The Roots of Quantitative The Roots of Quantitative Investing Investing

Drinking, Gambling and STIsDrinking, Gambling and STIs

Dan diBartolomeoDan diBartolomeo Northfield and Brunel UniversityNorthfield and Brunel University

At Boston University, August 2014At 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-tie-wearing East Coast surfer with a photographic memory that revels in math.”

diBartolomeo and Witkowski diBartolomeo and Witkowski (Financial Analysts Journal 1997)(Financial Analysts Journal 1997)

• Retail fund marketers could “game” the ambiguity in peer Retail fund marketers could “game” the ambiguity in peer groupsgroups– Call a value fund “growth”Call a value fund “growth”– Call a growth fund “value”Call a growth fund “value”– Both are likely to have performance that is substantially different Both are likely to have performance that is substantially different

than the peer groupthan the peer group– Advertise only the fund that outperformed the peersAdvertise only the fund that outperformed the peers

• Likelihood that a particular fund would be misclassified could Likelihood that a particular fund would be misclassified could be explained by observable fund characteristics. be explained by observable fund characteristics. – Not accidental but clearly purposeful Not accidental but clearly purposeful

• ““The best way to win a contest for the largest The best way to win a contest for the largest tomato is to paint a cantaloupe red and hope the tomato is to paint a cantaloupe red and hope the judges don’t notice”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 itMy ventures are not in one bottom trustedNor to one place, nor is my whole estate upon The fortune of this present yearTherefore 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 problemThe 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 CausalityEven 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 allwars, and the Third, which by eliminatingmankind altogether, will actually do thetrick."

Philip MacDonaldThe List of Adrian Messenger

We We FinallyFinally Arrive at Drinking, Arrive at Drinking, Gambling and STIsGambling and STIs• A regulatory innovation in 16A regulatory innovation in 16thth century Italy century Italy

• The “Problem of the Points”The “Problem of the Points”

• Geralamo Cardano to the rescueGeralamo Cardano to the rescue– TyphoidTyphoid– Other “cures”Other “cures”

• The “Book on Games of Chance”The “Book on Games of Chance”– Published 1663Published 1663– First modern treatment of probability theoryFirst modern treatment of probability theory– Also contained extensive sections on how to cheat at Also contained extensive sections on how to cheat at

cardscards

A Parting ApologyIf 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 luckNow 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 DreamWilliam Shakespeare