MATH
IS IN OUR FUTURES
By
Leo Melamed
Prize
in Innovative Quantitative Applications
CME
Center of Innovation
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 & 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, 30pound 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 eggbreaking 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 illbegotten
potential.
This
was when corners were rather the norm—often with participation
of the board of directors during the socalled “No
Math Too Dreadful” era. Once the board invoked the
socalled “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 brandnew 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 timedecay; what we knew as limit down or
limit up became volatility; and the CME Pricing Committee was
replaced by something called BlackScholes. 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 eighthgrade 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 littleknown
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 wellkept 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 threedimensional
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 threedimensional 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 threeway 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 afterhours 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 sidebyside
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 highspeed
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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