## Fischer Black: 1938 - 1995

Fischer Black died on 30 August, after a year-long battle with cancer. He was 57 years old. Black was one of the most brilliant economists of the generation.

Black started out as a Ph. D. in applied mathematics, and discovered finance while working at the consulting firm of Arthur D. Little, Inc., in the late sixties. A seminal influence in his transition from applied mathematics to finance was Jack Treynor, who was also at Arthur D. Little at the time. Treynor was one of the co-developers of the celebrated Capital Asset Pricing Model (CAPM). The key insight of the CAPM was that returns on an asset are proportional to beta, which is the sensitivity of the asset to fluctuations in the market index.

Black started working on the CAPM with respect to both empirical and theoretical work. One of the classic works on the testing of the CAPM is the paper

The capital asset pricing model: some empirical testsby Black, Michael Jensen and Myron Scholes from 1972. The methodology pioneered for this testing lives to this day. This paper discovered that low-beta assets seem to be generating ``too high'' returns as compared with that predicted by the CAPM. In characteristic fashion, Black was to explore this idea in two directions - in terms of developing new theories, and in terms of designing a fund which would exploit this anomaly.The greatest phase of his work is, of course, the development of the celebrated Black and Scholes formula which calculates the price of a call option. A call option is a contract that gives the holder a right, but not an obligation, to buy a given security at a specified date in the future at a specified price (called the strike price). If the market price on the expiration date is lower than the strike price, then the option proves to be worthless. The question of how a call option should be priced had been the subject of a long intellectual chase, commencing from the early sixties. Many economists, including Paul Samuelson of MIT, had attacked the problem, from both theoretical and empirical points of view. The team of Black and Myron Scholes intensely worked on this problem from 1968 to 1971, in a friendly competition with a brilliant student of Samuelson's named Robert Merton.

The solution was to demand a new level of mathematical firepower, in the field which has now become known as continuous time finance. The solution worked in two steps. First, the team came up with a differential equation which must represent the price of the option; if the option price failed to satisfy this differential equation, then there was an arbitrage opportunity, where you could earn unlimited profits through a certain position (where you short the option and go long on the stock). Next, they were able to find an analytical closed-form solution to this differential equation. Black's education in applied mathematics may have helped here - this differential equation turns out to have been studied before in physics. In the end, they were left with a simple formula which gave the price of a call option.

This option-pricing formula was a memorable landmark in the history of finance. At a deep level, it created a degree of understanding of options which paved the way for the largescale expansion of options markets. Without the formula, it was an extremely small set of extremely brave people who would have been comfortable with using options in their day-to-day life. After the work of Black, Merton and Scholes, options and option pricing were reduced to simplicity and clarity, and could be routinely taught in MBA programs.

This entire effort marked the beginning of a field, which is known as continuous time finance. Today, these methods are used to value derivative instruments which are wildly complicated as compared with simple options. The entire financial derivatives industry today, which trades in trillions of dollars a year, is built on the mathematical methods which were essentially developed in the early 1970s. Most people that I know in the profession think that the work of Black, Merton and Scholes deserves a Nobel Prize.

Black went on to a professorship at the University of Chicago, and was director of the Center for Research in Security Prices (CRSP) there. He always had a practical streak, and when he was invited to be a partner at Goldman Sachs in 1984, he accepted. He was an unusual, soft-spoken thinker on a Wall Street inhabited by fast talking hustlers. There is a famous story of a presentation by him, to an industry audience, where a smart-aleck kid asked him ``if you're so smart, howcome you're not rich''. Quick as a bullet, Black replied ``if you're so rich, howcome you're not smart?''.

When I look back upon Black's work, I'm struck by the depth of his insight into economics, even though his Ph. D. was in applied mathematics. Apart from the CAPM and continuous time finance, he worked on numerous problems including dividend policy, international trade, business cycles and labour economics. Many migrants into economics emphasise technical tools; but Black's work has always been characterised by a special intuition into microeconomics. His association with industry did not bog down his thinking with institutional details; his work has always had the elegant character of

simplemicroeconomics attempting to understand the world.Fischer Black was one of the great examples of the power of a rational mind in deciphering the universe. His life sets standards which we can all aspire to.

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