Popular Science Pieces and Profiles

"The world is our laboratory"

A Profile of Myron S. Scholes

[This profile was written for Quantitative Finance, where a slightly different version appeared in vol. 3, no. 2 (April 2003), pp. C20--C21. Jacob Bettany, my editor at QF, had the nice idea of using the quote from Prof. Scholes for the title. --- CRS]

It is no exaggeration to say that one of the main reasons a journal like Quantitative Finance exists is the work of Myron Scholes.

The story of the Black-Scholes-Merton model is well-known. Scholes became interested in the problem of derivatives while a Ph.D. student at the University of Chicago. There he had absorbed the main doctrines of Chicago School economics, with its emphasis on rational expectations, efficient markets, the drive towards the efficient frontier, and the utter absence of free lunches. Already fascinated by the problem of pricing, his interest in options was awakened around 1967 by a seminar from a fellow student working on convertible bonds. Shortly afterwards he got his first faculty job at MIT, where he supervised a large number of master's theses, in one of which a student tried to explain data on over-the-counter option pricing using the capital asset pricing model, with less than satisfactory results. There also he made contact with Fisher Black, who was already interested in options, and later with Robert Merton, who brought expertise in continuous-time stochastic processes to the problem of devising hedging strategies.

The central motivation for Scholes was the economic question of studying the efficiency frontier of portfolios --- how to construct baskets of assets with optimal trade-offs between risk and return, and in particular what happened in the limit of riskless portfolios. Surely there was no free lunch here, no large bills lying on the sidewalk to be picked up by arbitrageurs, but what did that imply?

The solution, in hindsight, is wonderfully simple. The proper price to put on an option should equal the expected value of exercising the option. If you have the option, right now, to sell one share of a stock for $10, and the current price is $8, the option is worth exactly $2, and the option price tracks the current stock price one-for-one. If you knew for certain that the share price would be $8 a year from now, the present value of the option would be $2, discounted by the cost of holding money, risklessly, for a year --- say $1. Every $2 change in the stock price a year hence changes the option price now by $1. If you knew the probability of different share prices in the future, you could calculate the expected present value of the option, assuming you were indifferent to risk, which few of us are. Here is the crucial trick: a portfolio of one share and two such options is actually risk-free, and so, assuming no arbitrage, must earn the same return as any other riskless asset. Since we're assuming you already know the probability distribution of the future stock price, you know its risk and returns, and so have everything you need to know to calculate the present value of the option! Of course, the longer the time horizon, the more we discount the future value of exercising the option, and so the more options we need to balance the risk out of our portfolio. This fact suffices to give the Black-Scholes formula, provided one is willing to assume that stock price changes will follow a random walk with some fixed variance, an assumption which "did not seem onerous" to him at the time, but would now be more inclined to qualify.

The formula, presented in the now-famous paper "The Pricing of Options and Corporate Liabilities", had the good fortune to appear shortly after the opening of the first major market for options, in Chicago, where traders rapidly adopted it. It also had the good fortune to go on to become one of the most-cited papers in economics, spawning a whole literature of applications, modifications and refinements. Ironically, when asked to name his least appreciated work, Scholes names a companion paper, also with Black, where they applied the model to empirical data on option prices. (Owing to a quirk of publishing, it actually appeared before the theoretical paper, which may have lessened its impact.)

Starting from an economic issue and looking for a parsimonious models, rather than building mathematical tools and looking for a problem to solve with them, has been a hall-mark of Scholes's career. "The world is our laboratory", he says, and the key thing is that it confirm a model's predictive power. There is a delicate trade-off between realism and simplicity; "tact" is needed to know what is a first-order effect and what is a second-order correction, though that is ultimately an empirical point.

The evaluation of such empirical points has itself become a delicate issue, he says, especially since the rise of computerized data-mining. While by no means objecting to computer-intensive data analysis --- he has been hooked on programming since encountering it in his first year of graduate school --- it raises very subtle problems of selection bias. The world may be our laboratory, but it is an "evolutionary" rather than an "experimental" lab; "we have only one run of history", and it is all too easy to devise models which have no real predictive power. In this connection, he tells the story of a time he acted as a statistical consultant for a law firm. An expert for the other side presented a convincing-looking regression analysis to back up their claims; Scholes, however, noticed that the print-out said "run 89", and an examination of the other 88 runs quickly undermined the credibility of the favorable regression. Computerization makes it cheap to do more runs, to create more models and evaluate them, but it "burns degrees of freedom". The former cost and tedium of evaluating models actually imposed a useful discipline, since it encouraged the construction of careful, theoretically-grounded, models, and discouraged hunting for something which gave results you liked --- it actually enhanced the meaning and predictive power of the models people did use!

Surveying the current scene in finance, especially the great diversification of instruments and the securitization of an immense range of commodities (e.g., energy, bandwidth, even carbon emissions), he remains convinced that the underlying problems of finance and financial theory remain the same. Reflecting the views of the Chicago school, he says that the goal of financial markets is to perform society's task of resource allocation; capital markets, in particular, must "marry" the people who have money to the people who can use it. The goal of finance is to evolve ways to make this work as smoothly as possible --- to match the desires of borrowers and lenders, while reducing the information they need to process. A hundred years ago those costs were so high that it only made sense to use security-style markets for a very limited range of goods --- capital, in the forms of equity and bonds, and very raw factors of production, like undifferentiated farm products and metals. As the transaction costs of market allocation have fallen, so have the informational costs, especially those arising from asymmetric information. This has expanded the range of goods which can be securitized, and the range of securities which can be offered. Crafting new instruments with different properties, especially those relating to risk and the timing of returns, in and of itself reduces the costs that arise from trying to force all means of raising capital for a firm (say) into the form of selling equity, when other structures might make more sense. The proliferation of instruments thus eases the task of making supply and demand meet by requiring fewer trade-offs, and this is true whether the supply and demand are those of capital for mortgages or electrical power. In Scholes's vision, the goal of finance --- the justification for the stochastic integrals and the derivative instruments --- is to simplify decision-making for non-financiers. (One may believe this yet hold reservations about the success of the undertaking.)

Scholes's theoretical contributions have received many honors, outstanding among them, the 1997 Nobel Prize, shared with Merton. (Black had died the year before, and the prize is not awarded posthumously.) Looking to the future, he says that the most promising direction for finance is confronting non-stationarity. Too much current work assumes stationarity, ergodicity, or very weak non-stationarities like mean-reversion. The importance to risk management of properly modeling large shocks is not likely to be lost on a man whose was a partner in the Long-Term Capital Management fund, famously and abruptly undone by just such shocks. But the broader intellectual point goes beyond more or less ad hoc adjustments to deal with occasional shocks and extreme values. Economies are not stationary even to first order, and developing genuinely evolutionary models is essential to actually understanding what markets do. What form non-stationary finance will take, no one can yet say; that it will retain the contributions of Myron Scholes is certain.