Fat Tails Everywhere? Profiling Extreme Returns: Part V

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Everyone talks about fat tails in markets, but how do you model it in an effort to estimate what may be lurking in the future? There are many possibilities, along with lots of statistical baggage. The main challenge is that trying to squeeze reality into one distribution to capture how markets actually work is challenging, to say the least. But the head of global multi-asset strategies at T. Rowe Price outlines a simple and arguably better approach in a new book on asset allocation.

First, let’s briefly review the problem. It’s widely recognized that financial markets exhibit fat tails – a tendency to suffer unusually extreme events that run afoul of expected frequency via so-called normal distributions. Consider the US stock market, based on the S&P 500 Index. Most of the time the returns behave and tend to follow a standard bell curve for the performance distribution. That is, extreme results are rare while most of the gains and losses are clustered around the mean. The trouble, of course, is that in the real world the theoretical normal distribution doesn’t always hold and so extreme results occur more often than a basic statistical model predicts.

One solution is to model returns with a distribution that factors in fat tails – the t distribution, for instance. Other options include using what’s known as Extreme Value Theory, which is a relatively robust methodology for modeling fat tails (see this primer, for example).

But throwing out a normal distribution entirely may not be wise because it’s still a useful tool for modeling market behavior most of the time. Enter Sebastien Page, head of global multi-asset strategy at T. Rowe Price. In a new book, he outlines a simple way to use two or more sets of normal distributions to model fat tail behavior in markets.

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