The Subprime Meltdown Hits Quant Hedge Funds

If you had asked me where the subprime meltdown was going to hit first, I would never have guessed "heavy-quant hedge funds." Yet so it has:

Blind to Trend, 'Quant' Funds Pay Heavy Price: by Henry Sender and Kate Kelly: Computers don't always work. That was the lesson so far this month for many so-called quant hedge funds, whose trading is dictated by complex computer programs. The markets' volatility of the past few weeks has taken a toll on many widely known funds for sophisticated investors, notably a once-highflying hedge fund at Wall Street's Goldman Sachs Group Inc. Global Alpha, Goldman's widely known internal hedge fund, is now down about 16% for the year after a choppy July, when its performance fell about 8%, according to people briefed on the matter. The fund, based in New York, manages about $9 billion. The fund's traders in recent days have been selling certain risky positions, according to these people. Early this week, those moves sparked widespread rumors on Wall Street that the entire fund might be shut down. A Goldman spokesman has said the rumors are "categorically untrue."

Campbell & Co., an $11 billion hedge fund that trades in the futures market as well as in stocks and bonds and is completely driven by such computer programs, was down 10% to 12% by the end of July. Quant funds -- "quant" stands for quantitative -- generally operate by building computer models of market behavior and then allowing the computer programs to dictate trading. A recurring characteristic of the recent trouble in financial markets is that many lenders, funds and brokerages were following statistical models that grossly underestimated how risky the market environment had become. "Our risk models failed to pick up the fact that we were due for a correction," says Keith Campbell, founder of Campbell & Co. "We were highly diversified. It was the perfect negative storm."... He told investors that the losses stemmed from "a unique combination" of factors.... "All [computer-driven] managers say the models make sense and look like they are working," says Bill Johnston, founder of Bayon Capital, an investment fund based in San Francisco that isn't computer-driven. "But then something happens which statistical probability suggests would never happen."... Renaissance Technologies Corp.... is holding up despite the market's downturn.... Other hedge funds declined to disclose to brokers or portfolio managers in charge of so-called funds of hedge funds just how badly wounded they have been by the recent extreme swings...

"Our strategy is fine. We were just hit by a sixteen-standard-deviation event." "Then it didn't happen: the universe isn't old enough for even one sixteen-standard-deviation event to have ever happened."

Tails are fat.

Comments

[Craig Tindale]

Enron was just a meme of the economic and political fraud to come , sub prime and AltA right through to AA Prime are dead meat close to a trillion dollars has been lost this will set off a good part of the $420T derivative risk

As Kindleberger put so well in his book, Manias, Panics, and Crashes:
"The implosion of an asset price bubble always leads to the discovery of frauds and swindles. The supply of corruption increases in a pro-cyclical way much like the supply of credit. Soon after a recession appears likely the loans to firms that were fueling their growth with credit declines as the lenders become more cautious about the indebtedness of individual borrowers and their total credit exposure. In the absence of more credit, the fraud sprouts from the woodwork like mushrooms"

read Hayman Captials letter to investors

http://www.dealbreaker.com/images/pdf/HaymanJuly07.pdf

[anne]

Brad DeLong:

"Our strategy is fine. We were just hit by a sixteen-standard-deviation event."

"Then it didn't happen: the universe isn't old enough for even one sixteen-standard-deviation event to have ever happened."

Tails are fat.

[Brilliant.]

[bigTom]

"Tails are fat"

Most likely the statistical theories are missing something pretty fundamental. Sweeping up all the unkowns that you don't even know you don't know about is bound to increase risk, and produce Annes fat tails.

[Ian Whitchurch]

The US housing bubble popped.

Whoda ever thunk that ?

[Ian Whitchurch]

The US housing bubble popped.

Whoda ever thunk that ?

[AP]

bigTom's right. If you over-fit a model you can be awfully certain about things that just aren't true.

[Rob]

Hey just because estimating stochastic variances is based on some very strong assymptotic assumptions doesn't mean we'll have a problem!

[David Lloyd-Jones]

Anne has the mathematics right. There ain't no normal curves in the Real World(tm.).

The tails are all long or fat or both. (I'm reminded of one financial guy's attack on Madelbrot, which went roughly "If Mandelbrot were right then the whole world would collapse every few years." But obviously the world *does* collapse every few years. Not even the most elementary mechanical cranks and gears of today's financial markets resemble those before September 1987.

But then around this joint we're pretty used to Anne having it right.

My one quibble with all the press coverage: everybody talks about the mortgage meltdown, but I simply don't see any such thing. Defaults, delays, and interesting unconventional re-financings of sub-prime mortgages don't amount to more than a couple or four percent of the whole.

What have melted down are two quite other things, faith in the managers of these funds, i.e. market panic, and the positions of over-leveraged investors in such mortgages, that's people getting broke.

The first are facing a run on their free cash, and will duly, and fairly, have to pay exorbitant rates on their borrowing to get through the crunch. The second are in many cases just fucked, to use the technical term, which is as it should be. That's tough on them (and I'm usually leveraged balls up, but have the grace to laugh when I lose), but it's no harm to the economy and no loss to the rest of us.

If anything it's a Good Thing. If "risk" is to have any meaning, there have to be losers now and then.

(BTW, Brad, I am rather suspicious of your NBER paper, but I've only skimmed it online, not settled in an arm-chair with the hard copy. I don't think there's any problem with your math: I think that your very enticing notions about noise traders benefitting from risk which they themselves cause is really an artifact of bad epistemology in your notion of what "risk" means. Time [for both of us, perhaps] to go re-read Hayek the Younger...)

[CapitalistImperialistPig]

As soon as an algorithm dictates a trading strategy, somebody can craft a strategy to exploit the prejudices incorporated in that algorithm. Sixteen SD events don't happen, but probability calculations become invalid (or rather change) as soon as people figure out how to exploit the rigidities of the strategy. My odds of tossing sixteen coins and getting sixteen heads are very slim (though not sixteen SD slim) but I can choose to place sixteen coins face up very easily.

[Ben Ross]

A few comments from a physicist. There may be several things going on.

#1
As noted above, tails are fat (compared to the Gaussian distribution, which is the one people use because they can solve the equations and because it's valid under certain conditions which have a lot in common with the conditions for perfect competition) - true. In physics (not always, but very often) as in economics.

#2
Overshoot. If the arbitrage strategy is a simple one based on prices, this doesn't happen. If corn is cheaper in Chicago than New York, when people start buying corn in Chicago and shipping it to New York, the Chicago price goes up and arbitrage ends when the prices are equal.

But if the premise of the arbitrage is that risk has been underpriced, the price of risk can go down and people, at first, keep making money. The unlikely event that was (or maybe was only thought to be) priced in excessively hasn't happened yet. More arbitrageurs pile in, the price correction overshoots, and risk becomes underpriced.
http://www.nytimes.com/2007/08/13/business/13hedge.html

#3
Any quantitative strategy is based on a model of market behavior. When a lot of money gets into the same strategy, the market changes its behavior. The model is inapplicable and the strategy doesn't work.

Example of #3 - A decline in value and liquidity of subprime mortgages caused prices of heavily shorted stocks (homebuilders, etc.) to go up last Thursday. This linkage wasn't (I imagine) in anyone's model; it was created by the quant strategies that assumed they were unlinked and therefore (this is undoubtedly an oversimplification) used one to hedge the other.

All the above, though, I think is more like the preface to the explanation than the explanation. A lot more has to do with Wall Street's incentives (short-term, self-centered, rewards for conformity rather than originality, etc.)...

[David Lloyd-Jones]

The reason commentary on all these M-sigma events, where M is a number larger than about eight, makes no sense at all is explainable by a nice phrase that turns up in Roger Lowenstein's very good book on the LTCM meltdown.

See, all of the dumb versions of modern financial theory are based on the non-interdependence of various assumedly random events. Like the price of cheese is supposed to be independent of the price of Ford coupe floor-liners.

This is often a reasonably safe assumption. Plus or minus.

(My one-time lover, Elizabeth Rubin -- yes, the very one who factors five digit numbers by looking at them, and rarely scores under 350 in four-handed Scrabble, you saw her breast-feeding on stage in the Met's Ring Cycle -- once explained shtetl economics to me. "Ya just gotta know how the price of apples relates to the price of rutabagas when the price of cattle drops against pigs.")

But the Long Term Capital Management quote? I knew you were waiting.

Roughly, from memory: "When the shit hits the fan, all the correlations go to one."

. * * *

For aficionados of this stuff, note that the Leeson overhang that hit Barings, and phenomena like it, are an admittedly interesting but not the major subset of this "correlations going to zero" in the face of the quants' view of reality. Imh(tentative)o, the main kind of loss of randomicity of correlations is simple animal panic, an endocrine, not a financial fact of life.

[David Lloyd-Jones]

Ben,

One form of Dead Cat Bounce is when the shorts cover.

The easiest example is that when any stock touches a dollar and is about to be delisted on the Big Board, it's a good buy as long as your connection to the floor is fast enough: the shorts have to cover before the thing stops trading.

This may account for last Thursday's action that you mention.

A recent example of this: after the courts settled the Northwest Airlines case five or six weeks ago, and the common stock became worthless, it traded hundreds of thousands of shares at thirty cents, up from eleven, exactly because the shorts had to cover. Famously,

"He that sells
What isn't his'n
Must buy it back
Or go to prison,"

even if the short-sold equity has no further legal existence! The thing itself doesn't exist, but the lender's claim on getting it back still does! Ain't law and finance a hoot?

[Paul G. Brown]

First - many distributions have 'tails'. Not just the Normal Distribution. I'd be surprised if anyone used Normal Distribution to model price volatility. But I digress.

Second - ceteris paribus. Learn it. Live it. Whenever you attempt to model a complex system by examining its history (whenever you attempt to, say, estimate the value of the variance of a random variable like mortgage default probability) your heart should repeat this little phrase in a flat, leaden and loud tone.

For the longest time the US had fixed rate mortgages. The mortgages in trouble are new, variable rate mortgages (ARMs). All things a NOT equal.

[Divination and Behavioral Models]

generally operate by building computer models of market behavior

A voice came suddenly out of the shadows, a soft, misty sort of voice.
'Welcome,' it said. 'How nice to see you in the physical world at last.'
Harry's immediate impression was of a large, glittering insect. (PA6)

'Sit, my children, sit,' she said, and they all climbed awkwardly into armchairs or sank onto pouffes… (PA6)

'Welcome to Divination,' said Professor Trelawney, who had seated herself in a winged armchair in front of the fire. 'My name is Professor Trelawney. You may not have seen me before. I find that descending too often into the hustle and bustle of the main school
clouds my Inner Eye.'

Professor Trelawney delicately rearranged her shawl and continued, 'So you may have chosen to study Divination, the most difficult of all magical arts. I must warn you at the outset that if you do not have the Sight, there is very little I will be able to teach you. Books can take you only so far ion this field…'
At these words, both Harry and Ron glances, grinning, at Hermione, who looked startled at the news that books wouldn't be much help in this subject.
'Many witches and wizards, talented though they are in the area of loud bangs and smells and sudden disappearings, are yet unable to penetrate the veiled mysteries of the future,' Professor Trelawney went on […] 'It is a Gift granted to few. You, boy,' she said suddenly to Neville, who almost toppled off his pouffe, 'is your grandmother well?'
'I think so,' said Neville tremulously.
'I wouldn't be so sure if I were you, dear,' said Professor Trelawney…

We will be covering the basic methods of Divination this year. The first term will be devoted to reading the tea leaves. Next term we shall progress to palmistry. By the way, my dear,' she shot suddenly at Parvati Patil, 'beware a red-haired man.'
Parvati gave a startled look at Ron… (PA6)

'In the summer term,' Professor Trelawney went on, 'we shall progress to the crystal ball – if we have finished with fire-omens, that is. Unfortunately, classes will be disrupted in February by a nasty bout of flu. I myself will lose my voice. And around Easter, one of our number will leave us forever.'

What is it, Professor?' said Dean Thomas at once. Everyone had got to their feet and slowly, they crowded around Harry and Ron's table, pressing close to Professor Trelawney's chair to get a good look at Harry's cup.
'My dear,' Professor Trelawney's huge eyes opened dramatically, 'you have the Grim.' (PA6)

'The Grim, my dear, the Grim!' cried Professor Trelawney, who looked shocked that Harry hadn't understood. 'The giant, spectral dog that haunts churchyards! My dear boy, it is an omen – the worst omen – of death!'

I was saying, my dear, that you were clearly born under the baleful influence of Saturn,' said Professor Trelawney, a faint note of resentment in her voice at the fact that he had obviously not been hanging on her words.
'Born under – what, sorry?' said Harry.
'Saturn, dear, the planet Saturn!' said Professor Trelawney, sounding definitely irritated that he wasn't riveted by this news. 'I was saying that Saturn was surely in a position of power in the heavens at the moment of your birth… your dark hair… your mean stature… tragic losses so young in life… I think I am right in saying, my dear, that you were born in mid-winter?'
'No,' said Harry, 'I was born in July.

'But surely you already knew that, Sybill?' said Professor McGonagall, her eyebrows raised.
Professor Trelawney gave Professor McGonagall a very cold look.
'Certainly I knew, Minerva,' she said quietly. 'But one does not parade the fact that one is All-Knowing. I frequently act as though I am not possessed of the Inner Eye, so as not to make others nervous.'
'That explains a great deal,' said Professor McGonagall tartly.

Professor Dumbledore – yesterday, when I was having my Divination exam, Professor Trelawney went very – very strange.'
'Indeed?' said Dumbledore. 'Er – stranger than usual, you mean?'
'Yes… her voice went all deep and her eyes rolled and she said… she said Voldemort's servant was going to set out to return to him before midnight… she said the servant would help him come back to power.' Harry stared up at Dumbledore. 'And then she sort of became normal again, and she couldn't remember anything she'd said. Was it – was she making a real prediction?'
Dumbledore looked mildly impressed.
'Do you know, Harry, I think she might have been,' he said thoughtfully. 'Who'd have thought it? That brings her total of real predictions up to two. I should offer her a pay rise…'

Can I have a look at Uranus, too, Lavender?' said Ron.

[Hari Seldon's Visible Hand]

Psychohistory (fictional)
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For the study of the psychological motivation of historical and current events, see Psychohistory

Psychohistory is the name of a fictional science, which combined history, sociology, and mathematical statistics, in Isaac Asimov's Foundation universe, to create a (nearly) exact science of the actions of very large groups of people, such as the Galactic Empire.
Contents

* 1 Underlying assumptions
* 2 Development of psychohistory
* 3 Limitations of psychohistory
* 4 Asimov on psychohistory
* 5 Psychohistory in other fiction
* 6 Literary influences
* 7 See also
* 8 Notes and references
* 9 External links

[edit] Underlying assumptions

The basis of psychohistory is the idea that, while the actions of a particular individual could not be foreseen, the laws of statistics could be applied to large groups of people and used to predict the general flow of future events. Asimov used the analogy of a gas: in a gas, the motion of a single molecule is very difficult to predict, but the mass action of the gas can be predicted to a high level of accuracy - known in physics as the Kinetic Theory. Asimov applied this concept to the population of the fictional Galactic Empire, which numbered in the quadrillions. The character responsible for the science's creation, Hari Seldon, established two postulates:

* That the population whose behaviour was modeled should be sufficiently large
* They should remain in ignorance of the results of the application of psychohistorical analyses.

[edit] Development of psychohistory

Later on in his career, Asimov described historical (pre-Seldon) origins of Psychohistory. In The Robots of Dawn, which takes place thousands of years before Foundation, he describes roboticist Han Fastolfe's attempts to create the science based on careful observation of others, particularly his daughter Vasilia. In Prelude to Foundation we learn that it was in fact one of Fastolfe's robots, R. Daneel Olivaw, that manipulated Seldon into practical application of this science.

[edit] Limitations of psychohistory

The fact that Seldon established a Second Foundation of psychic adepts to over see his Seldon Plan, can be taken as an indication that even Seldon himself had doubts about the ultimate ability of a purely mathematical approach to predicting historical process, and that he recognized that the development of psychic skills such as those used by the Mule, had the ability to invalidate the assumptions his models were based upon. The Seldon methodology, might therefore only work at a certain level of species development, and would over time become less useful.

[edit] Asimov on psychohistory

On September 25, 1987, Asimov gave an interview to Terry Gross on her National Public Radio program, Fresh Air. In it, Gross asked him about psychohistory:

Gross: "What did you have in mind when you coined the term and the concept?"

Asimov: "Well, I wanted to write a short story about the fall of the Galactic Empire. I had just finished reading the Decline and Fall of the Roman Empire [for] the second time, and I thought I might as well adapt it on a much larger scale to the Galactic Empire and get a story out of it. And my editor John Campbell was much taken with the idea, and said he didn't want it wasted on a short story. He wanted an open-ended series so it lasts forever, perhaps. And so I started doing that. In order to keep the story going from story to story, I was essentially writing future history, and I had to make it sufficiently different from modern history to give it that science fictional touch. And so I assumed that the time would come when there would be a science in which things could be predicted on a probabilistic or statistical basis."

Gross: "Do you think that would be good if there really was such a science?"

Asimov: "Well, I can't help but think it would be good, except that in my stories, I always have opposing views. In other words, people argue all possible... all possible... ways of looking at psychohistory and deciding whether it is good or bad. So you can't really tell. I happen to feel sort of on the optimistic side. I think if we can somehow get across some of the problems that face us now, humanity has a glorious future, and that if we could use the tenets of psychohistory to guide ourselves we might avoid a great many troubles. But on the other hand, it might create troubles. It's impossible to tell in advance."

[edit] Psychohistory in other fiction

Asimov's ideas figure prominently in Donald Kingsbury's novel Psychohistorical Crisis, a re-imagining of the world of Isaac Asimov's Foundation trilogy, set after the establishment of the Second Empire.

In Fantastic Four #542, Mister Fantastic, involved in the Marvel Universe's Civil War event, reveals that his real reason for supporting the superhero registration act which prompted the Civil War is due to his development of a working version of Isaac Asimov's fictional Psychohistory concept. Mister Fantastic's application of this science indicates to him that billions will die in escalating conflicts unless the act is made law.

The concept of psychohistory is also present in the Legend of the Galactic Heroes (銀河英雄伝説, Ginga Eiyū Densetsu) by Yoshiki Tanaka.

[edit] Literary influences

Literary critics have described Asimov's psychohistory as a reformulation, either for better or worse, of Karl Marx's theory of history (Historical Materialism) or Kant's theory of controllable history, though Asimov denied any direct influence.[1] Psychohistory also has echoes of work in the social sciences that by the 1960s would lead to attempts at large-scale social prediction and control such as Project Camelot and modernization theory.

[Marr]

If one starts with the premise that every economy we consider is unstable, then mathematics should tell us that ultimately a collection of successful hedge funds will create a singularity,

The proof is something along the lines that hedge funds remove vooatility by creating instruments that preserve asset prices over their cyclic period, essentially inverse filtering. Since the volatility is inherent (the premis) the net result of a successful hedging strategy would result in wide band spectral output, ot a singularity in time.

Another way to see the proof is to note that a successful hedge fund would have to become as large as the volatility, and would so dominate the spectral shape of the income distribution as to make it unbalanced.

[dsquared]

growwwl.

I continue my quixotic war against people using the phrase "fat tails" to describe events which very strongly suggest that there is no stable underlying distribution for these events to be in the tails of.

http://d-squareddigest.blogspot.com/2006/09/tail-events-phrase-considered-harmful.html

and related:

http://d-squareddigest.blogspot.com/2006/06/cave-in-theory-of-economics-my-four.html

I am still fond of the joke that most financial econometricians believe that the Crash of 1929 was just a particularly innaccurate observation of the true underlying 8% annual return on equities.

[cw]

"When the shit hits the fan, all the correlations go to one."

I prefer Paul Kedrosky's take (http://paul.kedrosky.com/archives/2007/08/11/predators_and_t.html) on this:

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.

[MattF]

"I continue my quixotic war against people using the phrase "fat tails" to describe events which very strongly suggest that there is no stable underlying distribution for these events to be in the tails of."

Thank you. I've often felt that statistical variation has an unacknowledged 'semantic' component-- particularly for unusual events. So, a 16-standard deviation event isn't 'rare', it's 'surprising',... and sufficiently 'fat' tails aren't a sign of funny statistics, they're a sign that you don't understand something.

[Marr]

Fat tails should occur when the number of samples in a market are insufficient to have the characteristic gaussian uncertainty. We would likely see this in markets dominated by hedge funds, according to my theory.

[Ben Ross]

Fat tails should also occur in a market with many small participants, if their actions are correlated. Such as a market with small traders who act on momentum or other technical analysis.

But I doubt fat tails are the best explanation of current events, since the end of the housing bubble was hardly a many-sigma event.

[Alex Tolley]

Isn't it about time we stopped using gaussians and talking about sigmas and use other distribution, possibly with "infinite variance"? Gaussians are used because they are very tractable, not because they are the correct distribution.

I also agree that the assumptions of independence makes little sense under a variety of market conditions. Classic case of incorrectly assuming markets are mathematically describable like physics.

[wcw]

Everything is mathematically describable.

Which is to say, you're no Goedel.

[mathias]

While anne is right that "tails are fat", I am a bit surprised that many comments on the current problems say things along the lines of: "why didn't they realize that returns are non-normal". I think they most likely did.

One has to realize that even models that show a "fat tail" behaviour can be absolutely useless when the underlying parameters change due to drastically changing market conditions.

Model parameters are (imho) most often calibrated on historical data which are assumed to be representative of future data. If this assumption is not correct and the environment changes in a drastic unforseen way, even models with "fat tails" may not help you at all.

[Richards Hedge Funds Blog]

I wonder how long quants bad rap will continue in the markets, probably 3-5 years. Many funds that use to sell themselves as black box quant models have been layering on an additional step in their investment process to account for model conflicts, checks and risk management processes. Similar to money managers combining both fundamental and momentum based trading indicators now many more managers are now talking about being a pure quant a bit less.

- Richard
Richard Wilson
http://richard-wilson.blogspot.com