Monday, June 5, 2017

Against The Gods

Our modern understanding of financial risk is built upon work that reaches back thousands of years. Peter L. Bernstein traces this history in his interesting book Against the Gods: The Remarkable Story of Risk. Bernstein avoids overly technical material and looks at the historical figures who made meaningful contributions to the way we think about risk today.

The book begins with ancient forms of gambling and early attempts to understand probabilities. It then covers Daniel Bernoulli’s early attempt to model rational financial decision-making when outcomes are uncertain. Bernstein frequently criticizes Bernoulli’s work as being a poor model of how people actually make choices. But, as I’ve explained before, I see no evidence that Bernoulli was trying to model human behaviour. He was modeling how we should make decisions, not how we actually make decisions.

When Bernstein makes it to Gauss’ contribution, he observes that “The normal distribution forms the core of most systems of risk management,” and “Impressive evidence exists to support the case that changes in stock prices are normally distributed.” But readers of Benoit Mandelbrot and Nassim Taleb needn’t get too excited. Bernstein later explains that when we look at a chart of the sizes of monthly changes in stock prices, there are too many large changes at the edge of the chart and that “A normal curve would not have those untidy bulges.” He concludes “At the extremes, the market is not a random walk.”

In further evidence that stock prices aren’t completely random, Bernstein cites a study of the S&P 500 from 1926 to 1993 by Reichenstein and Dorsett. If stock price changes were independent from year to year, then the variance of multi-year returns would grow linearly with the number of years. However, “the variance of three-year returns was only 2.7 times the variance of annual returns; the variance of eight-year returns was only 5.6 times the variance of annual returns.” This means that good periods tend to be followed by below average years, and bad periods tend to be followed by above-average years.

One comment I couldn’t follow was the assertion that if the market were fully rational, “At any level of risk, all investors would earn the same rate of return.” Is this some mathematical consequence of rational behaviour in the markets even when investors have rational levels of risk aversion, or is Bernstein asserting that risk aversion is irrational? The latter is clearly not true. It is perfectly rational for me to reject a double-or-nothing bet for everything I own. Even if I’m offered an extra $10,000 if I win, I’m still being rational to reject the bet even though it has a positive expectation of $5000.

Even though this book was written in 1996, Bernstein seemed to anticipate the financial meltdown of 2008-2009. “Mortgage-backed securities are complex, volatile, and much too risky for amateur investors to play around with.” They also proved to be too complex for professionals to handle safely.

An unfortunate typo in a discussion of the Fibonacci sequence is likely to leave some readers confused. Bernstein tries to make the point that the ratio of successive terms starting at 5 always begins 0.6... .  Unfortunately, the text says these ratios are always 0.625, which works for 5/8, but fails for 8/13, 13/21, etc.

Overall, I found this book entertaining and enlightening, although it has such breadth that I’m guessing experts could find much to criticize. It is definitely worth reading.

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