MATH IS IN OUR FUTURES
By Leo Melamed

Prize in Innovative Quantitative Applications
CME Center of Innovation
September 21, 2006

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It has to be obvious even to the most casual observer: Math is in our futures.

I mean, right from the beginning in 1898, when we were but the Chicago Butter & Egg Board on Fulton Street, we were inundated with numbers and math. Throughout our early checkered history there were grades, weights, and packaging requirements. For instance, you had to know that a carload of eggs amounted to 750 cases or 22,500 dozen, or that frozen eggs equaled 36,000 pounds packed in 1,200, 30-pound cans; or butter, 40,000 pounds, and so on.

And these specifications were rigorously enforced by the USDA. I mean, one pound or one dozen short and your delivery could be rejected. You might even end up in jail. Unless of course the inspector’s wife or her cousin was by sheer happenstance on your payroll. And if she wasn’t and your name was Sam Schneider, you might stand at the top of the steps and throw the inspector down the stairs rather than let him up into your egg-breaking plant, since you knew his math wasn’t up to the rigors of inspection.

Then there were price fluctuations and their monetary equivalents that you had to know: Shell eggs fluctuated at 5/100 cents per dozen, which was equal to $11.25 based on a carload; pork bellies, as well as turkeys, hams, frozen eggs, and boneless beef, fluctuated at 2.5 cents of a dollar, which was $9.00 per carload, and so on. And, because of the frenzied conditions in the pit, no calculators were allowed—although smoking was permitted since that was a requirement of membership.

Then there were trading limits you had to know, above or below which you could not trade. Except, of course, on the last two days of the delivery month, which had no limit. This was a necessary exception so that the futures and cash prices could converge at maturity. It also served to allow corners and squeezes to reach the full measure of their ill-begotten potential.

This was when corners were rather the norm—often with participation of the board of directors during the so-called “No Math Too Dreadful” era. Once the board invoked the so-called “Math Exception Conjecture,” which allowed onions to go up to a price that rivaled gold and then to come crashing down to below the value of the burlap bags in which they were delivered. This of course resulted in the “Futures Mathematics Prohibition Act” of 1958—which effectively banned onions from futures trade forever. Alas, elected officials are not known for their math skills.

When we launched the currency market in 1972, a revolutionary new set of math and numbers entered our world. Suddenly, a carload—yes, to this day we continue to call them carloads—contained a whole bunch of deutschmarks or yen instead of frozen eggs or eviscerated turkeys, and was worth some $80,000 dollars, a far cry from the numbers the Fulton Street gang was used to. Of course, it took a while for our customers to understand that when we told them we were now dealing in Swiss franc, we did not mean foreign hot dogs. And in the very beginning, the mathematics for our futures prices was based on yet another conjecture. Since no one on the floor was certain of the cash market price in FX, we operated on what was called the “Whatever Morrie Levy Thinks” conjecture.

And again you had to worry about a brand-new set of statistics: Weather, for instance, a highly important variable for chickens and cattle, was replaced by such things as interest rates, inflation, and foreign reserves. A few years later, foreign currency itself morphed into Treasury bills, Eurodollars, and stock indexes, bringing us yet another new math—discount rates, money supply, budget deficits. Then came still another revolution—options. This gadget replaced some of our traditional math verbiage with fancy words: For instance, spoilage became something called time-decay; what we knew as limit down or limit up became volatility; and the CME Pricing Committee was replaced by something called Black-Scholes. Fortunately our traders learned fast—they were, after all, mathematicians at heart.

So if anyone asks why in the world did the Chicago Mercantile Exchange team up with the Mathematical Sciences Research Institute to create a prize for the innovation of mathematical, statistical, or computational methods in the study and behavior of markets, the answer is not simply because President George H. Bush put math on the national agenda for improvement; not simply because U.S. students are ranked fifteenth in eighth-grade math, behind the Slovak Republic; not even because it was the only way to get Myron Scholes to stop nagging about it; but because mathematics, futures, and options are all intertwined. In fact, no one knows for certain which came first.

From the beginning, mathematics arose out of the need to do calculations relating to commerce and taxation. Isn’t commerce the very province of futures? And as far as taxation goes, where do you think the tax straddle was invented?

Math arises wherever there are difficult problems that involve quantity, structure, space, or change. That’s exactly what futures and options are for.

The great Hermann Hess told us, “For mathematicians there is no reality, no good and evil, no time, no yesterday, no tomorrow, nothing but an eternal, shallow, mathematical present.” That’s pretty much how our traders feel about futures!

Math, according to Bertrand Russell, is the subject “in which we never know what we are talking about, nor whether what we are saying is true.” That’s a darn good description of futures and options. And Albert Einstein told us that he didn’t believe in mathematics. Funny, that’s exactly what Warren Buffett recently said about derivatives!

Anyway, let me cut to the chase. Twenty years ago, a little-known conversation took place on the floor of the Merc that is the consequential nexus for today’s event. The conversation was classified by the Intelligence Division of the Commodity Futures Trading Commission—it’s a well-kept secret, but they have one—and embargoed until this very day. It was a conversation between Joe Siegel, a superb pork belly spreader, and Joe Fox, a hog broker whose family lineage dates back to the founders of the Chicago Mercantile Exchange. Alas, both Joes have moved on to the big trading ring in the sky.

They were as different as day and night. One, the son of an Orthodox rabbi, had been a Talmudic student. One month shy of becoming an ordained rabbi, his brother, Sam, convinced him to try his hand in commodities. It turned out Joe had a rare mathematical gift that enabled him to mentally juggle a spreading regime involving four or five different commodities in six or seven different delivery months. He was said to possess three-dimensional proficiency. The other, a German, was one of the nine Fox brothers of the famous Fox Deluxe Foods family that for years dominated exchange politics. Joe Fox did not trade for his own account but as a broker he held thousands of orders in his hand. And it was rumored he knew by heart every price and amount of every order in his deck. Needless to say, the two Joes were friends and, as members of this arcane profession, could peer into the future. That common bond resulted in the following conversation in December of 1986:

“You know what happened today, Joe?” said one Joe to the other Joe.
“Tell me.”
“I know for a fact that today, the board of governors approved Melamed’s black box.”
“Black box?” questioned the second Joe.
“You know, a machine for electronic trade.”
“Oh my God!” exclaimed Joe. “That could be catastrophic.”
“Yes,” the first Joe agreed, “it is bound to bring on algorithmic trading!”
“Much worse,” said the second Joe, “it will prove that if any loop in a certain kind of three-dimensional space can be shrunk to a point, without ripping or tearing either the loop or the space, then the space is equivalent to a sphere.”
“You mean,” said the first Joe, “that anything without holes has to be a sphere!”
“Exactly,” responded the second Joe, “like a three-way butterfly spread between pork bellies, hogs, and the Mexican Peso.”
There was a momentary silence until the first Joe whispered, “My Lord, it’s the end of our world.”

Reading the handwriting on the wall, the two Joes instantly knew that electronic trade would bring on a whole new paradigm of computer applications: things like black box trading, quant trading, programmed trading, and even someday white box trading—systems that may yet disintermediate the human trader entirely. They knew that while in the beginning, our Globex gadget would be only for after-hours trading, it wouldn’t be long before the damn thing would invade their trading day. Because one thing would morph into another and then another. First, the Globex machine would simply export our trading pits to the far corners of the world. Then they would trade side-by-side with open outcry. Then the Merc would allow an open API and it was “Katy, bar the door.

The two Joes understood that eventually financial engineers would build programmable electronic machines that could perform high-speed mathematical or logical operations that assemble, store, correlate, or otherwise process information. That ultimately automated trading strategies could be devised to exploit microtrends in price movements to make a profit faster and better than even they could. That automated strategies could cover the gamut from simple techniques that break down the size of orders for execution, to the very sophisticated mathematical trading models that anticipate volume curves, react dynamically to complex signals, and trade with stealth to minimize impact.

There was no getting away from it. The two Joes knew that it did not really matter who won the philosophical debate as to whether mathematics is created, as in art—or discovered, as in science. Once the Chicago Mercantile Exchange performed the marriage of its markets to an electronic venue, the wizardry of mathematicians and financial engineers would deliver us to the Promised Land.

And there, they expected, Grisha Perelman would be waiting. Thank you.

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