Bridge over ocean
1 November 1980 Financial Analysts Journal Volume 36, Issue 6

The Arc Sine Law and the Treasury Bill Futures Market

  1. Charles Dale
  2. Rosemarie Workman

A long succession of coin tosses in a game in which one person wins if a head turns up, the other if a tail turns up, is analogous to speculation in price movements of a financial asset, where the long investor wins if price moves up and the short investor wins if price moves down. If we predicted that, over the course of these two games, each player would be in the lead about half the time, we would be wrong.

The counterintuitive fact is that the odds overwhelmingly favor one player being in the lead the vast majority of the time. Indeed, each player being in the lead half the time is the least likely outcome. If a coin is tossed every second for a year, there is a 10 per cent chance that the lead will change hands for the last time before the end of the ninth day, remaining in the same hands for the next 356 days.

According to the so-called “arc sine law,” mechanical trading rules applied to price movements in financial assets will result in long periods of cumulative success, but equally long periods of cumulative failure. The long periods of success will tempt investors to apply trading rules to actual decisions. The long periods of failure make it very likely that such application will eventually blow them out of the market.

As long as a trading rule produces a consistent profit over long time periods, its advocates are unlikely to be dissuaded by theoretical arguments about random walks. Such rules will probably be around indefinitely.

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