Asymmetric risk

If decision-makers cannot take responsibility for their own decisions, there will be more black swans.
To understand asymmetric risk, we first need to know about ergodicity and non-ergodicity.
Ergodicity is a key property in dynamical systems or statistical mechanics, referring to a system where the time average equals the ensemble average (i.e., the statistical average of all possible microstates) over long-term evolution. Non-ergodicity is the opposite.
Imagine a gambler participating in a "fair" gambling game (e.g., roulette or a fair coin toss) with the following rules:
• Each bet: The gambler has a 50% chance to win $1 and a 50% chance to lose $1 (long-term expected return is 0).
• Two observation methods:
. Ensemble average (statistical average): Assume there are "countless parallel universes of gamblers," each playing 100 rounds of the game, and calculate the average return of all gamblers after 100 rounds. Since the game is fair, their returns will fluctuate around 0, with the long-term average approaching 0.
. Time average (single gambler): Observe the same gambler playing 100 consecutive rounds and calculate their net return (e.g., winning 30 rounds and losing 70 rounds, net return = 30×1 + 70×(-1) = -40).
Ergodicity analysis
• If the game is ergodic: After a single gambler plays enough rounds (e.g., 100,000), their time-average return (final net return/total rounds) will approach the ensemble average (0)—meaning, in the long run, they neither gain nor lose overall.
• But in reality, gambling is non-ergodic! Even if the game is fair (ensemble average = 0), a single gambler's time average may permanently deviate from 0 (e.g., losing 100 rounds in a row and going bankrupt, unable to continue). More critically, the gambler cannot "traverse" all possible states by repeating the game infinitely—because once bankrupt (entering a "negative return" state), they can no longer experience the possibility of "positive returns." In other words, a single gambler's trajectory is confined to a subspace of "limited funds" and "bankruptcy risk," unable to cover all possible return paths (e.g., "win first, lose later" or "lose first, win later" combinations).

• If the game is ergodic: After a single gambler plays enough rounds (e.g., 100,000), their time-average return (final net return/total rounds) will approach the ensemble average (0)—meaning, in the long run, they neither gain nor lose overall.
• But in reality, gambling is non-ergodic! Even if the game is fair (ensemble average = 0), a single gambler's time average may permanently deviate from 0 (e.g., losing 100 rounds in a row and going bankrupt, unable to continue). More critically, the gambler cannot "traverse" all possible states by repeating the game infinitely—because once bankrupt (entering a "negative return" state), they can no longer experience the possibility of "positive returns." In other words, a single gambler's trajectory is confined to a subspace of "limited funds" and "bankruptcy risk," unable to cover all possible return paths (e.g., "win first, lose later" or "lose first, win later" combinations).
Conclusion: The ensemble average of fair gambling (statistical results of all gamblers) may appear reasonable, but a single gambler's time average (actual experience) can be entirely different—this is the essence of non-ergodicity: long-term individual behavior does not equal group statistical averages. Through this example, we can relate it to reality: long-term stock market returns trend upward, but for individuals, a single misstep can mean exiting the market forever. Warren Buffett's famous saying—"Rule No. 1: Never lose money. Rule No. 2: Never forget Rule No. 1"—makes perfect sense here.
In the real world, many decision-makers make decisions with asymmetric risk, leading to tail effects. Take the stock market as an example: some people recommend stocks they themselves own—this is symmetric risk. If they recommend stocks they don’t own, that’s asymmetric risk. If someone puts themselves at risk, their words carry much more credibility.