“Statistics are like a bikini. What they reveal is suggestive, but what they conceal is vital” – Aaron Levenstein

On the 29 of March 1900 at the Sorbonne in Paris a young Ph.D. student was defending his doctoral dissertation titled “The Theory of Speculation”. It was a mathematical treatment of the observed fluctuations of French government bonds and their options. The main conclusions of the study were that:

1. there are no discernible trends in the market
2. the market has absolutely no memory of what it has done in the past
3. the difference of the logged returns are normally distributed

To this date these results still stand as the null hypothesis of modern finance and economics.

In recognition of the great work done the thesis was awarded the insulting grade of {mention honorable} instead of the usual {mention tres honorable}. The student, Louis Bachelier.

In retrospect, perhaps it is not too surprising that Bachelier was treated so shamefully by the academic intelligentsia. After all, at the start of the 20th century everyone still believed that we live in a world that is perfectly predictable and explainable. For Bachelier to come out and make the assertion that financial markets were totally random was close to heresy. It took Einstein, Heisenberg, Schroedinger, Dirac and many other great minds and the development of Quantum Mechanics to finally rid us of the deterministic Newtonian viewpoint.

To the first approximation Bachelier’s theory of market returns fits the observed data reasonably well. However upon closer inspection it becomes obvious that the market marches to a different drummer. Even to this day some people argue that there appears to be some evidence suggesting trends and business cycles, in at least, some segments of the market. Furthermore, Benoit Mendelbrot presented strong evidence that the differenced logged returns are not exactly normally distributed but have rather fat tails. As the recent Asian currency crisis showed us: the market might, or might not, have a long memory, but it certainly has a short temper.

On a quiet afternoon at the University of Chicago in the early 1950’s a Ph.D. student got an idea: could investors target risk and return levels by taking the partial derivatives of the correlation coefficients between the various asset classes. Consistent, systematic application of such procedures could provide investors with a portfolio that that would generate similar levels of return to their existing portfolio, but at a lower level of risk. Initially the idea was received with little enthusiasm. After all, who would be prepared to sit down with pencil and paper and do all the required calculations. Nevertheless, after some early hesitation as to the usefulness of such a model, the student: Harry M.Markowitz, was finally awarded a Ph.D in 1954.

Without the computer revolution that has accrued in the last few decades Markowitz’s mean/variance model would have languished in relative obscurity. However, due to the ubiquitous availability of today’s inexpensive computers with phenomenal processing power and sophisticated software, even the largest monster portfolio problem can be reduced to a tame and purring kitten.

“One of the greatest pieces of economic Wisdom is to know what you do not know” – John Kenneth Gaibraith

The development of Modern Portfolio Theory, the Theory of Efficient Markets, the understanding of risk/return relationships and the importance of portfolio diversification stands as one of the most valuable analytic tools in finance. On Wednesday, October 17, 1990 Markowitz shared the Noble prize in Economics with Merton Miller and William Sharpe. Not bad for an idea that was worked out in one afternoon.

Dated October 1970, a paper titled “A Theoretical Valuation Formula for Option, Warrants and Other Securities” was rejected for publication by the Journal of Political Economy. Soon afterwards the same paper publication was rejected for publication by The Review of Economics and Statistics. Neither journal even bothered to have the paper reviewed. After another three years (May/June 1973) and some minor revisions, the paper was finally published titled “The Pricing of Options and Corporate Liabilties”, authors: Black, F. and Scholes M.

“A man will fight harder for his interest than for his rights” – Napoleon

Armed with their newly formed option pricing formula it took them no time in finding a suitable candidate for their first field test: National General’s new warrants. Using historical data for their parameter estimations it appeared that the warrants were considerably underpriced. Without any further delay they bought a considerable parcel of these warrants, only to watch their prices tumble.

Two facts came out of the exercise. The first being that when estimating volatility it is not a good idea to use historical data, rather one should use the market’s implied volatility. The second, and more important fact: even if one does everything correctly, the market is still a harsh mistress.

Tuesday, October 14 1997 Professor Myron Scholes is formally notified that he is to share this years Nobel prize in Economics with Professor Robert Merton for their contribution to the $50+ trillion derivative market. Although overjoyed by the news, both Professors expressed their sadness that Fisher Black could not have shared their triumph. Black died in 1995 from throat cancer.

What conclusions can be drawn? Perhaps it is that great ideas, like great wines, take years to be truly recognised.

This article was written by Dr. Adam Kucera while a senior quantitative analyst at Commonwealth Bank of Australia.