This result explains why 50% of the people consistently lose money, while 50% consistently win. Let's compare stock trading to coin flipping (tails = loss, heads = gain). Then
- The probability that the number of heads exceeds the number of tails in a sequence of coin-flips by some amount can be estimated with the Central Limit Theorem and the probability gets close to 1 as the number of tosses grows large.
- The law of long leads, more properly known as the arcsine law, says that in a coin-tossing games, a surprisingly large fraction of sample paths leave one player in the lead almost all the time, and in very few cases will the lead change sides and fluctuate in the manner that is naively expected of a well-behaved coin.
- Interpreted geometrically in terms of random walks, the path crosses the x-axis rarely, and with increasing duration of the walk, the frequency of crossings decreases, and the lengths of the “waves” on one side of the axis increase in length.