The gap between a series' average return and its compounded return, which grows with volatility; losses need larger gains to recover.
A 20% loss requires a 25% gain to get back to even; a 50% loss requires 100%. This asymmetry means a volatile path compounds to less than a smooth one with the same average.
A useful approximation is compound return is about equal to average return minus half the variance. An asset averaging 10% with 30% volatility compounds at roughly 10% - 0.5 x 0.30^2 = 5.5%. The same 10% average at 10% volatility compounds at about 9.5%.
The practical consequence is that reducing large losses can add more to long-run wealth than adding to large gains, which is the arithmetic case for position-sizing and max-drawdown limits. It is also why levered products that reset daily can lag a multiple of their index over time.
Original diagrams for the ideas on this page. Illustrative, not real market data.
Equity curve and drawdown. An account balance plotted month by month. The fall from the $16,000 peak to the $12,000 trough is a 25% drawdown, and the shaded area lasts until the balance climbs back to the old peak.Working out a position size. Three numbers decide how big a trade is: the account, the share of it put at risk, and the distance from entry to stop. One percent of $25,000 is a $250 budget, and a $0.50 stop divides into that 500 times.
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