The Roots of Quantitative Investing
Drinking, Gambling and STIs
Dan diBartolomeo
Northfield and Brunel University
At Boston University, August 2014
Speaker’s Self-Serving Introduction
Page 35
“I turned to a man named Dan
diBartolomeo. Dan is the founder
of Northfield, a collection of math
whizzes who provide sophisticated
analytical and statistical risk
management tools to portfolio
managers.
Dan is an eccentric, bow-tiewearing East Coast surfer with a
photographic memory that revels
in math.”
diBartolomeo and Witkowski
(Financial Analysts Journal 1997)
• Retail fund marketers could “game” the ambiguity in
peer groups
– Call a value fund “growth”
– Call a growth fund “value”
– Both are likely to have performance that is substantially different
than the peer group
– Advertise only the fund that outperformed the peers
• Likelihood that a particular fund would be misclassified
could be explained by observable fund characteristics.
– Not accidental but clearly purposeful
• “The best way to win a contest for the largest
tomato is to paint a cantaloupe red and hope
the judges don’t notice”
Madoff Evaluated
Page 36
“Bernie Madoff was a fraud. And whatever he
was actually doing it was enough to put him
in prison. I knew it was true but it was so
hard to believe.”
Less than one day in early 1999 elapsed
between page 35 and page 36
“The Secret Formula that
Destroyed Wall Street” -- Wired
• “We are so accustomed to disguise ourselves to others that in the
end we become disguised to ourselves”
– Francois de la Rouchfoucald
• The Gaussian Copula
– A mathematical approach to marginal probability densities
– David Li, Journal of Fixed Income (2000)
– Adopted by all rating agencies and major structured product
issuers and guarantors (e.g. AIG) from 2005 onward
– Economic payoffs from a defaulted loan are not normally
distributed
– Results extremely dependent on extremely heroic assumptions
regarding the independence of mortgage borrowers
– Consider the approach of pre-Christian era rabbis
The Oops in Gaussian Copula
• Lack of correlation is a necessary but not sufficient
condition to establish independence for the Central Limit
Theorem
• Consider investing two hedge funds (this example
inspired by Iceberg Risk by Kent Osband)
– The two funds have offices in the same office building
– Each trading day the two fund managers meet for morning
coffee and flip a coin
– If the coin comes up heads, they hold exact same positions
– If the coin comes up tails, they go long and short against each
other
– What is the time series correlation of their returns?
An Older View of Diversification
“Believe me, no: I think my fortune for it
My ventures are not in one bottom trusted
Nor to one place, nor is my whole estate upon
The fortune of this present year
Therefore my merchandise makes me not sad”
Antonio in Shakespeare’s Merchant of Venice
A bit more on the Global Financial Crisis (or
failures of risk management are not new)
In the seminal text on financial
market risk, Against the Gods,
author Peter Bernstein illustrated
the concept of risk with
Rembrandt’s “The Storm on the
Sea of Galilee”.
On March 18th, 1990 this work was
among several priceless paintings
stolen from the Gardner Museum
in Boston. The museum had no
insurance.
We are the problem
The mental features discoursed of as the analytical, are in
themselves but little susceptible of analysis. We appreciate them
only in their effects. We know of them, among other things, that
they are always to their possessor when inordinately possessed, a
source of the liveliest enjoyment.
As the strong man exults in his physical ability, delighting in such
exercises as call his muscles into action, so glories the analyst in
that moral activity which disentangles. He derives pleasure even
from the most trivial occupation which brings his talent into play. He
is fond of enigmas, of conundrums, hieroglyphics; exhibiting in his
solutions of each a degree of acumen which appears to the ordinary
apprehension as praeternatural.
His results brought about by the very soul and essence of method,
have, in truth, the whole air of intuition.
What to Publish?
When we were first drawn together as a society, it had pleased God
to enlighten our minds so far as to see that some doctrines, which
we once esteemed truths, were errors; and that others, which we
had esteemed errors, were real truths. From time to time, He has
been pleased to afford us farther light, and our principles have been
improving and our errors diminishing.
Now we are not sure that we have arrived at the end of this
progression, and at the perfection of spiritual or theological
knowledge; and we fear that, if we should once print our confession
of faith, we should feel ourselves as if bound and confined by it, and
perhaps be unwilling to receive farther improvement, and our
successors still more so, as conceiving, what we their elders and
founders had done, to be something sacred never to be departed
from.
Michael Welfare, The Society of Dunkers
Defining the Investor Utility Function
• Three Views:
"can only be taken as a result of animal spirits - of a
spontaneous urge to action rather than inaction, and not
as the outcome of a weighted average of benefits
multiplied by quantitative probabilities.“
John Maynard Keynes on investor's decisions, 1923
"The age of the computer, systematic analysis, and
rational decision making based on economic theory has
dawned.“
Rudd and Clasing, Modern Portfolio Theory, 1982
"When it is a question of money, everybody is of the
same religion.“
Voltaire (in conversation)
Conceptual Problems in Statistical Tests in
Finance
• The Stephen Hawking Problem
– Why doesn't time work in reverse?
• The Heisenberg Uncertainty Principle
– Only finer detail helps
• The Scientific Method
– The implication of the detached observer
• The search for neatness
– The linear, normally distributed world
Moore’s Law and Quantitative
Finance
• Cheap Computer Capacity
•
– Napoleon with M-16s
– High kill ratio, but does it mean anything
– Data Mining
To clean or not to clean, that is the question?
– Data cleaning beyond your control
– Revised versus reported data
• “Just because we can doesn’t mean we should”
– Dr. Ian Malcolm (Jeff Goldblum) in Jurassic Park
Statistical Problems
• Survival Bias
– The health of 30 year old American males
• Picking the Appropriate Benchmark
– The slow rabbit problem
• Testing on In-Sample Data
– How to always be right
– What In-Sample Tests can do
• Meaning of T-Stats
– Spurious Correlation
Correlation Not Causality
Even trained statisticians often fail to appreciate the
extent to which statistics are vitiated by the unrecorded
assumptions of their interpreters... It is easy to prove
that the wearing of tall hats and the carrying of
umbrellas enlarges the chest, prolongs life and confers
comparative immunity from disease. A university degree,
a daily bath, the owning of thirty pairs of trousers, a
knowledge of Wagner's music, a pew in church,
anything, in short, that implies more means and better
nurture... can be statistically palmed off as a magic spell
conferring all sorts of privileges...
The mathematician whose correlations would fill a
Newton with admiration, may, in collecting and
accepting data and drawing conclusions from them fall
into quite crude errors by just such popular oversights as
I have been describing.
George Bernard Shaw, The Doctor's Dilemma
Market Inefficiencies:
Two Circumspect Views
Say not, "I have found the truth," but rather, "I have found
a truth.“
Say not, "I have found the path of the soul." Say rather, "I
have met the soul walking upon my path."
Kahlil Gibran, The Prophet
“I would never want to join any club that would accept me
as a member.”
Groucho Marx
Parameter Estimation Error
• Validity of parametric statistics
– Mean-Variance utility functions
– The not-so-efficient frontier
• Bayesian statistical adjustments
– “To thine own self be true”
– Bootstrap re-sampling: Monte Carlo or Las Vegas?
“In war, you have the known unknowns
and the unknown unknowns”
US Defense Secretary Donald Rumsfeld
A Perspective on the Era of
Quant Investing
“Between the Second World War to end all
wars, and the Third, which by eliminating
mankind altogether, will actually do the
trick."
Philip MacDonald
The List of Adrian Messenger
We Finally Arrive at Drinking,
Gambling and STIs
• A regulatory innovation in 16th century Italy
• The “Problem of the Points”
• Geralamo Cardano to the rescue
– Typhoid
– Other “cures”
• The “Book on Games of Chance”
– Published 1663
– First modern treatment of probability theory
– Also contained extensive sections on how to cheat at cards
A Parting Apology
If we shadows have offended, think but this and all is mended,
That you have slumb'red here while these visions did appear.
And this weak and idle theme, No more yielding but a dream.
Gentles, do not reprehend. If you pardon, we will mend.
And, as I am an honest Puck, if we have unearned luck
Now to escape the serpent's tongue, We will make amends ere long;
Else the Puck a liar call. So, good night unto you all.
Give me your hands, if we be friends,
And Robin shall restore amends.
Puck, (closing verse)
A Midsummer Night's Dream
William Shakespeare