The New York Times, among others, endeavored to shed more light on why quantitatively oriented funds like Global Alpha (down 26% YTD), Cliff Asness’s AQR (down 13% in August) and James Simon’s Renaissance Technologies (down 7% YTD) are doing so badly.

Short answer: these funds rely on models that look at statistical norms, and these are not normal times. The Wall Street Journal today quoted Lehman’s head of quantitative equity strategies, Matthew Rothman:

“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.”

That very statement reveals what’s wrong with models. Users attribute to them a reality independent of, and too often greater than the underlying situation they are meant to represent. Anyone who has worked on an M&A transaction will recognize the phenomenon. The model doesn’t simply become the medium for representing possible outcomes, it becomes more real than the messy, complicated companies involved.

Here, it is patently absurd to talk about a “one in 10,000 year event” for markets and instruments that clearly won’t exist in 10,000 years. It behooves someone who is dealing in mathematical terms to describe the probabilities more precisely. And the very fact that this supposed impossibly improbable event happened three days running says there is something wrong with his, and the general, assessment of the likelihood of outcomes. What happened this week wasn’t as extreme as the 1929 crash, and my calendar says that happened a mere seventy-eight years ago.

How can you judge what would be a “one in every 10,000 year” event, much the less a “one in every 100 year event” when you have at most 10 or 20 years of data? All sorts of things that affect equity values can and most assuredly will change over that time horizon, including shareholder rights, tax treatment, and transaction costs, which will in turn influence the equity premium required. So even if you are looking at a long data series (say 60 years), its relevance is questionable because the rights and underlying economic value of various instruments were not consistent over this time period (note that real asset and commodity prices can be studied more reliably over long periods because they are physical goods, not contractual instruments subject to changes in their prevailing rights).

Back to the immediate issue of the quant fund tsuris. Although the particulars of each firm’s approach no doubt varies considerably, in general quant funds look at mathematical relationships between various financial assets. Some models do rapid, automated trading to capture fleeting price anomalies, while others suggest trading ideas that traders review and decide whether to implement. Keep in mind that all three funds have been successful in the past (recall that James Simon is the fellow that earned $1.5 billion last year based on his fund’s performance).

However, one of the funny things about financial markets is that they have a propensity to behave abnormally (the syndrome is called kurtosis, or more colloquially, fat tails). Distributions of events in financial markets do not follow a normal distribution (the well known bell curve). Instead, events that are remote from the mean of the distribution are more likely to happen than in a normal distribution (Markets also exhibit skewness, which is an asymmetrical distribution around the mean. Equities have negative skewness while commodities have positive skewness).

Yet many widely-used valuation techniques, such as the Black-Scholes options pricing model, assume a normal distribution.

Now the models used by these firms may indeed have made some allowance for the deviance from normal distributions in the price behavior of most financial assets. But the real problem is whatever they assumed ain’t what’s happening now.

In the abstract, this situation might not even be an indictment of their strategy. Often, savvy investors take positions that move against them, which they hold, enduring large paper losses, until eventually they are proven correct.

But the problem the hedge funds face is the word “eventually.” The inability to hold some positions long enough played a big role in LTCM’s collapse. For example, it took a big bet on swap spreads, which in the 1997 emerging markets crisis, had widened to historically unheard of levels. LTCM wagered they would narrow. Then Russia defaulted and the spreads widened further.

LTCM’s problem, common with hedge funds, is that they are financing their positions. As the positions move into greater losses, their funding sources demand more capital (either cash or collateral). At some point, the hedge funds become capital constrained and start having to liquidate their positions even if the position is likely to work out in the long run. They lack the staying power to see it through.

In LTCM’s case, it took swap spreads roughly a year after the fund’s crisis to revert to normal levels, far longer than anyone at the time thought possible.

The New York Times discusses not only the problems at Global Alpha but the concern that Goldman’s proprietary trading desk may have been using some of the same trading strategies, meaning the firm may be taking losses along with its hedge fund investors.

Dave FIf returns are not normally distributed in the markets why does the CFA Institute require its candidates to learn all the normal distribution-based statistics?

Yves SmithBeats me. Intellectual laziness? I thought this was common knowledge among finance geeks. Clearly I am mistaken.

Mathematician Benoit Mandelbrot studied the distribution of financial market returns extensively. From Wikipedia:

Mandelbrot found that price changes in financial markets did not follow a Gaussian distribution, but rather other Lévy stable distributions, having theoretically infinite variance. He found for example that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7, rather than 2 as in a Gaussian distribution. “Stable” distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.“Gaussian” is a normal distribution.

Dave FThe question was more snarky than anything; it should be common knowledge among finance geeks, and if it isn’t they should be reading The Black Swan. Or wikipedia entries on Mandelbrot.

Yves SmithSorry to have missed the humor. I am sometimes too literal-minded. But your factoid is pretty eye-opening nevertheless.

Steve DiamondThis is why I serve a basic intro to the thinking of Mandelbrot in my finance classes. I actually spoke to him several times a few years back – he was shocked at the widespread acceptance of “efficient” markets theory in business and law schools – he claims such theorists rely on a primitive grasp of math.

disYves,

Here

http://www.ft.com/cms/s/030ba626-48f9-11dc-b326-0000779fd2ac.html

The FT reports that the average quant hedge fund is down 15%.

They are on average leveraged 4x.

Oh boy! This calls for a vicious cycle of margin calls and forced selling to meet them which further deterioration of assets to further margin calls…

It’s a bloodbath and the markets should be a pinball machine these week.

disAlso another good piece from the FT

http://www.ft.com/cms/s/8eebf016-48fd-11dc-b326-0000779fd2ac.html

there is also a mini crisis in commercial paper.

Ufff, it sure going to be a scary week.

LuneIn other words, “the market can remain irrational longer than you can remain solvent.” –Keynes.

Wall Street is painfully finding out that some maxims never go away, no matter how many models, math equations, and money you throw at them…

Yves SmithLune,

Touche.

AnonymousAs a quant equity manager (we’ve been hit, but not nearly as hard as others) – I can tell you that you are all completely missing the point. The 1 in 10,000 years analogy is correct; the problem was that a major fund was unwinding, therefore selling good stocks and covering bad ones. The problem is NOT with quant modeling, but with leverage (which we don’t use).

I really wish the media/bloggers would take the time to understand the industry and the dynamics of the situation before making knee-jerk , misguided comments.

Yves SmithDear Anon of 4:39 AM,

OK, you asked for it. I normally strive to be polite, but I cannot believe someone who claims to have a statistical background is defending the widespread “one in every 10,000 year” BS.

LTCM had a similar meltdown and massive selling a mere 10 years ago. What happened last week is not an out of bounds event. Anyone who know financial history knows that markets are subject to mania, meltdowns, and panic. Models that don’t allow for that are bunk.

In addition, the data used in most of the models is specious. It assumes historical consistency when changes in markets (transaction costs, trading volumes relative to the value of underlying assets, increasing use of derivatives, particularly indices, and imperfect relationships between derivative and cash prices) make the comparability of data over time questionable. Even if you have a 20 year data series, the data of 20 years ago has little relevance for markets today.

Go read Mandelbrot and then maybe we can have a real discussion.

AnonymousThe map is not the territory, the map is not the territory…

AnonymousInvestment world is a QUANTUM world (not to cofuse with QUANT world). So, Any price has a decent probability once the market is excited by external forces( like an electron in atom can move to any energy level even with a mimnimal energy excitment). So, all the models and quants just need to go home and leave the markets to traders. Please…

Boris ( QUANTUME PHYSICIST, TRADER)

borisc.blogspot.com

AnonymousIt is tiring to read baloney from mathematicians

No you are not in a normal distribution look at the equities markets (NO GAUSS NO POISSON)

No! every one using your pair trades do not harm your performances since your model is « when we buy it goes up »

Yes! your models are flawed, as they are more an inspiration of the St Petersburg paradox «bet further money against the odds ad infinitum »

No! the probability of adverse occurrence on bets which are outside normal distribution cannot be explained through normal distribution.

Yes! your models are skewed on the upside with a postulate « the convex reflexivity of markets » Yes! they fail to read inflexion points.

No you cannot factor all the variables in your models even a liquidity crunch was not a base case scenario.

All the models which were fed in 1987 under the same trivial assumptions have proved to be a failure.