The Workshop · The Math · trading in probabilities · lesson 2 of 10
The same average return, taxed by the size of the swing.
Take a strategy that averages 12% a year and run it three ways: calmly, normally, and wildly. Same average. Watch where each one ends up after twenty years.
The average return is the number in the brochure. What you actually compound at is smaller, by roughly half the volatility squared. At 15% volatility the drag is about 1.1% a year: annoying. At 30% it is 4.5% a year: and a 12% strategy is quietly a 7.5% one. At 45% the drag eats most of the return: you can average 12% a year and end up with less than you started with.
Fact. Geometric growth ≈ arithmetic average − ½ × volatility². This is not a market opinion; it is the arithmetic of multiplying returns together. It is why a leveraged ETF that tracks 3× the daily index can lose money over a year in which the index went sideways.
You stop treating volatility as free. Two strategies with the same average return are not equal; the calmer one compounds more of its average into money. And when you want more return, the honest route is to take a calm strategy and size it up, knowingly, with the bigger swing that comes with size, rather than to take a wild one and hope. The ratio of return to swing is the asset. Size is the dial.
The desk sizes every position to the same daily risk, not the same dollars, a quiet stock gets more shares, a wild one fewer, so that no single name sets the book's volatility. The house book's Sharpe (return per unit of swing) is shown before its return for exactly this reason, and lesson 7 lets you turn the size dial on the real numbers.
Keep this: return per unit of swing is the number; the return alone is the brochure.
The Workshop is education, not advice. Replayed numbers are averages over many trades, after average trading costs (2 bps a side on a stock, 1 on a fund, included for fairness; yours vary by broker and liquidity) unless stated, and are not forecasts; the live record is on the engine page. Analytical tools and historical measurements for educational and informational purposes only; not investment advice or a recommendation. Replayed figures are hypothetical: today's rules applied to past prices, after modelled costs, and no account was traded on them. Hypothetical results have inherent limitations and do not represent actual trading. Past performance, including backtested results, does not guarantee future outcomes. Trading stocks involves substantial risk of loss. About · Support · Terms · Privacy · Refunds Open the deskManualThe EngineChangelog