The Hindu Business Line : A tribute to a formula born 35 years ago

WHEN a professor of economics decides to narrate the story of "one man's intellectual adventure at the very centre of modern finance", blending in both quantitative finance and financial engineering, to depict the never-ending "human quest to defeat the dark forces of time and ignorance", it is difficult to continue the J. K. Rowling on my desk. So, I hastily bookmark the chapter `The Secret Riddle' and turn to Perry Mehriling's Fischer Black and the Revolutionary Idea of Finance, from Wiley (www.wiley.com), to learn more about the man who was absent at the podium to accept the Nobel Prize in Economics eight years ago, because he had died only two years earlier. Eventually, it was Robert C. Merton who shared the prize with Myron S. Scholes.

At the Nobel Banquet, however, on December 10, 1997, Merton would speak of the bittersweet moment, with he and Scholes greatly missing their friend and collaborator, Black.

"Your Majesties, Your Royal Highnesses, Ladies and Gentlemen," begins the Presentation Speech by Professor Bertil Näslund of the Royal Swedish Academy of Sciences (http://nobelprize.org). "If a Swedish company has to pay $10 million for a machine in six months, it runs the risk that the exchange rate will change. In order to protect itself against a future increase in the value of the dollar, the company can purchase an option with the right, but not the obligation, to buy dollars in six months at a predetermined price," is an example he gives, before outlining the work of "the three young Ph.D.'s connected with the Massachusetts Institute of Technology" on option valuation and the publication in 1973 of the Black-Scholes formula for pricing stock options.

The magical formula moved "almost immediately from the pages of an academic journal to concrete practice at the Chicago Board Options Exchange."

Widely applied, the model finds mention in current news too. Such as, Celestica Inc reporting that estimated fair value of the stock-based options is amortized to expense over the vesting period, on a straight-line basis, and determined using the Black-Scholes option pricing model; a Deloitte's survey reporting that the Black-Scholes model was chosen by 41 per cent of all companies while 11 per cent opted for a lattice model; and the financial report of Infosys mentioning the model in the paragraph on `stock-based compensation'.

Even without the Black-Scholes formula, Fischer would still have been famous for his other works, argues the author, mentioning the wizard's work on pricing commodity futures, bond swaps and interest rate futures (Black-Derman-Toy model), and global asset allocation (Black-Litterman model).

Fischer's fertile intellect also honed in on the theory of money and business cycles, where he mounted a searching critique of macroeconomic orthodoxy, and sketched the beginning of an alternative, informs the book. "Although largely ignored during his lifetime, Black's views anticipated later developments in macroeconomics, including the rational expectations revolution that would win the Nobel for Robert Lucas in 1995, and the real business cycle theory that would win the Nobel for Edward Perscott and Finn Kydland in 2004."

A chapter titled `What do traders do?' narrates how the 1985 presidential address at the American Finance Association went on, for the speaker was Fischer. He stood up and the audience settled for the usual 45 minutes to an hour, writes Perry.

"But after only 15 minutes Fischer sat down. Was he finished? Yes, he was. The audience was stunned, and not just by the unexpected hole now open in their schedule. Fischer's words rang in their heads: `We might define an efficient market as one in which price is within a factor of 2 of value; i.e., the price is more than half of value and less than twice value. By this definition, I think almost all markets are efficient almost all of the time. `Almost all' means at least 90 per cent.'"

One constant that Perry perceives throughout the evolution of Fischer's though was his focus on trading as a game played between active and passive traders, "which is to say between the informed or `news' traders (such as Goldman Sachs) and uninformed noise or `nice' traders (such as Wells Fargo)."

Fischer came to see that the central issue was the price of time, reasons the author.

"Some traders are buyers of time, and others are sellers, and their interaction determines the price of time." Therefore, the problem boils down to conceiving the price of time in an equilibrium setting!

Fischer never took a course in either economics or finance, you learn in the prologue. His "intellectual formation was in physics and mathematics, and his success in finance came from applying the methods of astrophysics".

Perry cites this quote of Fischer: "One of the things I like about doing science, the thing that is the most fun, is coming up with something that seems ridiculous when you first hear it, but finally seems obvious when you're finished."

To outsiders, though, Fischer was "a computer with blood in its veins" because he surrendered himself to the problem he was working on, and allowed it to take control of his interactions with other people, as Perry would explain. "When possessed by a problem, Fischer tended to treat the people around him as little more than data banks for his CPU to query."

His style was also to lay some outrageous notion on the table and then sit quietly while people reacted to it. A useful insight is that "the devious complexity of office politics, whether in academia or business, simply defeated him, and he learned to keep himself out of it as much as he could."

Another practical lesson is about the way he worked, as described by Fischer's colleague at Goldman Sachs: "In going about his research, Fischer made the most of three ordinary tools: pencils, paper, and manila folders.

As ideas played about in his head, he was quick to write everything down, and he kept copies of the material he needed or might need. Then, he filed it all where he could find it and use it. It was a simple, elegant approach that freed his mind to do the work he loved."

Fischer learned the capital asset pricing model (CAPM) from Jack Treynor in the 1960s; they both talked the same language, while everyone else talked economics, remarks Perry. The two had co-authored How to use security analysis to improve portfolio selection. By demonstrating how to blend traditional security analysis techniques with the new CAPM, they provided a framework that was to transform investment management over the next three decades.

"In the world of CAPM, people with low tolerance for risk hold only a fraction of their wealth in the stock portfolio and the rest in safe assets, so that the return on their overall portfolio won't vary much," is a short primer on the model from Perry. But the real world is different, and Fischer had three reasons to offer: "Costly information, costly management, and costly selling, all frictions that cause the real world to deviate systematically from the ideal."

The chapter titled Tortuous Economic Intuition introduces readers to the making of the Black-Scholes option pricing formula.

A few snatches that can help you feel the mood: "Black pulled from his file a single sheet of paper containing the differential equation he had derived, and they began to work together... Scholes brought his own approach to the problem in a number of dimensions. For one, whereas Black's approach was to look for an appraisal price (what the price should be), Scholes naturally approached the problem from the perspective of speculative arbitrage."

Interestingly, Scholes was attracted to the analysis of Case Sprenkle, a graduate student at Yale who had come up with an incomplete formula for the options price containing parameters that he estimated from the data. "Having this proto-formula in mind, Black and Scholes achieved the key breakthrough by thinking not about what had to be in the formula but rather about what had to be absent from it."

Black and Scholes went public with their formula and the proposed application to securities valuation at a conference organised at MIT on July 27-29, 1970.

Disappointingly, it was when the pair tried to get their result published in economic journals that they discovered how low finance ranked for economists. "In the fall of 1970 their paper was rejected in short order by both the Journal of Political Economy and the Review of Economics and Statistics, in both cases without even being sent out for referee report," recounts Perry.

"The editors saw the contribution as a narrow technical one at best, but also not really economics, and hence not even worth considering."

At the memorial service for Fischer in October 1995 it was "a veritable who's who of the financial revolution" in attendance. Treynor was philosophical.

He said, "For most people, ideas scarcely exist until they are reduced to symbols — to words or mathematics. But Fischer's greatest contributions were in a far country beyond symbols.

"For him research meant abandoning the comfortable, familiar forms rather than merely refining or extending them — letting go of the old, in order to grasp the new. Research was a lonely journey into that far country — a journey from which one can never really go home again."

Alethea, Fischer's eldest daughter, spoke last, and she remembered her dad as one who worshipped at the altar of logic, "but at his desk he sought the sublime, and found it".

Find Fischer Black... , a must-read for the weekend, as a tribute to a formula that was born 35 years ago.

Economics@TheHindu.co.in

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A tribute to a formula born 35 years ago