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 / Spring 2006 / Issue 42(originally published by Booz & Company)


Derivative Wisdom

Idealized Investors
The capital asset model assumes, among other things, an idealized world in which investors are rational and risk averse, and in which they demand higher returns for higher risks. While these conditions are obviously not true in all instances, such assumptions make the model useful in the way that all formal scientific models are useful: It enables analysts to reach conclusions about stock prices and investment strategies that are generally true. The model suggests that larger, more diversified portfolios of stocks are in general less risky than smaller, less diversified portfolios. It even enables analysts to calculate how many different securities would have to be included in a portfolio to achieve diversification (the short answer: at least 15).

The capital asset model took shape when economics and finance were adopting a stylized, mathematical view of the world that built on several strands of earlier economic and statistical inquiry as well as contemporary research. In economics, this view of the world is known as the neoclassical synthesis; people are assumed to act rationally and in their own best interests. In finance, “efficient markets theory” teaches that the price of a stock reflects the market’s rational assessment of its true underlying value at any given moment. The theory suggests why, as some earlier economists and statisticians had noticed, stock prices follow a “random walk” rather than an observable trend. It implies that future stock prices are unpredictable.

The efficient markets hypothesis uses the same kind of stylized assumptions as the capital asset pricing model, but (as Mr. Bernstein notes) the finance professors who tested it on real market data found that it had powerful explanatory properties. In 1969, Harvard professor Michael Jensen published an exhaustive analysis of mutual fund performance over 10 years, from 1955 to 1964. Only 26 of the 115 funds that Dr. Jensen studied outperformed the market; on average, mutual fund investors would have made 15 percent more money if they had held a broadly diversified portfolio of stocks. A wide range of subsequent studies confirmed and amplified this finding for the behavior of markets all over the world and in all subsequent time periods. Apart from the few Warren Buffetts of the world, professional investors and money managers are generally unable to consistently even match the overall market, let alone beat it.

Quantifiable Potential
The most useful single tool that emerged from this theoretical ferment is the Black–Scholes formula for pricing options, developed by Fischer Black and Myron Scholes in the early 1970s, with additional refinement by Robert C. Merton, who had been working on the problem independently. Dr. Scholes was an assistant professor at the Massachusetts Institute of Technology, where Dr. Merton was a graduate student. Dr. Scholes and Dr. Merton were awarded the 1997 Nobel Prize in economics for their work; Fischer Black would have shared it had he not died of cancer two years earlier. Dr. Black had studied physics, social relations, and applied mathematics (in which he had a Ph.D.), then had worked with Mr. Treynor at Arthur D. Little and later became the first “quant” hired by Goldman Sachs. (“Quant” is the colloquial Wall Street name for the relatively new breed of financial specialist who devises sophisticated, computer-based mathematical analyses of prices and options.) He appeared, Zeliglike, in and around the intersections of many of the most profound ideas of modern economics and finance, though he never took a course in either subject.

Determining the right way to price stock options may not seem like a big deal, but it had long eluded financiers, traders, and theorists. For example, one simple and familiar type of “call” option is the incentive stock options companies grant to executives. These give the holder the right to buy a stated number of shares of the company’s stock at a set price, typically the price the stock is trading at when the option is granted, for a specific number of years. But what is the option worth at any given moment? It all depends on the future price of the stock. If the price rises, each option will be worth the difference between the future price and the price at which it can be exercised. If the stock does nothing or declines, the options are worthless. Before Black–Scholes, nobody could really say what an option was worth.

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Modern Finance Resources:
Works mentioned in this review.

  1. Peter L. Bernstein, Against the Gods: The Remarkable Story of Risk (John Wiley & Sons, 1996), 400 pages, $19.95
  2. Peter L. Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street (Free Press, 1992; John Wiley & Sons, 2005), 352 pages, $16.95
  3. Emanuel Derman, My Life as a Quant: Reflections on Physics and Finance (John Wiley & Sons, 2004), 304 pages, $29.95
  4. Perry Mehrling, Fischer Black and the Revolutionary Idea of Finance (John Wiley & Sons, 2005), 392 pages, $29.95
  5. Hersh Shefrin, Beyond Greed and Fear: Understanding Behavioral Finance and the Psychology of Investing (Harvard Business School Press, 2000), 378 pages, $44.50
  6. Lauren Aguirre et al., “Trillion Dollar Bet,” Web site based on the February 8, 2000, WGBH Nova documentary: Click here. 
  7. Wikipedia, the free online encyclopedia edited by its readers: Click here.
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