Predators, Prey, and the Fat-Tail Problem in Quant

A quote in today’s WSJ on the troubles quant funds had this week is worth pondering:

“Wednesday is the type of day people will remember in quant-land for a very long time,” said Mr. Rothman, a University of Chicago Ph.D. who ran a quantitative fund before joining Lehman Brothers. “Events that models only predicted would happen once in 10,000 years happened every day for three days.” [Emphasis mine]

This will, of course, immediately get many people barking about “fat-tailed” distributions, with unlikely events far more likely than financial modelers assume.

The trouble with that is that we have the same conversation every time there is a market crisis — Fat tails! Fat tails! — and the tails of quant models get diligently fatter, only to blow up again in the next crisis. Some of that is because of model flaws in quant, and some is because financial predators go after the quants, but the effect is the same.

So, the real message is that fat-tails is the wrong way to think about things. Stocks, generally speaking, alternate between two modes: one that can be usefully and profitably modeled using distributions; and another mode that is essentially distributionless, with all stocks moving together and then apart like a school of tiny fish responding to a predator. These are species (no pun intended) of regime change in models, and the lesson for me is that most quant models are no better than ever at detecting such changes and responding accordingly.

Relatedly, here is Harvard endowment manager Mohamed El-Arian a few weeks back in a Financial Times column alluding to some non-quant implications of the current shift:

Indeed, we may well be in the middle of a regime shift: exiting a world in which the difference among individual investors’ performance was essentially a function of the degree of their exposure to the most illiquid and leveraged asset classes, and entering a world where more sophisticated risk management capabilities will increasingly be the main differentiator.


  1. Josh Stern says:

    IMO, the correct (though not particularly useful) way to describe probabilities of market events is to say that these probability distributions are non-stationary and have memory. In other words, people learn from past markets and they constantly adopt new strategies. The market is not a natural system that behaves the same way from year to year due to natural laws. It is a social system and it should be expected that it will exhibit new behavior in the future.

  2. Since “all models are wrong, but some are useful”, any model which “predicts” something every 10,000 years should not be leveraged because it can’t be tested (or even back-tested!). Sure, write books on it, blogs, dvds, give classes, win the nobel prize, but don’t build a multi-trillion dollar leveraged financial complex on its back!
    There’s so much qualitative BS that goes into most financial models (e.g., volatility assumptions), to say nothing of things completely left out (e.g., the probability that country X will default on its loans, devalue their currency, etc). Even if these qualitative assumptions are plugged into “fancy math formulas”. E.g., Black-scholes, lognormal distributions, etc.
    You can call this unmodeled stuff “fat tail” or a “non-stationary distribution”, but that’s just fancy professor-talk: it’s common sense. Leverage magnifies errors, and all models have errors.
    Newton’s F=ma has errors. It’s fine to predict where a ball will land if I throw it, but not if I forgot to model a cross-wind (left out something), or if I’m travelling to one of jupiter’s moons (leverage).
    Even insurance companies get in trouble sometimes, and I believe they generally don’t leverage their models (correct me if I’m wrong there).
    I’m reminded of the space shuttle — originally engineers thought 1 failure in 1000 launches, but experience has shown it’s more-likely 1 per 100 (or worse).

  3. No quant expects the quant tools to work all the time. We’re fully aware of black swan events. The trick is not to go gangbusters on leverage to the point where you wash yourself out. While Tue-Thu was tough, Friday was an utter reversal of that trend. The trick is to be able to weather short term anti-correlations to partake in the eventual long term reversion. And in fact it helps to reposition during the short term blips as our fund did on Thursday. Net-net we’re ahead as other conservative funds are.

  4. Hmm: “… because financial predators go after the quants …”, “It is a social system …” …
    Has anyone ever done a reasonable market model not looking at it as some sort of statistical bell curve, but as one of the predator-prey feedback systems? It’s quite well-known that those systems can have periods of stable steady growth, and then mass disruption (something like smart-money preys on dumb-money, but then all the dumb-money is devoured, which leads to a fallow time until new dumb money enters …)

  5. >>> a social system …
    Exactly. Because human intelligence and aggregate human intelligence (crowds) always beat the system.
    It is the quntessential marketplace, one model always works–until it doesn’t.

  6. It seems to me that the issue of quant models is similar to the issue of traders not testing trading models using out of sample data. The behavior predicted by the model probably works very well over some finite interval, but as soon as behavior in the market place changes in respect of some exogenous event, then the model stops being useful. Short of modeling the expected behavioral changes resulting from unpredictable events (good luck!), the quant models will always blow up at some point.

  7. This is like people saying the housing issues are subprime issues rather than a adjustable mortage issues. The problem here isn’t quant. The problem here, as it has been for eternity, is leverage. Unleveraged funds do not blow up because the s&p was down 3%.

  8. Josh Stern says:

    Leverage always adds risk, and, maybe more importantly, it shortens time horizons because it places limitations on buy and holding. But the focus here is on how some quants got their probability models screwed up. The answer, from everything I’ve read, is that they implicitly assumed probabilistic independence between events that turned out to be correlated. In the case of MBS, correlated market losses occurred due to (in no particular order) correlations in U.S. wide housing downturn, origination fraud, mis-ratings by Moody’s, and a crowded trade with an imbalance of leveraged players on one side. In the case of the equity losses, the correlation problem was apparently due to an imbalance of leveraged players with similar strategies, many of whom were also experiencing MBS losses and redemptions at the same time.
    Going back to the big picture, probability models with large numbers of moving parts that don’t make implicit independence assumptions will be computationally and statistically intractable. But when modeling a social system that changes over time, how can one be sure that variables which were not correlated in the past won’t be correlated in the future? You can’t be sure.

  9. >>> But when modeling a social system that changes over time, how can one be sure that variables which were not correlated in the past won’t be correlated in the future? You can’t be sure.
    You can be sure of a hueristic element built into social systems that cannot be built into computer models. Not in 2007.