The finance and economic worlds are not ergodic. Got it. This is a very important concept especially when we are faced with highly uncertain events. This concept should be getting more attention and investors should appreciate what this means at a high level.
It can best be explained through a simple example. Play Russian roulette with one bullet and a six-chamber gun. The odds of getting shot are 1 out of six. If a thousand-person sample repeats the process, the likelihood of being shot will be the sample average. However, if you played the game 1000 times is a row, you would be shot well before you reached 1000 tries.
It can best be explained through a simple example. Play Russian roulette with one bullet and a six-chamber gun. The odds of getting shot are 1 out of six. If a thousand-person sample repeats the process, the likelihood of being shot will be the sample average. However, if you played the game 1000 times is a row, you would be shot well before you reached 1000 tries.
An ergodic process would have the same result cross-sectionally versus through time. The expectational average and the time average will give you the same result. No difference. Yet, in finance, economics, and gambling, most systems are non-ergodic. While there may be only a 4% chance of company bankruptcy in any year, the likelihood of going bankrupt over 20 years is much greater than 4%. Ergodicity is one of the important concepts that drive the views of Nassim Taleb.
Thinking through ergodicity is especially important when discussing risk. For example, wealth is not ergodic. An investor may believe that the growth of his wealth has some expected value given an average return, but if we walk through time, wealth can go to zero even though we have a positive expected value. A gamble may have a positive expected value, but you may go bankrupt without getting that expected gain. Risk through time is path dependent, and there is an absorption barrier, bankruptcy. Consequently, thinking about growth of wealth is as important as thinking about expected return. These concepts are well-explained by Ole Peters in his work, Ergodicity Economics.
I am not presenting the subtly of this work justice, nor am I presenting all of the implications relative to current thinking on risk and utility. The focus is on the simple concept that economic systems are path dependent. Wealth is sensitive to paths and you can lose everything even for positive bets if you play the game over time. The real world can be painful because we don't get the benefit of large samples of repeated play. Ole Peters says it nicely, "Ergodicity takes the story out of history."
I am not presenting the subtly of this work justice, nor am I presenting all of the implications relative to current thinking on risk and utility. The focus is on the simple concept that economic systems are path dependent. Wealth is sensitive to paths and you can lose everything even for positive bets if you play the game over time. The real world can be painful because we don't get the benefit of large samples of repeated play. Ole Peters says it nicely, "Ergodicity takes the story out of history."
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