Attack the Week (ATW)

March 24, 2024

Sunday Thoughts

Ergodicity is a concept originating from statistical physics but has found applications across various fields, including economics and finance. At its core, ergodicity describes a system's property where, given enough time, the system will cover all possible states or configurations. In a more technical sense, a process is ergodic if its time averages (observing one system over time) and ensemble averages (observing many systems at one point in time) are equal. This means that, over a long period, the behaviour of a single entity will reflect the collective behaviour of many such entities observed at a single point in time.

“Never cross a river that is on average 4 feet deep”

- Nicholas Taleb

Source: Dall-E

Take a simple coin toss game. The result of 1000 people flipping a coin (half will have heads and half will have tails) will be the same as one person flipping the coin 1000 times. This is an ergodic process.

Russian roulette, meanwhile, provides a stark and dramatic illustration of non-ergodicity, where the difference between ensemble averages and time averages reveals profound implications for risk and outcomes. In the classic game of Russian roulette, a revolver is loaded with a single bullet in one of six chambers. The cylinder is spun, the gun is pointed at one's head, and the trigger is pulled. The chance of the bullet firing is 1 in 6, or approximately 16.67%. The sample average of having an 83.3% survival probability doesn’t really matter for an individual playing the game repeatedly, where the probability of survival is ultimately zero.

One of the most cited applications of ergodicity in finance is in the context of the Kelly criterion, which is a formula used to determine the optimal size of a series of bets. If one were to invest, the Kelly criterion would help to decide how much of their portfolio to risk in each investment to maximize the long-term growth rate of their wealth. I have written about it extensively in the Macrobook series.

The concept of ergodicity illuminates the importance of considering the time dimension and repetition of investment decisions. It challenges the traditional mean-variance analysis, which focuses on the expected return and volatility of single investments or portfolios without accounting for the path dependence and multiplicative effects of real-world investing. Ergodicity suggests focusing on strategies that ensure positive outcomes over time, emphasizing the sustainability and survivability of investment approaches rather than just their short-term performance.

The core tenets of a successful approach are, therefore:

1. Understanding Path-Dependence: How wealth accumulates over time depends significantly on the sequence of returns, not just the average return.

2. Avoid Ruin: Adopt strategies that minimize the probability of catastrophic losses, recognizing that recovering from a significant loss requires disproportionately high returns.

3. Consider Time Horizons: Align investment strategies with the time horizon, understanding that risk characteristics can change over time.

4. Embrace Diversification: Diversification can help mitigate non-ergodic risks by spreading exposure across multiple independent opportunities.

These are just a few of the core elements I want to home in as we walk through an entire investment process in the Macrobook series.

We don’t want average returns; we want to be compounding and performing way better than that.

If you are curious and want to be part of the journey, join the pack today.

Let’s now see what the week has in store for us.

Attack!