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The FTX Fiasco, Ergodicity and Something About Coins

The recent FTX developments1 are a stark reminder of the gravitas of managing other people’s money. Unsuspecting wealth evaporated practically overnight. Besides the alleged fraud, the key members of FTX and Alameda Research seem to have misunderstood a concept that has previously led many to similar ruin.

No, not leverage – although that exacerbates the problem – but rather ergodicity, or the lack thereof in markets.

As people rummaged through social media posts looking for missed indications of FTX’s downfall, there were vexing examples of Sam Bankman-Fried (SBF) and the CEO of Alameda (snippet below) misunderstanding the Kelly criterion2 – a special case of ergodicity and a well-known strategy for bet sizing.3

"If you abstract away the financial details there’s also a question of like, what your utility function is. Is it infinitely good to do double-or-nothing coin flips forever? Well, sort of, because your upside is unbounded and your downside is bounded at your entire net worth. But most people don’t do this, because their utility is more like a function of their log wealth or something and they really don’t want to lose all of their money. (Of course those people are lame and not EAs; this blog endorses double-or-nothing coin flips and high leverage.)"

“World Optimization” - Tumblr, 06/20/2021

So what is ergodicity and why does it matter?

The Basics

Ergodicity actually applies to systems more broadly.4 A randomly varying system is said to be ergodic if its expected value and its long-term (i.e., over time) average are the same.

Ole Peters, a thought leader in ergodicity (particularly as it pertains to economics), explains this concept simply in a typical coin-toss experiment5:

Toss a fair coin.
If heads, your wealth increases by 50%.
If tails, your wealth decreases by 40%.
So what happens to your wealth, on average?

20221122-chartIf we take the average across many systems (or players in this case), the expected value (or ensemble / collective average) is a 5% gain per round (50% chance heads * 1.5x + 50% change tails * 0.6x). Notice the plus sign here – this reflects the additivity of the collective expected value.

In contrast, a single individual’s path decays toward 0 (or ruin) with an average 5% loss per round (1.5 * 0.6 = 0.9 = 10% drop over 2 rounds). This reflects the multiplicativity (or geometric growth) of the scenario for an individual – and shows that the system is non-ergodic.

How does this make any sense? The above chart helps visualize the scenario by simulating 100 players (grey lines) over 250 rounds. Although rare, a few players’ winnings are so large (i.e., not losing) that it skews the average (red line) to a gain, while the likelihood of any individual player is a certain loss (median blue line).


Leverage, like with FTX, can exacerbate this perversion of expected value and utility theory without consideration of ruin.6 There is an “optimal” fraction of wealth (the Kelly fraction) that we can apply that contributes to a gain over time, but is based on known expected returns and is not directly applicable to real-life unknowns. Luckily there are applications for embracing non-ergodic assumptions beyond betting strategies.

For our team, we continue to question assumptions, like ergodicity, and harness these realities in our research and portfolio construction. As an example, in The Efficient Frontier Is Not Real: A Case for Lottery-like Assets (September 20, 2022) we demonstrated a method of resampling to create more robust estimations of risk and expected return vs. just using historical returns – as “any replay of the tape would lead evolution down a pathway radically different from the road actually taken."7 Our tendency is to be more tail-aware, as the simple examples here show that drawdowns can significantly impact wealth over time.

On a personal level, it impacts how we should deal with individuals. A client’s risk aversion or fears are probably not “irrational” by utility theory standards but reflect the non-ergodic reality of their situation. Rory Sutherland summarizes this beautifully: “Experience and perception happen at the individual level, and therefore your job is to improve that rather than improve things at the average level.”8

Applying the deep structure of ergodic systems to financial markets is profound. In his book Range, David Epstein talks about this and “thinking outside of experience” and across domains, particularly in “wicked” learning environments.9 The market is certainly wicked and should force us to think more deeply about problems in general. Unfortunately, markets and market players can be wicked in more ways than one.

Important Disclosures & Definitions

1 From $32 billion to criminal investigations: How Sam Bankman-Fried’s crypto empire vanished overnight, CNBC, 11/15/2022; FTX Declares Bankruptcy, Forbes, 11/14/2022

Using the Kelly Criterion for Asset Allocation and Money Management, Justin Kuepper, Investopedia, 08/23/2022

Bigger is Better, Twitter post, Sam Bankman-Fried, 12/10/2020; Ex-Alameda CEO Explored Race Science, ‘Imperial Chinese Harem’ Polyamory, Sander Lutz, Yahoo Finance, 11/15/2022

Ergodicity, Wikipedia, 10/31/2022

Random Multiplicative Dynamics, Ole Peters, Ergodicity TV, November 2021

Leverage Efficiency, Ole Peters and Alexander Adamou, Arxiv, Cornell University, 01/24/2011

Worlds Hidden in Plain Sight: Thirty Years of Complexity Thinking at the Santa Fe Institute, April 2019

A Creative Springboard to a Better Kind of Economics, Ergodicity TV, October 2022

Range: Why Generalists Triumph in a Specialized World, David Epstein, May 2019

Performance data quoted represents past performance. Past performance is no guarantee of future results; current performance may be higher or lower than performance quoted.

AAI000211 01/31/2024

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