rule will act countercyclically.

  7. isomorphismes Says:

    To rephrase what I just wrote: if we can get countercyclical adaptability “for free”, then of course we should take it. My example of a modern material is perhaps misleading though, because putting roller balls on the bottom of an earthquake-prone building, punting on gamma, spending research dollars on adaptable materials, and all other examples of anti-fragile betting I can think of come at a cost.

  8. isomorphismes Says:

    **And now I read http://online.wsj.com/article/SB10001424127887324735104578120953311383448.html I learn that NNT abhors the Taylor rule. Clearly I don’t understand what he’s talking about.

    Favor businesses that benefit from their own mistakes, not those whose mistakes percolate into the system.

    I can’t think of any examples, but he goes on to mean s/businesses/industries/ who do not lose from their competitors’ mistakes.

    A firm with highly leveraged debt has no room for error

    Sounds like robustness vs fragility. Margin requirements and capital ratios reduce fragility, they don’t cause a profit during catastrophe (that would be hedging—which costs).

    Great size in itself, when it exceeds a certain threshold, produces fragility and can eradicate all the gains from economies of scale.

    Again, where is the antifragility? Maybe smallish firms are more adaptable and agile and this is beneficial in certain industries. But surely I want a share of Cargill with its stranglehold over salt mines supplying the United States’ cities every year with rock salt, and “adaptability to changing market conditions” is of no benefit in this market. Just keep owning the same land with the mine on it, run the same delivery process, and wait until the next North American snow.

    To see how large things can be fragile, consider the difference between an elephant and a mouse: The former breaks a leg at the slightest fall, while the latter is unharmed by a drop several multiples of its height.

    Large animals’ lives are dominated by gravitationsl forces (∝x³) whilst small animals’ lives are dominated by surface forces (∝x²). Wash an elephant with as much water as you want. Mice by contrast are “fragile” to surface forces.

    This explains why we have so many more mice than elephants.

    Trial and error beats academic knowledge.

    Seems to have nothing to do with fragility or otherwise, but something he likes to repeat. Personally I think both facts and reasoning are important, and that diversion of academic effort into trivia is unrelated to that dichotomy and to the present topic.

    Decision makers must have skin in the game.

    Also unrelated to antifragility. Just another point NNT and everybody with a brain agree on. Or wouldn’t the skin in the game make all the decision-makers inefficiently risk-averse and all pile onto the same sure things, therefore a more fragile system? Now we’re just back to regular life where it’s not obvious how to improve everything under the sun by following this simple plan.

    Either I don’t understand what this concept is, or NNT is amalgamating.

  9. alex c Says:

    Does anyone have recent data on the performance of NNT’s fund?

  10. Opening2Minutes Says:

    I just simply wanted to commend you on the article.

  11. Kevin Says:

    Jared,

    Medicine does save lives, but it took thousands of years to get to that point. Still, we got there. Taleb is not saying that we can’t make improvements on understanding risk in the system, and improve VAR and understand risk better.

    But there will always be the chance of a new disease coming in that we are completely unprepared for, despite all the medical knowledge in the world.

    We will never conquer risk, finance is not physics.

  12. Algernon Parsimony Says:

    Great article. It is not just in option/futures pricing that NNT gets it continuously, and actually hilariously wrong. Most pages in the book contain some glaringly “fanciful” interpretation of fact or wildly imaginative (I am trying to be nice here) extrapolation. Always without basis or backup. His refusal to defend his positions is as convenient as it is transparent. I am going to just hit a couple of the sillier statements.


    “The simpler, the better. Complications lead to multiplicative chains of unanticipated effects. Because of opacity, an intervention leads to unforeseen consequences, followed by apologies about the “unforeseen” aspect of the consequences…”

    Non-intervention leads to unforeseen consequences as frequently as does intervention. In fact, his whole argument is that one cannot determine outcome when processes are left to their own devices…by very definition, unforeseen consequences. And apologies are often made for non-intervention. I would venture more frequently than the reverse. Ask Neville Chamberlain about this. Ask Clinton.

    “…the centralized nation-state is on the far left of the Triad, squarely in the fragile category, and a decentralized system of city-states on the far right, in the antifragile one. By getting the characteristics of the latter, we can move away from the undesirable fragility of the large state.”

    I am not sure if he does not know history or assumes his readers do not. For his sake I hope he is taking us for suckers, and does not believe this drivel. The very existence of the nation state is testament to the long term fragility of the city state. City states aggregated precisely because the stressors of near continuous small shocks proved insurmountable existential threats. The anti-fragile larger states gradually eroded their ability to maintain any societal goods, freedom, commerce and safety, proving how very fragile a nation state was in an emergent nation-state world.

    Later NNT points to large nation-state wars as indications of fragility, but the very fact that devastation on global scale could take place without the loss of even a single large state (though Austria-Hungary broke up and Turkey lost their fading empire) is proof of nation-state robustness…and he has no proof to say otherwise.

    “Or take the health category. Adding is on the left, removing to the right. Removing medication, or some other unnatural stressor— say, gluten, fructose, tranquilizers, nail polish, or some such substance— by trial and error is more robust than adding medication, with unknown side effects…”

    Unless you have AIDS or Cancer, Crohn’s disease or Leukemia, Pneumonia or Anthrax, Polio or Malaria. In that case the numbers very much favor addition of medicines…and devil take the hindmost side-effect. NNT’s continuous assumption that only he can perform a CBA (cost-benefit-analysis) would be galling if his constant puffery did not render it a bit sad.

    “Almost all people answer that the opposite of “fragile” is “robust,” “resilient,” “solid,” or something of the sort. But the resilient, robust (and company) are items that neither break nor improve, so you would not need to write anything on them— have you ever seen a package with “robust” in thick green letters stamped on it?”

    Again, NNT invents a narrative then BUSTS IT WIDE OPEN, even though the narrative is only in his head. Not true. Robust and resilient are terms that often accompany phrases like “thrives on adversity” and “came back stronger than ever” and “likes a challenge” and about a thousand prosaic sportscaster reliables. Perhaps the ultimate example of how imbued society is with this REVOLUTIONARY anti-fragile concept is simple “no pain, no gain”.

    “A fellow who looked like a banker had a uniformed porter carry his luggage (I can instantly tell if someone is a certain type of banker with minimal cues as I have physical allergies to them, even affecting my breathing). About fifteen minutes later I saw the banker lifting free weights at the gym, trying to replicate natural exercises using kettlebells as if he were swinging a suitcase. Domain dependence is pervasive.”

    Or perhaps the fellow was wearing an expensive suit, or was in a hurry, or believed that porters have to pay rent like everyone else, or believed that it benefited him in the eyes of co-workers, clients, friends, or…dare I say it…the fairer sex, to act the part of a patrician on entry. Almost every example in the book is dependent on the reader buying, without reservation, NNT’s interpretation of facts, attitudes, and interactions. Heck of a way to run a philosophical railroad.

    Okay, one more…though I could do this all night.


    “The dulling of the pilot’s attention and skills from too little challenge is indeed causing deaths from flying accidents.”

    This is one of those blatant selective stories NNT indulges himself in. If auto-pilots are making things less safe, for which I challenge him to provide evidence, can the same thing be said for improvements in areas like
    - Lightning strikes
    - Ice and snow management
    - Engine failure recovery
    - Reduced structural failure of the aircraft
    - Stalling management
    - Fire management
    - Bird strike
    - Ground damage (crews)
    - Volcanic ash damage (filters)
    - Controlled flight into terrain practice
    - Electromagnetic interference
    - Runway safety improvements
    - Controlling criminal acts and military action
    - Cessation of attacks by a hostile country
    - Improved airport design
    - etc. etc. etc.

    Each of these items made it easier on the pilot…have they reduced pilot effectiveness? Of course not. His argument is, once again, not just wrong headed, but silly and transparently unsupportable.

    And I am still in chapter 2!

    Maybe more later.

  13. haig Says:

    I like Taleb, I think his rhetoric is extreme, but I can forgive that since his concerns are genuine and passionate. I don’t agree with everything he says, and I agree with this article that Taleb’s extreme skeptical empiricism discounts our ability to increase our knowledge and improve our theoretical formalizations, however, there really is an irreducible uncertainty to complex systems that we can never work around. I won’t go into the details, but from a complex-adaptive systems perspective, we will never have complete knowledge of the probability space of possible events when dealing with complex systems, and when dealing with asymmetric risks that blow us up, Taleb’s heuristics are the most sane way to approach things. Ironically, if Taleb’s ideas are put into place in our financial systems, his method of trading options would never be profitable, but the benefit to society would be immense.

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Jared Woodard specializes in trading volatility as an asset class. With over a decade of experience trading options and other volatility products ... Read More

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