Excerpt

Let’s say I offer you the following gamble: You roll a die, and if you throw a six, I will give you one hundred times your total wealth. Anything else, and you have to give me all that you own, including your retirement savings and your favorite pair of socks. I should point out that I am fantastically rich, and you needn’t worry about my ability to pay up, even in these challenging times. Should you do it?

The rational answer seems to be “yes”—the expected return on your investment is 1,583⅓ percent in the time it takes to throw a die. But what’s your gut feeling? Perhaps you are quite happy with your present situation; maybe you own a house and a nice car and a private jet—would you be one hundred times happier if you were one hundred times richer? And how much less happy would you be if you suddenly had nothing?

This example illustrates a common flaw in thinking about risky situations, one that can make us blind to excessive risks and which appears to have been a factor in the financial markets in recent years. As we will see, the calculation of the enormous expected return essentially assumes that you have dealings with parallel universes. Consequently, financial models can fall prey to the assumption that traders will regularly visit the parallel universe where everything comes up sixes. An analysis of risk and return that prohibits such eccentricities gives rather different answers. We will start with an outline of the classical treatment of risky problems, then offer an alternative, and finally discuss the practical consequences of both perspectives.

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