Fractal Finance, Part II

In Fractal Finance, Part I we saw that fractals can be useful in describing complex, seemingly chaotic patterns in nature.  We also saw how Wall Street took advantage of the same advances in information technology that made the study of fractals possible starting in the 1980s, to come up with computer-driven black-box trading schemes.  For example, index arbitrage strategies were widely blamed for the Black Monday crash of October 1987.

Wall Street is always on the look-out for new "angles", opportunities to better skin a cat in a place already full of very sharp razors.   The sheer quantity of money moving around attracts very bright individuals, at least the variety who get high on making as much money as possible with the seat of their pants and the money of others. Wall Street is also home to some of the hugest and most ruthless egos to be found anywhere, resulting in a kind of kindergarten for genius gunslingers, but that's material for a subsequent post.

Unlike what most people may think,  professional traders don't usually make huge "straight"  up-and-down bets;  there's  simply too much risk involved. They leave this type of activity to end-user speculators and investors (e.g. hedge or pension funds), and mostly involve themselves in market-making and arbitrage.

Market-making is the workaday, mundane function of providing secondary market liquidity in return for a thin "spread" profit between bid and offer prices. This is the foundation upon which rests most trading revenue and is the training ground for all junior traders.

The real action, however, where whiz-kids can and do make a difference playing with the firm's own money, is in arbitrage and arbitrage-related activities, where profit margins are modest but risk is usually well-defined, small and manageable.  The trick there is to identify new "angles"  and take advantage of them early on, when profit margins are still fat, i.e. before other players get a whiff of the action and pile in too.

(If you are not familiar with arbitrage and risk, Richard Bookstaber's A Demon of Our Own Design is an excellent and enjoyable book, written by a true insider. Also, see the personal note at the end of this post.)

The basic principle of arbitrage is simple: if A=B and B=C,  then by definition  A=C.   Financial arbitrage is, of course, more complicated than simple math since it involves a variety of different risks, ranging from simple execution risk (the ability to complete a trade as planned), all the way to counterparty risk (an entity on the other side of the trade fails).

The basic elements common to all arbitrage operations are:

1. The amounts of money involved are very large.  Since profit margins are small a lot of capital must be applied in order to make a decent return, in dollar terms.
2. Trading is very active.  Again, because of such small margins, which can appear and disappear within minutes, if not seconds, traders have to pounce on them fast and often.
3. Heavy leverage is always used to boost returns.  Twenty-to-one is considered conservative, fifty-to-one is standard and 200-to-one is not unheard. (Or was, we now live in the Age of De-leverage).

And where do fractals fit in?  Where is self-similarity in markets?

One does not need to study price charts in major, liquid markets for long to realize that they look very similar in all time frames.  Do this: take the daily chart of any reasonably active stock or commodity and start narrowing the time frame, i.e. reduce the time unit to hourly, 30-minute intervals, 10-minutes and so on.  You will see that fluctuation patterns are, more or less, similar.  Now, expand the time frame by looking at weekly, monthly, etc. charts.  Again, similar patterns.

 S&P 500 - One Day Chart  (Friday, June 26 2010)

 S&P 500 - One Year Chart

The study of patterns is not new in markets, of course. It has been going on for ages as technical analysis, wave theory, Fibonacci trading, etc. What is new, however, is the massive size of computing, communications and network capacity now being applied to markets, causing trading to become unrecognizable when compared to even ten years ago.  It is estimated that  an astonishing 70% of all volume in U.S. stockmarkets is now driven by so-called "high frequency" trading, where buy and sell orders are generated by algorithms residing in black-box computers,  taking advantage of arbitrage opportunities between the prices of shares, indexes, trackers, futures and other derivative instruments.

In Part III I shall present my conviction that such developments are detrimental to the overall health of financial markets and, indeed, the entire real economy.

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I first heard of the words arbitrage and arbitrageur in 1981 during the Mobil - Marathon - U.S. Steel takeover battle. At the time, I was in grad school getting my Master's degree in ChE - and mentally a million miles from Wall Street though a stone's throw  away.  

I was introduced to David P., a major-league arbitrageur at the time, who tried to explain what he did.  I found it all extremely boring in those, my early Joe Engineer days:  oil prices were setting new records and Wall Street was flat on its back.  It wasn't until several years later that I realized who David really was. Or, for that matter, who one Carl Icahn was, whom I had met at one of David's parties and, having never heard of him until then, cheekily asked: "And what do you do for a living?"  I still blush at my ignorance.

China Revalues Yuan: It Takes Two To Tango

Fractal Finance, Part II will follow on the next post.  I believe China's decision to revalue the yuan merits a post first.

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Following months of wrangling with the United States, during which unsubtle threats of trade war were hurled hither and yon,  China finally announced yesterday that the yuan's peg to the dollar will be allowed more flexibility.  The currency "jumped" 0.2% higher versus the dollar.  If this revaluation seems unimpressive given the intensity and importance of the matter, that's because it is unimpressive.  But, China does things its own way, particularly during its current transition from a command economy to free-market capitalism.  Old habits die hard, absolute power corrupts absolutely, you can't teach an old dog... you get the point.

But the yuan's revaluation is not exactly my subject today.  Instead, I want to focus on something Hank Paulson said back in his final days as Treasury Secretary:  The world, he said, was suffering from a "savings glut" - and pointed at China and the oil producers.

Now, back then I thought his comment was disingenuous, if not downright asinine.  After all,  I clearly saw the problem as a sea of bad debt and the popping of the easy credit bubble.  But,  as if often the case, it takes two to tango and,  in fact, some concepts can only be defined in relation to their matched opposites.  Good requires evil, light makes sense only because of darkness, ying needs yang.

Likewise, for every  incremental unit of savings to exist we must, by definition, create an incremental unit of debt.  Interestingly, however, debt can be, and mostly is, today created out of thin air, a situation otherwise known in theology, cosmology and other such -ologies as creatio ex nihilo.  Furthermore, unlike other matched pairs, the creation of fiat currency debt-savings is strictly unidirectional, i.e.  it is the  willingness (or necessity) to assume debt that creates savings and never the other way around.  I can walk into a bank and apply for a $1 million mortgage, thus putting into motion a process that may ultimately result in, say, the holding of a CMO by a bank in China, i.e. a piece of the "savings glut".

But I can't do the opposite: I can't stroll into a bank and ask it to generate $1 million in savings for me.  That's the crucial - if obvious - difference within the duality of money as debt and debt as money.  In other words, sure it takes two to tango - but there is only  one leading partner on the dance floor: the borrower.

Stop right there, you cry.  Didn't all parties on the other side of the credit bubble, the mortgage and leveraged loan originators, the brokers, packagers, servicers, rating firms, the investment banks.. the whole nearly-criminal gang - didn't they salivate and cry out for ever more "product" to chop and shop around as CMOs, CLOs, CDOs?  What do you make of that?

Well, I say that if people had decent incomes from decent jobs and could thus afford to live a middle-class lifestyle and save a bit on the side, as they did up to the mid-70s, well then they wouldn't need to borrow to cover the most basic necessities of life.  Like a home, an education and medical care.  Who ever imagined it was normal to go into hock for years on end just to pay for a college education, for heaven's sake?

So, to go back to Hank Paulson.  Indeed, he spoke truthfully - from an accountant's point of view.  But oh, what a tangled web of (half)truths we weave, when we set out to deceive.. It's not like a billion Chinese came begging to America to create a trillion dollars' worth of  a "savings glut" for them now, is it?

And how about China?  What is it doing with all that debt-uous  "money" it has piled up over the years?  It is in a lather trying to convert it as fast as possible into "hard" assets, like oil and iron ore deposits, ports, etc.   That's a game of "hot potato" on a grand scale or, quite literally, "pass the buck". 

Maybe now we better understand why there was such an absolute need for the dollar to go up against the euro, the only serious adversary for global reserve currency status, eh?  Particularly since the US is creating another trillion-plus dollars in fresh "savings" this year...

Fractal Finance, Part I

Dedicated to the memory of Dr. Thai McGreivy

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Fractals are everywhere in nature:   a bush by the side of the road, the pattern of electrical discharge in lightning, a piece of broccoli, the shell of a nautilus, frost crystals.. In short, the apparent complexity of natural shapes can frequently and elegantly be described by simple mathematical iterative functions.  For example, the Mandelbrot set is generated by the iteration of the complex polynomial  z_n+1 = z_n² + c. Its plot on the complex plane leads to shapes of breath-taking beauty.

Fractals exhibit self-sameness, i.e. no matter how small or large the "piece" that one observes it always looks the same - or very similar - to the whole.  For example, a florette of broccoli  is essentially a smaller-scale  replica of the entire head.  This is very obvious in a particular variety of broccoli, pictured below.

     

 Romanesco Broccoli

The study of iterative and recursive mathematics goes back centuries.  But widespread study of fractals really took off when personal computers made massive iterative computation and plotting available to everyone. For example, you too can download your very own fractal software here (chaospro).

My first exposure to fractals (though I didn't know them by that name back then) came in graduate  engineering school, when a professor started talking about chaos functions and how they could possibly be used to model and ultimately predict share prices.  I didn't pay attention;  the world was in the the final stages of the oil crisis (Iran hostage era), oil prices were zooming and I was a committed Joe Engineer who cared much more about modeling weight-distribution equations for the products of synthetic fuel reactions.

Oh yes, we engineers would have saved the world, don't ya know, and salvation didn't involve stocks, bonds or mutual funds.  Financial markets were moribund, anyway.

Of course, the bull started its historic run right then, in August 1982, with impeccably contrarian timing.  They say "no one rings a bell at the beginning and the end of bull markets", but that's wrong.  Look at the chart below: markets do ring bells, but most people are too busy listening to the ambient noise, instead.

August 1982: The Bell Tolls For S&P 500

It was around the same time that IBM came out with the PC and Benoit Mandelbrot's work was first noticed by the financial community (he worked at IBM for 32 years starting in 1958).  It was the era of the random walk hypothesis and his fractal formulas were a slap on the face of mathematical economists (not that many took notice).  He claimed that markets weren't random but fractal, i.e. exhibited a complex behavior that could be broken into smaller and smaller self-same bits.  The idea was that  price fluctuations could be described by fractal functions, i.e. they were not random and were, thus, predictable - maybe.  He eventually wrote a book on the subject, The (Mis)behavior of Markets

To the army of academic economists who had religiously staked entire careers (and Nobel  prizes) around the exact opposite notion this was heresy on a grand scale.  The application of fractals to finance looked suspiciously like the hocus pocus of financial astrology, a kind of mathematical alchemy that sought to transmute simple formulas into traders' gold.

On Wall Street itself, marketing and trading departments didn't pay much attention, since they were busy selling "scientific" portfolio management based on the academics' random walk theories.  Their apple cart was hitched to a different, and differently profitable, horse and they saw no need to upset it.

Furthermore, most financial firms did not yet possess the massive computing capacity necessary for fractal calculations.  They were still in the initial stages of stitching together communications and data networks for their day-to-day operations and didn't have the time or resources for fractal mumbo-jumbo.  The age of information had dawned, but it was still early days.

But, things change.  By the late 1980's computers were increasingly used for crude black-box trading (crude by comparison to current practice).  It involved mostly arbitrage between share prices, index futures and options and it is considered the culprit of the October 1987 meltdown. The market was horribly overextended and due for a correction, anyway, but the speed and depth of the plunge took everyone by surprise, myself included.

Left unattended, computer programs kept issuing sell orders for baskets of shares to "profit" from  price discrepancies with index futures. Algorithms saw shares as mere numbers, mathematical data points with no physical correlation to a company's products, plant and equipment, technological know-how, profits, jobs or any other fundamentals.  That's what you get when you mix simple math with the base emotions of fear and greed - and by the time human beings came to their senses the Dow was down 22% in a single day, now dubbed Black Monday.

 The Market Burps on Black Monday, October 1987

In Part II, coming shortly, I shall examine what happened next and how we are now in the completely uncharted seas of Fractal Finance with robotic, high speed trading.

Je T'Aime Moi Non Plus

Remember how just a few weeks ago Frau Merkel and Monsieur Sarkozy locked horns about bailing out Greece and potentially just about everyone else? (I wonder, who will eventually bail out the bailiffs?) . Well... the pair have now decided to put on a brave show of kiss, kiss, no tell - for the good of their Union, you understand.

Photo: WSJ

To symbolize their re-found and re-energized affection for each other, the pair have also chosen a song, once very popular during their more.. how shall we put it... salubrious days.

Take it away, maestro...

From Wikipedia:

Je t'aime moi non plus.. "was originally written for and recorded in 1968 with Gainsbourg's then girlfriend, Brigitte Bardot. However, Bardot pleaded with Gainsbourg not to release their recording of the song: she was married at the time, to German businessman Gunter Sachs. Gainsbourg complied.  Later that year, Gainsbourg met, and fell in love with, English actress Jane Birkin, on the set of their film Slogan. "Je t'aime... moi non plus" was re-recorded with Birkin replacing Bardot, and was released early in 1969".

P.S.  For franco-challenged readers, Je t'aime moi non plus translates to I love you ..me neither.   Wink, wink, nudge, nudge, say no more?

Hell Goes Soft (er)

A note on the new look of Sudden Debt.

Tiffany blue, baby blue.. call it whatever, the new design and colour palette of Sudden Debt is undoubtedly much "softer" than the previous harsh red and black, deliberately chosen over four years ago as a warning to the looming dangers of the credit bubble.  The blog not only sounded but even looked accusatory, as if Sudden Debt was the Spanish Inquisition and yours truly the Torquemada of Debt, committing heretical lenders and borrowers to burn in, well, Hell.

Since then the credit bubble has burst spectacularly and today there is not a soul on this planet who has not heard of sub-prime lending, credit derivatives, sovereign default probabilities, etc.  In other words, Sudden Debt has accomplished the mission of warning about, chronicling and lambasting the Permagrowth culture that was founded on ever-expanding credit and inflating asset prices.  To continue doing so would be akin to beating a dead horse, a function entirely foreign to my outlook and interests in life.

So, where do we go from here?  For one, I believe it is imperative to now make fun of  High Finance instead of continuing to accuse it of malfeasance.  The reason is as simple as Charlie Chaplin's The Great Dictator.  Ridicule is an extremely potent weapon, when used judiciously.

To this end, here are a couple of classic clips from my favourite Brit comedy show, Monty Python's Flying Circus. Watch both, they are quite short.

The Spanish Inquisition, Part One

The Spanish Inquisition, Part Two

They no longer make stuff like this, unfortunately.  Today, we are more apt to shake our heads, shrug our shoulders apathetically and stay put.  May I point out that, in the end, it was ridicule that brought down Tricky Dicky?

A final note: an entire generation has grown up thinking that economics is all about predicting market behaviour.  Even very smart people take this view for granted, instead of pausing to ponder what the word economics actually means.  But then again, they don't think about what democracy means, either. In the age of economics as market analysis, we call it representative democracy, probably because it merely represents democracy instead of being the real thing.

Warren's Grande Bouffe

Today, some comic relief.

The price of a lunch with the Oracle of Omaha, also known - appropriately enough - as Warren Buffett, has soared to $2.63 million.  All going to charity, of course.

In the chart below we can distinguish three periods for this Grande Bouffe: in 2003 David Einhorn, the famous (some would say infamous) hedge fund manager paid $250,100 for his lunch, a whopping tenfold jump from the previous high of $25,000.  Mr. Buffett's days as a cheap date were clearly over.

What's On The Menu?

The price of Lunch (obviously capitalized..) moved briskly upwards after that, reaching over $600,000 in 2007;  but it was in 2008 and Mr. Zhao Danyang's whopper $2.11 million that Warren got to be a serious lunch date.  Mr. Danyang was yet another fund manager, this time from China (where else..?).  I wonder if he got his money's worth?  My bet is that the Oracle kept the subjects limited to the menu and See's Candy (yum).

This year's bidder is anonymous.  Given the massive unpopularity of financiers these days it's just as well.  We don't want voters scandalized any more than absolutely necessary, even if it's for a good cause.

P.S. Do you like the new look?

In Memoriam: Thai McGreivy

Dr. Thai McGreivy, a regular commenter on this blog, passed away on Sunday night after unexpectedly suffering a massive heart attack the previous Monday.

Thai made many friends here;  though I didn't get to meet him face to face, I greatly appreciated and respected his insightful, passionate and often humorous remarks on the issues presented in Sudden Debt.  He was my friend.

For me, his enduring legacy will always be fractals, a subject that I was only vaguely familiar with until Thai explained that our world's complex beauty can be best described through the simple elegance of fractal mathematics.  He used a picture of the Mandelbrot set as his avatar to keep reminding us of the importance of fractals in everyday life.  It wasn't long before I, too, started discovering fractals everywhere, from a bush on the side of the road where I went biking (a passion that we apparently both shared), to persistently similar fluctuations in financial markets.  In fact, I was working on a piece called Fractal Finance when I was told of his untimely passing.

But I will always have a much more personal, emotional and lasting appreciation of Thai.  You see, some weeks ago I presented fractals to Sofie, the love of my life.  Sofie is, among other things, an extremely gifted and talented artist whose paintings are eerily evocative of fractal images.  As soon as she saw the infinite sequence of  images generated by the simple formula  z_n+1 = z_n² + c  tears of joy came to her eyes.  "I have always known of this deep within me" she said, "I am so happy to see it before my eyes.  Thank you so much."

Thank you Thai.  We shall always remember you.

An Image Generated From The Mandelbrot Set

Now Hear This: You Are Evicted From Eden

Homo Economicus is being thrown out of Monetary Eden, a place of previously lush and lazy living on the cheap.  Notice of eviction has been posted at 28o44'N 88o23'W (see below).

Deepwater Horizon Burning In The Gulf Of Mexico

What does money have to do with deepwater-rig oil spills, you may ask?  Pretty simple, really: fiat money debt relies on Permagrowth to keep the game going, i.e. to provide the near-religious belief that debt is currently serviceable and always repayable in the future.  Take Permagrowth away and it all falls apart - unless we manage to give our financial/monetary regime a radical makeover before it's too late.

The fact that we have gone so far as to drill for petroleum (Permagrowth's  fuel of choice) in places and ways that guarantee ecological disasters is proof enough that Permagrowth is unsustainable.  The same can be said for most other resources, from clean water to basic foodstuffs.

From an engineer's point of view, BP (and most other oil and gas companies) routinely drill for oil in such inhospitable locations, obviously without first guaranteeing the quick resolution of serious emergencies.  Is it because they are criminally negligent?  No, I honestly don't think so - they aren't that stupid. 

The simple answer is they can't.  Scarcity of low-hanging-fruit resources means that producers competing for whatever remains MUST cut corners, if they are to bring their products to market at a marginal price that is affordable to an already over-burdened/over-indebted consumer.  Let me put it another way:  all other things equal, what should be the price of fossil fuels if we were to adequately price in spills?  Or  climate change?  Or geopolitical risk? Or lives lost to "police actions"? Or outright wars?

Bottom line: Our fearless leaders have been injecting trillions of fresh debt into the system to prevent it from collapsing from... too much debt.  But the only way to service this debt in perpetuity (once created, all fiat debt is perpetual unless it gets written-off/defaulted) is through Permagrowth.  It's like a dog chasing his tail that keeps getting shorter and shorter.

Well, the Louisiana disaster is another reminder that Permagrowth is over and our days in Monetary Heaven are numbered.

(There is a parallel here with the securitization and derivativization of toxic debt: loan originators had to drill very deep into the pool of potential borrowers to come up with "raw material" to manufacture CDOs, CLOs and other such "products".  What they came up with stank to high heaven, of course, and since they couldn't afford to adequately guarantee their products it wasn't long before the whole thing collapsed.)