Suppose an opportunity has a 60% chance of gaining 50% and a 40% chance of losing 50%. Its expected return is +10%. That sounds like a good bet, and taken once, it is.
But if we expose the entire capital base to it again and again, the compounded growth rate is about −3.3% per round. The opportunity has positive arithmetic expectation and negative geometric growth. Repeat it 100 times and the typical outcome turns $10 million into about $330,000.
Expected value tells us whether an opportunity is worth taking. It doesn’t tell us how much capital to expose to it.
Why a Good Bet Can Lose Money
Gain 50%, then lose 50%, and you’re down 25%, not back to even. The loss lands on the bigger base the gain created, so every swing in value takes something off the top. In this example, that drag is larger than the edge.
The +10% is also an average across many people each taking the bet once. A family doesn’t get that average. It gets one path, in sequence, with each result compounding on the last. At full exposure, the average of all possible paths is pulled up by a handful of extraordinarily lucky ones, while the typical path loses about 97%.
Size Turns an Edge Into Growth
Now change one thing. Expose 40% of capital to the same opportunity each round, hold the rest in reserve, and the compounded growth rate goes from about −3.3% to about +2.0%. Over 100 rounds, the typical path turns $10 million into about $75 million instead of $330,000. Same odds, same payoff, same edge. The only thing that changed was position size.
That 40% is what the Kelly criterion produces for this payoff, the exposure that maximizes geometric growth. Past roughly 78%, the same opportunity shrinks capital again. In real markets we never know the probabilities that precisely, and the penalties for missing aren’t symmetric. Sizing at half the optimum still compounds about 1.5% per round, three-quarters of the maximum. Sizing well above it gives up the capital base. The sizing decision is asymmetric too.
Position Size Is the Output
Real portfolios don’t offer a coin flip with known odds, but the principle carries straight over. Too little risk and the edge doesn’t matter enough. Too much and variance can overwhelm it, create a drawdown we can’t recover from, or force us out before the expectation has enough repetitions to show up.
That’s why we define the risk first. When the evidence supports taking a position, we decide how much capital we’re prepared to put at risk, define the exit, and let those two numbers set the size. If I’m prepared to risk $100,000 and the exit is 5% below entry, that’s a $2 million position.
Ten Positions Can Be One Risk
Then there’s the portfolio. Ten positions each risking 1% add up to 10% of planned risk. If they’re independent, it’s unlikely all ten reach their exits at once. If one market driver moves all ten, they can, and correlations tend to rise exactly when the portfolio is under the most stress. A gap can also carry a price through its exit, so planned risk isn’t the most we can lose. Ten 1% risks tied to the same driver can be one 10% risk.
The compounding math applies here too. A 30% drawdown needs a 43% gain just to get back to even, which is the same drag at the scale of the whole portfolio. That’s why the risk budget answers to the portfolio, not just to each position.
Capital Compounds Geometrically
Expected value matters. But capital compounds geometrically, not arithmetically, and a family lives one path through it. The edge is in finding favorable opportunities and sizing them so we survive the losing sequence and still have enough capital exposed when the favorable side of the distribution arrives.
A positive expected value tells us an opportunity is worth taking. Position size decides whether it ever compounds.
Risk before return. Exit determines outcome.
Mike Shell is the Founder, Chief Investment Officer of Shell Capital Management, LLC, a registered investment adviser, and portfolio manager of ASYMMETRY® Managed Portfolios. This observation is for informational purposes only, reflects opinion as of the date written, and is not investment advice or a solicitation. Past performance doesn’t guarantee future results. All investing involves risk, including loss of principal.