Mandelbrot and Hudson trace a common modeling foundation through portfolio construction, capital-asset pricing and option valuation, arguing that a misspecified price process can propagate into several different financial decisions.

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The Black-Scholes formula permitted the same frequent recalculations of value that the market itself did. It also, to be manageable, had to assume away all kinds of complications, Black later recalled. For instance, they followed Markowitz, Sharp, and Bachelier in assuming that a stock's risk, or volatility, can be gauged by the bell curve standard. Black and Scholz started talking their ideas out with another MIT colleague, Robert C. Merton. He was a Columbia engineering undergraduate, a Caltech master's student in applied mathematics, and then an MIT economist, and he was bit badly by the markets bug. As a grad student, he would rise early to get down to the local brokerage house for the opening of trading. Only after a few hours of watching the tape and placing his bets would he go to class. Now at MIT, as an assistant to Samuelson, Merton was also working on the options problem and made some useful mathematical suggestions to Black and Scholes.

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Bigger is better. the academics themselves turned from disparaged outsiders to valued insiders many joined or became consultants to big financial houses some sharp markowitz shoals and merton received no bells the whole edifice hung together provided you assume baccaliere and his latter-day disciples are correct variance and standard deviation are good proxies for risk as markowitz posited provided the bell curve correctly describes how prices move. Sharpe's beta and cost of capital estimates make sense, provided Markowitz is right and, in turn, Bachelier is right and Black-Scholes is right. Again, provided you assume the bell curve is relevant and that prices move continuously. Taken together, this intellectual edifice is an extraordinary testament to human ingenuity. But the whole is no stronger than its weakest member. The crash of October 19, 1987, took many by surprise. On one day, the Dow plunged 29.2%. Something was wrong. The academics said that fall should not have happened.