# The Paradox of Economic Modeling

January 26th, 2009

The Economist recently issued a “special report on the future of finance.” I’m going to comment on a few of these articles in the coming days.

The section on the failure of mathematical modeling was really interesting.

Benoît Mandelbrot, the mathematician who invented fractal theory, calculated that if the Dow Jones Industrial Average followed a normal distribution, it should have moved by more than 3.4% on 58 days between 1916 and 2003; in fact it did so 1,001 times. It should have moved by more than 4.5% on six days; it did so on 366. It should have moved by more than 7% only once in every 300,000 years; in the 20th century it did so 48 times.

In Mr Mandelbrot’s terms the market should have been “mildly” unstable. Instead it was “wildly” unstable.

Many models assume something close to “normal” distribution.  Mandelbrot’s analysis suggests that the distribution is anything but “normal”.

Models are interesting descriptors, but not necessarily as predictors. Even a reasonably “accurate” model only works until it becomes widely accepted, at which point its assumptions become increasingly divorced from reality. When everyone is using the same model, if the model suggests you should buy, you’ll find there are no willing sellers. The other paradox of modeling, is that if you could accurately ascertain the value of X at some time in the future, the prediction would be invalidated by free market arbitrage:

Assume that the price of a commodity at time T0 \$500/unit. Let’s assume that you know that the price of a commodity will be \$1000/unit at some time (Tf) in the future. Of course, you would like to buy a bunch of \$500/commodity at T0 and hold it until Tf, selling it for a riskless profit.

However, as you begin buying at T0, and as others following that model also begin buying, the price should rise, and as long as there is opportunity for “riskless” profit (i.e., the price at Tf minus price at T0 > opportunity cost) the price will continue to rise until it reaches its limit, the \$1000 discounted for time preference. The process of arbitrage can occur very rapidly in a free and liquid market.

The paradox is this: because you “knew” the future value would be \$1000, the now value is \$1000 and a new future value must be established.

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