Ergodicity

Mathematicians of probability give the phenomenon the name ergodicity. It means, roughly, that (under certain conditions) very long sample paths will end up resembling each other. The properties of a single sequence stretching over a vast horizon would be similar to the Monte Carlo properties of an average of many shorter paths. In practice, ergodicity captures the idea that time eliminates the annoying effects of randomness: over the long run, luck evens out, bad outcomes eventually catch up with those who have been temporarily lucky, and genuine skill—or lack thereof—comes to dominate.

History, while unable to lend itself to controlled experimentation the way hard sciences can, is often potent enough to deliver most possible scenarios over medium to long time spans. A janitor who wins the lottery cannot be expected to win another if he lived a thousand years; his long-term state would be that of an ordinary person who rarely wins lotteries. Conversely, someone who is skilled but has suffered from bad luck in life would eventually rise in performance. The lucky fool might have benefited from a random run, but over the longer run he would slowly converge to the state of a less-lucky fool. Each reverts to his long-term properties.

This same logic applies directly to financial track records. Consider the classic exercise: a large initial cohort of managers with an equal chance of making or losing money each year. Purely by randomness, about 3% will show a profit five years in a row. The survivorship bias ensures that we only notice—and anoint—those winners, while the silent majority of losers are forgotten. Yet ergodicity tells us that these celebrated performers are not a breed apart; looking forward, we should expect them merely to break even in any future period. They will fare no better than those of the initial cohort who failed earlier in the exercise. In the long run, their results return to the same mean.

The human resistance to this message can be fierce. When I once told a “Master-of-the-Universe” type that track records were less meaningful than he thought, he found the remark so offensive that he violently flung a cigarette lighter at me. His ego was inflated by the temporary success of his department of “great traders” who attributed their market fortunes to the soundness of their business, their insights, or their intelligence. They subsequently blew up during the 1994 bond market crash. Several years later, it was hard to find any of them still trading—a stark illustration of ergodicity at work.

The key practical takeaway is that a track record, taken in isolation, is neither meaningful nor relevant. We also need to know the size of the population from which the performer emerged. Without knowing how many managers tried and failed, we cannot assess the validity of observed success. If the initial population includes merely ten managers, the survivor might warrant a serious investment. If the initial pool comprises 10,000, the results are indistinguishable from noise. The latter situation is the modern reality: so many people are drawn to the financial markets, trying and failing, that a hot streak by itself is nearly always a fluke. When you meet a manager who puts too much emphasis on their track record, the appropriate response is to have a sudden lunch appointment to rush to.