Beyond the Average: Mastering the Hidden Mathematics of Compounding
A unified framework for leveraging Skewness, Ergodicity, and the Power Law.
Posted on December 15, 2025
Investing is rarely a problem of asset selection; it is a problem of mathematical categorization. Most portfolio failures stem from a “Category Error”: treating a volatile asset that requires harvesting as a compounder, or treating a durable compounder as a trade.
This framework proposes a wealth architecture segmented into functional ‘Buckets.’ While the market as a whole is governed by the same forces, different assets express these forces differently.
Therefore, we do not group assets by sector or geography. We group them by their Dominant Mathematical Nature:
Bucket 1 optimizes for Optionality (breaking path dependency, avoiding ruin).
Bucket 2 optimizes for Skewness (capturing the unpredictable 4% that drive all market wealth).
Bucket 3 optimizes for Ergodicity (durability over time).
Bucket 4 optimizes for The Power Law (asymmetric upside).
By matching the strategy to the math, we avoid the fatal error of treating a Power Law asset like a Compounder, or a Compounder like a Trade.
I. THE THEORETICAL FOUNDATION
Before defining the buckets, we must clarify the forces at play.
1. Skewness (The Bessembinder Law)
Hendrik Bessembinder’s research demonstrated that stock market returns follow a Positive Skew.
The Reality: The median stock underperforms Treasury bills. A tiny minority (approx. 4%) generates the entirety of the market’s net wealth.
The Implication: In a concentrated portfolio, the statistical probability of picking a long-term loser is high. And predicting which stocks will be in the 4% is virtually impossible.
2. Ergodicity (The Risk of Ruin & The Time Problem)
While Bessembinder defines the distribution of returns (the terrain), Ergodicity defines the experience of the investor (the path).
The Ensemble Average: If 1,000 investors play a game once, the group may show a profit.
The Time Average: If one investor plays that game 1,000 times, they may go bust.
The stock market is Non-Ergodic. The volatility drag (variance drain) ensures that your personal compounded return will be lower than the asset’s average return. In a non-ergodic system like the stock market, the path matters more than the average.
The Trap: If you hit zero (total ruin), you cannot play the next round.
The Drag: Even without total ruin, a significant crash forces you to spend years recovering just to get back to “even,” killing your compounding speed.
Example: The Downhill Skier
Think of investing like a downhill ski race.
The Goal: To reach the bottom (financial freedom) as fast as possible.
The Trap: If you ski out of control to maximize speed, you risk hitting a tree (The “Absorbing Barrier”).
The Reality: If you crash, your average speed for the race drops to zero. It doesn’t matter how fast you were going in the first sector.
The Conflict: Speed vs. Completion
To win the race, you must balance Speed (Returns) with Survival (Risk Management).
Deeply Non-Ergodic (Bucket 4): This is skiing a “Double Black Diamond” run at full speed. One wrong move results in a wipeout. It requires intense focus and “brakes” (Harvesting).
Near-Ergodic (Buckets 2 & 3): This is a groomed run. You can maintain a high average speed with a very low probability of hitting a tree.
The Translation: This is the mathematical proof behind the racing adage: “To finish first, you must first finish.” Warren Buffett’s Rule #1 (“Never lose money”) is simply a command to prioritize finishing the race over momentary speed.
BUCKET 1 — CASH
The Infinite Option
Function
To preserve optionality, break path dependency, and avoid ruin. Cash is not a “dead” asset waiting to be deployed—it is a perpetual call option with no expiration date.
Mathematical Nature
Path-Breaking: Cash prevents forced selling during drawdowns. It ensures you are never a forced seller at the worst possible moment.
Ruin Prevention: Cash is the buffer that keeps you away from the Absorbing Barrier. It guarantees you live to play another round.
Uncorrelated: Cash has no counterparty risk, no volatility, no dependency on market sentiment.
Optionality: The true return of cash is not its yield—it is the IRR of the opportunities it allows you to seize when others cannot.
Management Rule
Strategic Patience.
Cash is not idle; it is waiting. It is the weapon of patience—and patience is the ultimate competitive advantage.
The Axiom: Cash earns its return not by what it yields, but by what it enables—and what it prevents.
BUCKET 2 — THE INDEX
Systemic Survival & Skewness Capture
Function
To guarantee exposure to the economic system’s average return without the risk of individual ruin—and to automatically capture the unpredictable 4% of super-winners that drive all market wealth.
Mathematical Nature
Ergodic: The index survives over time.
Self-Cleansing: It systematically deletes losers (Left Tail) and adds winners (Right Tail).
Skewness Capture: It automatically owns the “Bessembinder 4%” without requiring prediction. Since no one can reliably identify which stocks will be the super-winners in advance, the index solves this problem structurally.
Management Rule
Passive Buy & Hold.
Zero Optimization.
The Axiom: The Index is not designed to be intelligent. It is designed to be immortal—and to guarantee you own the winners you could never have predicted.
BUCKET 3 — THE COMPOUNDERS
The Engine of Wealth Creation
Function
To generate wealth through Endogenous Growth: retained earnings reinvested at high rates of return over long durations.
Mathematical Nature
Effectively Ergodic: While individual stocks carry risk, high-quality compounders possess such durability that the “absorbing barrier” (bankruptcy) is statistically negligible.
Time-Dominant: The return is driven by the duration of holding, not the variance of price.
Structural Criteria
A valid Compounder must demonstrate:
High & Sustainable ROIC: Evidence of a moat.
Reinvestment Runway: Ability to redeploy capital internally (Organic Growth > Financial Engineering).
Low Volatility of Operations: Cash flows are predictable, rendering stock price volatility essentially “noise.”
Management Rule: Buy & Monitor
In this bucket, Volatility Harvesting is a mathematical error.
Selling a compounder to “lock in profits” interrupts the exponential curve. The tax paid and the friction incurred permanently lower the terminal wealth.
The “100-Bagger” Clarification
The rare 100x outcomes are not a separate category. They are the extreme, a-posteriori expression of Bucket 3 when durability and reinvestment persist long enough for both earnings growth and multiple expansion to compound.
A “100-bagger” is simply a Bucket 3 asset that was:
- Mathematically valid (Compounder).
- Held for a sufficient duration.
- Not interrupted by the investor.
BUCKET 4 — THE AMPLIFIERS
Capital Acceleration
Function
To accelerate capital growth by exploiting Volatility, Convexity, and Individual Skewness.
Mathematical Nature
Non-Ergodic: High risk of ruin. High volatility drag.
Bessembinder Dominant: The majority of these assets will eventually mean-revert or fail; a few will deliver asymmetric returns.
The Role of Volatility Harvesting
Because these assets are Non-Ergodic, “Buy & Hold” is dangerous. The volatility acts as a tax on compounding.
Therefore, Harvesting is Structural.
We systematically trim excessive deviations (Right Tail events).
We recycle that “fragile paper wealth” into “anti-fragile assets” (Buckets 1, 2, or 3).
Management Rule
Aggressive Rebalancing.
Tax as Insurance: Capital gains tax is the premium paid to insure against the asset returning to zero.
Zero Attachment: An amplifier is not a pet; it is a utility.
II. THE CRITERIA OF UNTOUCHABILITY
When does a Bucket 3 asset earn the right to be held forever, regardless of valuation or volatility? This occurs when the Investor becomes a greater risk to the compounding process than the Asset itself.
A stock becomes “Untouchable” when five conditions accumulate:
- Invariant ROIC: Return on Capital remains high across multiple economic cycles.
- Frictionless Reinvestment: The company absorbs massive capital without diluting returns.
- The Moat Paradox: The larger it gets, the stronger it becomes (Network Effects/Scale).
- Non-Existential Volatility: Daily price swings no longer threaten the portfolio’s survival.
- Inverted Asymmetry: The risk of selling (tax friction + opportunity cost + error in re-entry) mathematically exceeds the risk of holding.
The Intervention Risk:
At this stage, the primary cause of compounding failure is Interruption Risk—the human urge to “do something.” Inaction becomes a strategic competence.
III. THE GOLDEN RULE OF THE SYSTEM
Functional Integrity
A portfolio fails when assets are forced into roles they cannot perform.
An asset destined to be Harvested (Bucket 4) will rarely become a 100-bagger.
An asset destined to Endure (Bucket 3) must never be optimized via trading.
Final Synthesis:
Bucket 1: Break Path Dependency. The Infinite Option.
Bucket 2: Survive the System. Capture the Unpredictable 4%.
Bucket 3: Let Time Create Wealth.
Bucket 4: Accelerate without Ruin.
Wealth does not come from what you optimize. It comes from what you identify correctly—and then leave alone for a very long time.