Risk of Ruin

Compounding only rewards the accounts that are still open. A system with a genuine edge and a beautiful long-run growth rate is worthless to a trader who gets wiped out in month three — because here’s the uncomfortable truth that organizes everything: a positive expectancy does not protect you from ruin. Edge tells you the game is worth playing; risk of ruin tells you whether you’ll still be at the table when the edge finally shows up.

This course climbs the survival ladder in six rungs:

• What ruin actually is — the absorbing barrier (an account too small to keep trading), the classic gambler’s ruin result that even a fair game bankrupts a finite purse, and the paradox that a winning system can still ruin you.
• Expectancy and the edge — the per-trade engine, expectancy = (average win × win rate) − (average loss × loss rate), and the win-rate-vs-payoff-ratio trade-off that lets a system win 35% of the time and still print money.
• R-multiples — the elegant bookkeeping that normalizes every trade to a single unit of risk.
• The classic risk-of-ruin formula — how edge, odds, and the number of units of risk in your bankroll combine into a survival probability that falls exponentially in your capital, with fully worked examples.
• Drawdown distributions — depth, duration, and the dreaded time under water treated not as single numbers but as random variables; the same system run twice gives two very different worst-cases.
• Sequencing risk — without cashflows the order of returns is irrelevant, but add withdrawals and order becomes destiny: a crash in retirement year one ruins you, the same crash in year fifteen barely registers.
• Monte Carlo ruin curves and stops — estimating ruin by brute force, plotting ruin against risk-per-trade, and the stop-loss arithmetic that turns a risk budget into an exact position size.

Master this and you’ll have the survival half of the quant toolkit that Kelly and Monte Carlo only hinted at — sizing positions so a bad month is a flesh wound, not a funeral. A graded final exam closes the loop, because the trader who survives longest, not the one who bets biggest, is the one who gets to compound.