MATH IS IN OUR FUTURES
Remarks
By Leo Melamed
at the
Inaugural Celebration of the CME-MSRI Prize in Innovative Quantitative
Applications awarded to
Professor Stephen Ross of MIT.
September 21, 2006

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 and 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 5/100cents 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
Franks---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 Bush put math on the national agenda for improvement;
not simply because US students are ranked 15th 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, options, and derivatives 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 Buffet 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 bellie
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 posses
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, programme 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 out-cry. 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 micro-trends 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.
# #
#
Return to top of page | Return
to Index | Home Page
DISCLAIMER:
This page is for information purposes. The information was obtained from sources believed
to be reliable, but no representation is made as to the accuracy or reliability. Neither
the information, nor any opinion expressed, constitutes a solicitation or the purchase or
sale of any securities, commodities, financial instruments or services. Past performance
is not indicative of future. |