How much to risk: the Kelly criterion

In the previous course you risked 1% per trade, and in the lesson on volatility-based entries the position size adapted to the market. One question remains: why 1%? Why not 5% – if the strategy has a positive expected value, will it not make more? The answer is mathematical, and a little surprising.

The Kelly criterion#

In 1956 Bell Labs researcher John Kelly worked out what share of capital to bet so that an account grows fastest in the long run. For a strategy with a fixed ratio of win to loss, the Kelly criterion says:

f = p − (1 − p) ÷ b

• f – what share of the account to risk per trade,
• p – the win rate (share of winning trades),
• b – how many times bigger the average win is than the average loss.

Example: a 40% win rate and a win twice the loss (2R against 1R). f = 0.4 − 0.6 ÷ 2 = 0.10, so risk 10% of the account per trade. That sounds like a lot – and it is.

What a simulation shows#

The same strategy (40% win rate, 2R win, 1R loss), 200 trades, 20,000 random runs. The only thing that changes is the risk per trade:

Three things follow from the table:

• Full Kelly really grows fastest – but with a drawdown of around 80%. Who would keep trusting and trading a strategy on the way from 10,000 down to 2,000?
• Beyond the Kelly number, growth falls. Twice Kelly risks far more and still ends up almost where it started. Here, more risk means less money.
• Small risk is slow but calm. A 12% drawdown is livable, an 80% one is not.

The biggest trap: an overestimated strategy#

The Kelly criterion needs the win rate and the win-to-loss ratio. But you do not know them – you only have an estimate from a backtest, and you know from the testing module how optimistic that tends to be. What if the real win rate is not 40% but 35%?

Then the Kelly number is only 2.5%. Anyone still risking 10% bets four times more than they should. The simulation: a median account after 200 trades of 0.39× – 100,000 shrinks to 39,000 – and 70% of runs end in a loss. Yet the strategy still has a positive expected value. It was ruined by the bet size, not by the strategy.

With the same overestimated strategy and a 1% risk, the median ends at 1.08×: not much, but the account survives and you have time to spot the mistake.

How to use the Kelly criterion in practice#

1. Calculate the Kelly number from honest results – out of sample or from a forward test, not from tuning.
2. Treat it as a ceiling, not a target. Professionals usually use a quarter to a half of the Kelly number, often less.
3. Remember correlations. The Kelly number applies to the total risk, not to each position separately – three correlated trades are one bet.
4. If the Kelly number comes out zero or negative, your data says the strategy has no edge. Do not trade it.

That is why in practice traders stick to 0.5–2% per trade: far below half of the Kelly number from the example, with a margin for estimation error. The so-called risk of ruin – the chance that a drawdown wipes out the account or forces you to stop – is then small.

Common myths#

• "Kelly is optimal, I will bet full Kelly." Optimal for growth, not for your nerves and not for overestimated inputs.
• "Positive expected value = I cannot lose the account." You can – with bets that are too big.
• "More risk = more money." Only up to the Kelly number. Beyond it, more risk means less money.