Speculators Foresee No Catastrophe

In the latest American Economic Journal, Pindyck and Wang work out what financial prices and their fluctuations suggest about what speculators believe to be the chances of big economic catastrophes. Bottom line: [simple models that estimate the beliefs of] speculators see very low chances of really big disasters. (Quotes below.)

For example, they find that over fifty years speculators see a 57% chance of a sudden shock destroying at least 15% of capital. If I apply their estimated formula to questions they didn’t ask in the paper, I find that over two centuries, speculators see only a 1.6 in a hundred thousand chance of a shock that destroys over half of capital. And a shock destroying 80% or more of capital has only a one in a hundred trillion chance. Of course these would all be lamentable, and very newsworthy. But hardly existential risks.

The authors do note that others have estimated a thicker tail of bad events:

We obtain … a value for the [power] α of 23.17. … Barro and Jin (2009) … estimated α [emprically] for their sample of contractions. In our notation, their estimates of α were 6.27 for consumption contractions and 6.86 for GDP.

If I plug in the worst of these, I find that over two centuries there’s an 85% chance of a 50% shock, a 0.6% chance of an 80% shock, and one in a million chance of a shock that destroys 95% or more of capital. Much worse chances, but still nothing like an existential risk.

Of course speculative markets wouldn’t price in the risk of extinction, since all assets and investors are destroyed in those events. But how likely could extinction really be if there’s almost no chance of an event that destroys 95% of capital?

Added 11a: They use a power law to fit price changes, and so would miss ways in which very big disasters have a different distribution than small disasters. But to the extent that this does accurately model speculator beliefs, if you disagree you should expect to profit by buying options that pay off mainly in the case of huge disasters. So why aren’t you buying?

Those promised quotes:

An emerging literature has used historical data to estimate the likelihood and expected impact of catastrophic events. … We take a different approach from earlier studies and ask what event arrival rate and impact distribution are implied by the behavior of basic economic and financial variables. We do not try to estimate the characteristics of catastrophic events from historical data on drops in consumption or GDP, nor do we use the estimates of others. Instead, we develop an equilibrium model of the economy that incorporates catastrophic shocks to the capital stock, and that links the first four moments of equity returns, along with economic variables such as consumption, investment, interest rates, and Tobin’s q, to parameters describing the characteristics of shocks as well as behavioral parameters such as the coefficient of relative risk aversion and elasticity of inter-temporal substitution. We can then determine the characteristics of catastrophes as a calibration output of our analysis. …

We assume that discrete downward jumps to the capital stock (“shocks”) occur as Poisson arrivals with a mean arrival rate λ. …We therefore use data for the US economy from 1947 to 2008 to construct average values of the output-capital ratio, the consumption-investment ratio, the real risk-free rate, and the expected real growth rate. …

We obtain a mean arrival rate [of shocks] λ of 0.734 for the jump process and a value for the distributional parameter α of 23.17. These numbers imply that a shock occurs about every 1.4 years on average, with a mean loss … of only about 4 percent. …. [The] probability of one or more shocks with loss larger than L occurring over time span T is … 1 − exp [ −λT(1 − L )α] . For example, if we consider as catastrophic a shock for which the loss is 15 percent or greater, the annual likelihood of such an event is … 0.017. … The probability that at least one catastrophe (with a loss of 15 percent or greater) will occur over the next 50 years is … 0.57. …

Barro and Jin (2009) … estimated α [emprically] for their sample of contractions. In our notation, their estimates of α were 6.27 for consumption contractions and 6.86 for GDP. (more; ungated)

GD Star Rating
Tagged as: ,
Trackback URL:
  • Why expect there to be no jumps in the true risks? It seems strange to me that you seem to expect that an event that destroys 95% of capital could be estimated based on things like equity returns which are themselves based on things like ‘property rights’ that could well be destroyed along with that 95% of capital. (Given how complex modern finance is, and based on fragile computer records, is it even possible for full records of financial holdings to be accessed after such an extreme event?)

    Perhaps past X% destruction of capital, contracts in general no longer pay out and that constitutes the filter on speculators’ estimates. Consider Nazi German & Imperial Japan: both suffered terrible catastrophe on the scale of 1 in centuries, but far from *complete* destruction of capital (both were manufacturing various things up until surrender, for example, so we know there must have been a fair amount of capital still there); but how many contracts formed under Nazi Germany were carried forward and executed post-war? Are Nazi stocks and bonds worth anything right now? Could one meaningfully interpret Nazi Germany stock prices pre-1939 to estimate the risk of the thousand-year reich being more like 10 years, especially given that investors were aware of how regime changes can wipe out financial holdings as had recently happened post-WWI in Germany with hyperinflation and most dramatically during WWI in Russia with the expropriation of almost everyone?

    • The numbers are estimating capital destroyed from the point of view of the investors no longer getting access to their returns. If capital can be stolen from investors overall but not destroyed then these numbers over-estimate the chances of destruction.

      • Investors can also simply die, resulting in an underestimate.

      • This data is not tracking individual investors to see what happened to them. It is tracking the changing prices of overall categories of investment. So it implicitly ignores the possibility that investors get lower returns because they die.

      • I don’t follow. If there is risk to investors of dying, then that will show up in their willingness to make long-term investments and their discount rates. ‘Overall categories’ are, in the final analysis, made up of individual investors.

      • The risk of disaster only depends on two parameters in the model, and the discount rate isn’t one of them.

      • Nick Beckstead

        Doesn’t that seem like a big problem?

        If there is an risk of doom of a certain size per year, that should show up in the discount rate. If it was 1 in a million per year, we couldn’t really tell. But then the article concludes that the risk of doom is less than 1 in a million per year.

        Also, 1 in a million over the next two centuries seems really implausibly low, sufficiently that it makes me highly skeptical overall. I would like to understand this better though.

      • I think they did their modeling fine. But of course they are fitting a power law to expectations that are mostly about small disasters. So the projection of that power law to big disasters is probably of course be less accurate. But at least it gives us ball park figures to work with.

  • David Milovich

    Say that “badness levels” A, B, and C respectively destroy 50, 95, and 100 minus epsilon percent of capital. The area under the probability density function for badness interval [A,B] could be much smaller than the area under the PDF for badness interval [C,infinity).

    The authors’ model can only infer that the latter area is smaller by restricting to a certain low-dimensional class of possible PDFs, a restriction is based on little more than mathematical convenience. I find it more plausible that in the interval [C,infinity) the PDF will have a very different form than in [A,B] because I expect that in [A,B], what will matter most is how people (individually and collectively) react to negative shocks (e.g., Ferdinand’s 1914 assassination didn’t have to lead to WWI, and the Cuban missile crisis could have lead to WWIII); I expect that in [C,infinity), human reactions will matter little.

  • Alyssa Vance


    In physics, when theory doesn’t match reality, it proves the theory is wrong.

    In economics, when theory doesn’t match reality, it “proves” reality is wrong.

    • I have no idea what you are talking about.

      • Alyssa Vance

        This paper starts off with a pages-long list of assumptions, none of which are in any way justified, and uses this to “prove” a preposterous conclusion (one in a hundred trillion?!). Any scientist would immediately conclude one or more or the assumptions were wrong (argument by reductio ad absurdum). When, as here, a model gives output that’s physically nonsensical, you throw the model out. It is the height of chutzpah to claim that the model is fine, and instead reality must be thrown out.

        Saying your theory assigns a 1 in 10^14 chance to something which *already* happened on a modestly smaller scale (eg. fall of Rome), and that we therefore shouldn’t worry about it, is only slightly less silly than “proving” 2 + 2 = Cornflakes and then holding a press conference announcing the end of world hunger.

      • Do you know what fraction of investment capital in the Roman Empire was destroyed at a discrete “fall of Rome” event? You do know that every theory paper in physics also includes a list of assumptions, right?

      • If you object to the fall of Rome, then how about another much better characterized threat than societal collapse: asteroid impact. We have well-characterized distributions of impacts, a long data series to choose from, estimating economic damage is little harder than estimating effects of nuclear war, and so on. At even a quick eyeball, is the risk of asteroid impact consistent with the claimed estimates?

      • Nick Beckstead

        I agree with your general point but would put in a couple of caveats. I think comets would serve your point more simply/clearly than asteroids.

        My understanding is that most asteroids that would cause this type of damage have been tracked, we’d know about them more than a decade in advanced, and we’d divert them (though I don’t think it’s reasonable to have the level of confidence in all this to bring your p(megadisaster) down to 10^-14). For more info, see http://www.givewell.org/shallow/asteroid-detection.

        However, I think the threat from comets is about 1% the size of the asteroid threat and many of those haven’t been tracked and may be untrackable.

  • arch1

    Can anyone help me understand the meaning of a statement such as “over fifty years speculators see a 57% chance of a sudden shock destroying at least 15% of capital”?

    I can’t access the article so I’m wildly guessing that much of the statement’s meaning, to the extent that it even *has* a well defined meaning, is built into a particular set of authors’ assumptions about investors and about the world.

    But when I in my ignorance try to imagine a set of assumptions which could simultaneously be a) true, b) a sound basis for statements such as the above, c) even roughly consistent with a commonsense English interpretation, I come up empty.

  • efalken

    That’s weird. Barro (2005) finds a disaster probability of 1.5-2% per year with a distribution of declines in per capita GDP ranging between 15% and 64% is consistent with the observed 3.5% equity risk premium. That’s a couple orders of magnitude greater than 1.6 in 100k.

    • I was going to mention your own theory of asset prices & risk before I saw your name pop up here. I’m surprised you didn’t bring it up. My recollection is that you think people are concerned with relative wealth. And if a “common shock” damages most portfolios, you won’t look that bad relatively speaking, so that risk will not be incorporated into the price. A catastrophic shock sounds like the sort of thing your theory would predict is ignored by asset prices.

      • It would certainly be interesting to see the analysis redone with an added parameter to represent a focus on relative returns.

  • math freak

    If the author’s goal is to expose readers to an interesting model that demonstrates how smart they are they have succeeded … lots of good quality work in the paper.

    If the goal was to meaningfully quantify the economic risks they describe, then they are deluding themselves … neither they, nor anybody else can do this in any defensible way either.

    When dealing with these long range estimates over a long period of time, it usually always comes down to this metaphor: based on what we know now, at this instant, here is what we predict … which completely ignores what we don’t know which is the direction that the true threat is likely to come from …

    with all of these studies, a more honest answer might be based on what we know here is what we predict, we don’t know much, so our prediction is not worth much at all …

    prediction all comes down to information, regardless of how enthusiastic the prediction market folks are, there is no clairvoyance or any of that … there is simply info aggregation …

    the market participants have limited information on the major risks they are supposedly assessing …a group of folks trading equities is supposed to reveal the liklihood of a virus, a nuclear attack global warming, and the other risks in the appendix, through some form of risk premium … come on man, this is nonsense, its sophisticated nonsense, but its nonsense all the same

    it is as simple as that. apart from some basic high level guesses, we collectively (these markets) don’t know very much at all, so using a markets pattern to inform ones views through a fancy model still doesn’t escape the issue that the markets only reveal known information now … markets reflect known information now … and that’s it … hasn’t got as much to do with prediction and the future as most think it has… its a reflection of current information now, nothing more, and if current information is sparse, or not closely linked to the event being predicted, the prediction is weak, markets don’t magically pull information from thin air, all they do is aggregate it … pure and simple.

    in some instances there is good quality information, and markets are viable, in other instances there is no information, and they are useless. that is the case with this, anybody looking at market equity structures to guage the threat of nuclear/virus/global warming/exestential risk is full of shit…

  • VV

    Seriously, speculators aren’t unable to predict a financial crisis three months in advance, and you lend any credibility to questionable 100 years extrapolation of their predictions?

    I know you are professionally invested in the efficient market hypothesis, but this preposterous.

    • VV

      aren’t unable -> are unable

  • In addition to the other points being made below about the ability to retain property rights in circumstances where 85% of value has been destroyed one also must factor in the individual incentives of employees at investment companies and individual investors.

    As we saw in the mortgage crisis the incentives to the employee at a financial institution can diverge significantly from the incentives to the employee. Even assuming an even that cost the country 50% of capital value left investment institutions intact employees at such institutions may rationally expect to lose their jobs in such a situation and that probability is likely unrelated to whether prior decisions properly accounted for such an extreme event.

    More generally, any event that causes such a devastating loss of capital likely involves a massive loss of life as well. If you are dead you don’t care about your portfolio so the rational investor will discount the effects on their portfolio by the chance that they are dead.

    • This model OVER-estimates the chances of disaster if investors lose because of theft of property, rather than its destruction, or if some property loses value because other property increases in value, such as with big tech innovations. The paper has other parameters that account for time discounting, such as might be changed by a big risk of death. So death risks don’t matter for these estimates.

      • Jess Riedel

        I’m honestly confused about how to reconcile this

        > if you disagree you should expect to profit by buying options that pay off mainly in the case of huge disasters. So why aren’t you buying?

        and this

        > This model OVER-estimates the chances of disaster if investors lose because of theft of property, rather than its destruction

        If it’s generally thought that there will be no protected property right in the scenario that 80% of value is destroyed, then no one will buy options that pay off mainly in the case of huge disasters. Won’t then the probability of such a disaster inferred from the market be much lower than the actual probability? (Sorry for such a basic question.)

  • Nick Beckstead

    I’d like to hear what you think about this story. For hard-to-quantify catastrophic risks below a certain size x per 50 years, it isn’t rational for speculators to try to incorporate views about those risks in their thinking. Because of this, markets aren’t sensitive to hard-to-quantify catastrophic risks of size f(x) per 50 years. (Let’s say f(x) is smaller than x because the market is incorporating more info.) f(x) is larger than 10^-14 or 10^-6, and is maybe more like 10^-2. But in any case, this kind of study couldn’t show that the probability of hard-to-quantify catastrophic risks per 50 is less than f(x). (Please don’t jump on my guesses about f(x); I’m more interested in thoughts on the form of the argument.)

    • Yes of course this model is mostly driven by speculators’ expectations for small disasters. So if the distribution of big disasters is fundamentally different from that of small disasters, this model will miss that. But this model is a power law, many kinds of disasters are reasonably fit by power laws, and we often use the power that fits small disasters to estimate the chances of big disasters.

      • But this begs the question raised by proponents of “existential risk.” (That’s the issue, isn’t it?) Their claims are tantamount to denying the power-law’s applicability. The point is trivial (isn’t it?) that extrapolating based on a power law to small disasters (or expectations regarding them) will give you a miniscule probability for hyper-disasters.

        Most people think there was a significant probability of nuclear war during the Cuban missile crisis. The power law doesn’t seem to apply to eliminate this possibility. Why?

        You’ve discussed this: power laws don’t apply within classes of explosions. Explosions are rare, but not so rare as the power laws would suggest.

        During the height of the cold war, mutually assured destruction created nuclear peace. No one seriously contemplated a limited nuclear war. The onset of nuclear war was (probably) explosive. At least that was the assumption. (Otherwise, it would be too tempting for Washington to obliterate Moscow or St. Petersburg and say oops!)

        To discount (explosive) existential risk, you can’t legitimately assume a power law applies.

  • Peter McCluskey

    “over two centuries, speculators see only a 1.6 in a hundred thousand chance of a shock that destroys over half of capital. And a shock destroying 80% or more of capital has only a one in a hundred trillion chance” … “So why aren’t you buying?”

    I don’t buy because the prices I see bear no resemblance to that. I just looked at puts on the S&P 500 expiring in December 2015. It would cost me $0.65 to get an option that would pay $124 if the S&P 500 dropped 90% in that time (a strike price of 300).

    Eric Falkenstein’s work suggests that there might be some speculator behavior that that is consistent with the crazy numbers you mention, but if it isn’t being arbitraged to lower S&P 500 put prices, why should I believe I can exploit it?

    • The model includes strong risk aversion, so it isn’t clear to me that the prices you quote are inconsistent with the model.

      • IMASBA

        Indeed, people shouldn’t just assume directly proportional and linear risk aversion. Partly because in human psychology loss hurts more than profit excites and because there is no stock market safety net (you’re screwed if you lose your fortune, the fact that your investment strategy had positive expected return, and still does, on average, and that the average of the stock market is still going up doesn’t help the individual who lost his fortune).

      • Doug

        I can’t access the paper, but listed put option prices indicate *way* higher risk-neutral probabilities than what’s presented in the paper. Several orders of magnitude at least.

        Risk aversion can explain maybe a 100-200% premium, but a 10,000% premium risk aversion premium is just ridiculous.

        I can’t access the paper, but it seems more likely that the extreme numbers are from a mis-specified model rather than market participants putting such ridiculously low P-values on large capital wipeouts.

  • Robert Koslover

    Forgive me if this was mentioned somewhere and I missed it, but in regard to “if you disagree you should expect to profit by buying options that pay off mainly in the case of huge disasters” can you give an example of such an investment, especially if it would be both practical and available to a person of ordinary means?

    • crocodilechuck

      Buy out of the money put options on stocks. This is Nicholas Nassim Taleb’s Empirica hedge fund’s strategy (and, indeed, how Taleb made his ‘F _ _k you’ money in the crash of October, 1987.


      • IMASBA

        That’s a parasitic strategy that only works as long as no more than a few people use it. Then again, if you’re living off of the stock market you’ve already decided that working for a living isn’t for you…

      • Ronfar

        You still have counterparty risk. If the entity you buy the options from isn’t around to honor them after catastrophe strikes, you don’t make money.

      • Doug

        Taleb is a charlatan and an idiot, who isn’t respected by anyone serious in finance.

        Buying out of the money put options is historically a terrible investment strategy. Options are systematically overpriced because there’s a lot more natural buyers of insurance than sellers. You’ll get big intermittent gains, but those will be more than offset by the rise in option premium following the crash. (Like how re-insurance premiums rise following hurricanes).

        There’s an ETF that’s basically perpetually long out of the money put options, it’s called VXX. In under five years it’s lose 96.93%.


  • Lord

    Much (most?) capital these days is in intangibles and could only be destroyed if knowledge of it were destroyed, yet it is probably more likely the ownership is destroyed than the knowledge itself. Capital itself has a high depreciation and a short half life unless regenerated between patent expiration and product displacement. The return is only the return after this regeneration and a sudden loss of capital would be followed by suddenly higher returns for those remaining.

  • There seems a conflict between this miniscule estimate of existential risk and Robin’s (belated) embrace of the doomsday argument (after Katja Grace rebutted the self-indication dodge). Did Robin really “update” after reading Katja’s thesis?

  • Pingback: Links 11/4/13 « naked capitalism()

  • My strategy over the last five years has been playing both sides against the middle. Selling put credit spreads on a downside bias and call CS on an upside bias has given me a 93% chance of a winning trade! and a 66% chance of a gain when you factor in that I need three winners to neutralize out a loss.

    Secondly, if you are patient enough to “leg into” each trade (I.e., purchase the call or put side of the CS prior to selling the accompanying put or call strike), then your odds for success are higher.

    And finally, if you skew your put:call CS ratio in the opposite direction of the market bias, then your odds for success are even higher.

    Obviously, I have had more losing trades on the call side the last five years because of the ultra-bullish bias but, because half of my put CS trades are put on with the knowledge that I wouldn’t mind being assigned the underlying if my trade lost, I have made up about 54% of those losses with covered calls.

    Bottom line: I don’t know where the markets will be tomorrow or next mont, so I play an odds-on strategy where idiot politicians, Wall Street noise, existential events and company news or reports won’t derail me.

  • Jonas

    Those are trading markets. Tail risks are priced with the assumption that they can bail out before it hits (trader’s overconfidence, so to speak).