The Ergodicity Problem: Why “Average” Returns Are a Lie
The Ergodicity Problem: Why “Average” Returns Are a Lie
If 100 people play Russian Roulette, 83% survive. If 1 person plays it 100 times, 0% survive. Why avoiding “Zero” is the only rule that matters.
Executive Summary
- Ensemble vs. Time:
Ensemble Probability: The average outcome of a group at a specific moment. (e.g., “The stock market returns 10% on average”).
Time Probability: The outcome of one individual over a long period.
🚨 Crucial Truth: Finance is NOT ergodic. The group average does not apply to your single life trajectory if you hit a “absorbing barrier” (Ruin/Bankruptcy). - The Volatility Tax: A portfolio that goes +50% then -50% has an arithmetic average of 0%. But in reality, $100 → $150 → $75. You lost 25%. Volatility eats wealth. “Average Return” hides this destruction.
- Survival First: To capture the market’s long-term compounding, you must fundamentally remove the risk of going to zero. Once you hit zero, you can never compound again. This is why Tail Hedging and Barbell Strategies are not “costs,” but “survival fees.”
The Russian Roulette Analogy
A banker offers you $10M to play Russian Roulette (1 bullet, 6 chambers).
Ensemble View: “5 out of 6 people become rich! Positive Expected Value!”
Time View: If you keep playing, your probability of death approaches 100%.
Lesson: Never take a risk that can end the game, no matter how high the potential reward.
Mechanic: Arithmetic vs. Geometric Reality
Survival
Prerequisite
Absorbing
Barrier (Zero)
Compound
Geometric Mean
Non-Ergodic
Real Life
Simulation: The Cost of Volatility (Start Capital: $100)
Scenario: Win 50% / Lose 40% (Repeated)
| Feature | Ensemble Perspective (Theory) | Time Perspective (Reality) |
|---|---|---|
| Definition | Average of all parallel universes | Average of your single timeline |
| Ruin Impact | “1 person bankrupt implies 99 others are fine” | “If I go bankrupt, my game is over” |
| Goal | Maximize Expected Value (EV) | Maximize Geometric Growth (CAGR) |
“Markets allow you to borrow money, but they do not allow you to borrow time. Once your capital hits zero, no amount of future ‘average returns’ can save you. Survival is the only alpha.”
Essential Resources
INTERNAL
BMT Playbooks