The title of this column (including the two extra periods) is that of Emanuel Derman’s book, which has the eye-catching subtitle, “Why Confusing Illusion with Reality Can Lead to Disaster, on Wall Street and in Life.” The book has six chapters grouped into three pairs:
I. Models;
II. Models Behaving, and
III. Cohomology of Simplicial Complexes.
Just kidding, of course, your guess is right. One thing that I am confident that you cannot guess based on the title, is that the first chapter is concerned with the author growing up in South Africa as “the accidentally-conceived last child of Jewish parents who immigrated from Poland (now Belarus) to Cape Town in the mid-1930s.” Ten interesting pages are devoted to his membership in Habonim, a coeducational Zionist youth movement, which, he says “left its marks on me, many of them good.”

Large parts of the book are about physics, for examples the puzzles of the positron, which “Dirac found to be a hole in the sea of electrons.” Reading this material made me happy that there aren’t such paradoxical things in probability to make one think deeply about the nature of reality and turn to thinkers like Schopenhauer and Spinoza for help. See the complex network of pleasure, pain and desire on pages 86–87. Most of the book is considerably more fun and filled with interesting quips. Speaking about gravity, Derman says, “Newton was confident that the power of the distance was precisely 2. Had he been a social scientist he would probably have proposed a power of 2.05 ± 0.31.”

Some of Derman’s stories are borrowed from others: Freeman Dyson wrote in his essay Frogs and Birds, “Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizons. They delight in concepts that unify our thinking … Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at a time.”

Derman began his professional life as a physicist, “studying fundamentals and mastering theory. Then in 1985, I migrated to the center of the quant world at Goldman Sachs. My colleagues were as smart as academics but more interesting. Their work was an interdisciplinary mix of modeling, mathematics, statistics, and programming.” Academic experts on finance may think they know what mathematics he is referring to, but when the narrative turns to an event in his academic life at Columbia, we learn that he had to use Google to figure out what “the fundamental theorem of finance was.” I have read the statement he includes on page 141 and can’t figure it out. Google must have grown up since then.

The lack of one familiar fact is more than made up for by the new ones that I saw there. If you haven’t seen Fischer Black’s paper on “Noise” in the Journal of Finance, volume 41 (1986), 529–543, then you should go to JSTOR and read it. Derman devotes a lot of ink to discussion of deficiencies of the efficient market model and CAPM, but perhaps the most persuasive argument is given in the figure on page 184 that compares simulated stock prices to four years of the S&P 500. I almost said that the picture is worth the price of the book, but the picture can be had for the price of one photocopy so that doesn’t make much sense economically.

Of course, at its heart this is a book about models. Derman explains that the widespread shock at the failure of quantitative models in the mortgage crisis of 2007 results from a misunderstanding of the difference between models and theories. Theories describe and deal with the world on its own terms and must stand on their own two feet. Models stand on someone else’s feet. Models try to squeeze the blooming buzzing confusion into a miniature Joseph Cornell box, and then, if it more or less fits, assume that the box is the world itself. Intuition is more comprehensive. It unifies the subject with the object, the understander with the understood, and the archer with the bow.

People expect either too much or too little from financial models. One must begin boldly but expect little. If a little success is actually attained, one must grow greedy. Then when one has gone only a little too far, desist. Derman has more concrete advice, quoting from a Modeler’s Hippocratic Oath that he wrote with Paul Wilmott. The third point is “I will not be overly impressed by mathematics. I will never sacrifice reality for elegance without explaining to its end users why I have done so.”

Wise words and there many of them in the book that I haven’t quoted. At $26 it is a bargain, and I am looking forward to reading his other book, “My Life as a Quant: Reflections on Physics and Finance.”