How much to bet: Kelly, risk of ruin and time in the market

Take two traders, give them the same strategy with the same signals — and let each choose just one number: what percentage of capital to bet per trade. In five years, one multiplies the account, the other ends at zero. No difference in logic, no difference in data; only bet size. Position sizing is the most underrated decision in systematic trading — and the only one entirely under your control.

Kelly: the mathematics of the optimal bet

The question “how much to bet” was settled mathematically in 1956 by John L. Kelly at Bell Labs — curiously, in a paper about information transmission, not markets. For a repeated bet with win probability W and a ratio of average win to average loss R, the optimal fraction of capital is:

f* = W − (1 − W) / R

Example: a strategy wins 55 % of the time (W = 0.55) and the average win is 1.5× the average loss (R = 1.5). Then f* = 0.55 − 0.45/1.5 = 0.25 — Kelly says bet 25 % of capital. This f* maximizes the long-run geometric growth rate — no other constant fraction compounds capital faster. Edward Thorp carried the formula into practice: first beating blackjack with it, then Wall Street.

Why nobody sane bets full Kelly

The Kelly curve has an unpleasant shape. To the left of the optimum you grow more slowly, but more calmly. To the right of the optimum growth declines — and beyond twice f* you lose money in the long run even with a winning strategy. An overbet winning wager is a losing wager; volatility eats more than the edge earns.

And there is a second, more practical problem: you do not know W or R. You only have estimates from a backtest — and as we wrote about overfitting, estimates from history tend to be systematically inflated. A Kelly computed from embellished numbers sits to the right of the true optimum — precisely in the zone where winning turns into losing. Hence the craftsman's rule: bet a fraction of Kelly. Half Kelly keeps roughly three quarters of the growth rate at roughly half the volatility — and, above all, creates a cushion against estimation error. Quarter Kelly is common for strategies with a short history.

Size for the left tail, not the average

Kelly assumes you know the distribution of outcomes. But markets have fat tails — the extreme day arrives more often than the textbook allows. The practical consequence for sizing: position size is dimensioned by the left tail of the distribution, not by the average trade. The question is not “how much do I usually make”, but “what happens to the account when the fifth percentile arrives — and do I survive it?” Ruin is an absorbing state: zero does not compound. That is exactly why we read results as Monte Carlo distributions — sizing is set against the worst-case boundary we see there.

Guardrails set in advance: when a strategy is switched off

Risk of ruin, moreover, is not a one-off calculation at deployment — it is monitored continuously. Every strategy carries, from walk-forward and Monte Carlo analysis, its extreme scenarios known in advance, good and bad alike: we know what its best and worst predicted paths look like, and both must be acceptable for production before the strategy is given its first money. The same goes for losing streaks — how many consecutive losing trades still sit within the distribution is known upfront.

Then a hard rule applies: a strategy that crosses its pre-set guardrails is switched off. Nobody gets to live in the belief that the situation will turn around — it does not perform, it ends. We treat risk management strictly and programmatically: cutting a loss follows rules defined in advance, not in the heat of the moment. At the trade level this means that essentially every isolated trade has its own stop loss; and where it makes more sense, the whole bet is the stop loss — the position is sized so that even its full loss is acceptable, and respected, in advance.

The second axis: time in the market

Annual return is only half the story. The other half: what share of time did the strategy need to hold capital in a position to earn it? This metric is called market exposure — the share of time “at work” — and we watch it in the results as closely as the return itself. Capital in a position is occupied; capital out of a position is a free resource.

A rhetorical question: which is better — strategy A, earning 50 % a year while in the market 60 % of the time, or strategy B, earning 20 % a year while in the market only 50 % of the time?

Standalone arithmetic is clear: A earns more per unit of exposure (50/60 ≈ 0.83 % per percent of time in the market, B only 20/50 = 0.40). If you may run only one, take A. But the question has a second layer: strategy B leaves capital free half the time. If an uncorrelated strategy C exists to fill those gaps, the portfolio B+C can compound a higher return with a smoother equity curve than A achieves alone — because the same pool of money works two independent sources of profit. So the honest answer is: it depends on whether you are building a strategy or a portfolio. And composing strategies over one pool of capital — running them concurrently — deserves its own article: Strategy portfolios: one pool of money.

How we work with it

Sizing here is not a gut number: position size leans on the distribution of outcomes (drawdown percentiles from Monte Carlo, not averages), a fractional approach to Kelly is the default, and market exposure is reported with every test — because without it, returns cannot be compared honestly and a portfolio cannot be composed honestly. The closing rule: signals decide whether you make money; sizing decides whether you are still there when it happens.

Want to know what sizing your strategy can carry — by distribution, not by feel? Get in touch →