Prof. Jayanth R. Varma’s Financial Markets Blog

A blog on financial markets and their regulation

Credit losses and the Mandelbrot parable of the receding shore

During the last year and a half, expected credit losses have always
been around twice the actual credit losses recognized by the
banks. Long ago, banks had recorded only $100 billion of losses and
people estimated that total losses would be $200 billion. Now that a
trillion dollars of writedowns have taken place, estimates of total
losses seem to be around two trillion dollars.

This reminded me of Benoit Mandelbrot’s parable of the
receding shore (“Forecasts of Future Prices, Unbiased Markets,
and Martingale Models”, The Journal of Business,
39(1), 242-255, January 1966):

Once upon a time, there was a country called the Land of Ten
Thousand Lakes … The widest was a sea 100 miles across, the width of
the rth Biggest was 100/√r, so that the smallest
had a width of only 1 mile. But each lake was always covered with a
haze that made it impossible to see across and thus identify its
width. … The people of that land were expert at measuring distances,
however; they also knew all about the computation of averages … They
knew, therefore, that as one of them stood on an unknown shore, he had
before him a stretch of water of expected width equal to 2 miles. He
could very well travel 1 mile to reach the center of “the”
expected lake; but he could never go beyond this point! Suppose,
indeed, that he succeeded in sailing forth to a new total distance
just short of 100/√r miles. In the meantime, the other
shore would have “moved on,” to a new mean distance from
him equal precisely to 100/√r. It is clear therefore that
those Lakes were ruled by Spirits who would never let them be crossed
by a stranger. However far the traveler might sail, the Spirits would
spread the lake ever farther, and the stranger would always remain
right in the middle of water; his boldness should eventually be
punished by death, but all travelers were eventually reprieved by a
special grace.

I learnt more about fat tailed distributions and power laws from
reading Mandelbrot than from reading anybody else (including
Embrechts), and after four decades, the parable of the receding shore
is still perhaps the best introduction to the subject. This parable
also seems to be a good explanation of what is going on today. We are
all now waiting to be “reprieved by a special grace.”


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