The Kelly criterion: the maths behind position sizing

The lesson in plain words

The same lesson as the slides above, written out in full.

1. The Kelly Criterion

Welcome. Most investors obsess over what to buy. Far fewer think carefully about how much to buy. The Kelly criterion, developed by John Kelly at Bell Labs back in nineteen fifty six, provides a mathematical answer to that second question. Given your edge, what fraction of your capital should you put at risk? Kelly finds the size that maximises the long run growth rate of your money. One note before we begin. This is financial education only, not financial advice.

• Most investors obsess over what to buy; far fewer think about how much.
• Kelly gives a mathematical answer to the position-sizing question.
• It finds the bet size that maximises long-run growth given your edge.

A quick note: This is financial education only, not financial advice. Do not buy, sell, or hold anything based on this lesson.

2. The Sweet Spot

The intuition is a balance. Bet too small, and you leave money on the table, your capital grows too slowly. Bet too large, and a string of losses can devastate your account, even if you genuinely have an edge. Kelly finds the sweet spot between those two mistakes. For a simplified even payoff bet, the formula is just two times your win probability minus one. So if you win sixty per cent of the time, Kelly says to risk twenty per cent of your capital per trade. That sounds aggressive, and it is.

• Bet too small and you leave growth on the table.
• Bet too large and a losing streak can devastate you, even with a genuine edge.
• Kelly finds the sweet spot between the two.
• For a 60% edge with even payoffs, full Kelly says risk about 20% per trade, which is aggressive.

3. Why Professionals Use Half

Here is why almost nobody bets full Kelly in the real world. Full Kelly produces the fastest long run growth, but also the wildest swings, drawdowns that are genuinely stomach churning. So professionals typically use half Kelly, or even quarter Kelly. You give up a little growth in exchange for a far smoother ride, and crucially, a safety margin. Because Kelly assumes you know your exact win probability and payoff, and in reality you are only estimating both. Overconfidence is the norm, not the exception, so betting a fraction of what Kelly suggests protects you from your own optimism.

• Full Kelly maximises growth but produces stomach-churning drawdowns.
• In practice, most professionals use half Kelly or quarter Kelly.
• That gives up a little growth in exchange for a far smoother ride.
• Because you are only estimating your edge, a fraction builds in a safety margin.

4. What the Output Says

How to read the output. If Kelly says zero or negative, you do not have an edge, so do not take the trade. That is actually one of its most valuable outputs, it tells you when to stay out. One to ten per cent is a modest edge, and this is where most genuine real world edges fall. Ten to twenty five per cent is a strong edge, where full Kelly is aggressive and half Kelly is more practical. And if Kelly suggests above twenty five per cent, treat it with suspicion. Either it is an extraordinary opportunity, or, far more likely, your estimates are too optimistic. Double check your win rate and payoff assumptions before ever sizing that large.

• Zero or negative: you have no edge, so do not take the trade. That is a valuable answer.
• 1 to 10%: a modest edge, where most real-world trading lives.
• 10 to 25%: a strong edge; full Kelly here is aggressive, so use half.
• Above 25%: recheck your win rate and payoff, your estimates may be too optimistic.