An idea from information theory
In 1956, John L. Kelly Jr., a scientist at Bell Labs, published a formula for how much of your capital to commit to a favourable, repeated opportunity. The Kelly criterion maximises the expected logarithm of wealth — which, over many repetitions, means maximising the long-run growth rate.
Here p is the probability of winning, q = 1 − p is the probability of losing, and b is the payoff odds.
Try it yourself
Adjust the probability and payoff below to see how the optimal fraction changes — and how quickly it falls to zero when there is no edge.
Try it: the Kelly calculator
A simple repeated bet: win the payoff with probability p, lose your stake otherwise.
Why professionals use “fractional Kelly”
Full Kelly sizing is mathematically optimal only if your estimates are exactly right. In practice they never are, and overestimating your edge leads to over-betting, which can be ruinous. Many practitioners therefore use a fraction — often half — of the Kelly amount, accepting slightly lower expected growth in exchange for much smoother outcomes.
Over-betting is far more dangerous than under-betting. Position sizing is risk management.
Kelly in our protocol
Kelly sits alongside Mandelbrot, Taleb and Spitznagel in the intellectual lineage of our Quantitative Investment Management Protocol, informing how exposures are sized so that no single position can threaten the long-term compounding of the whole.
This article is provided for general information and education only and does not constitute financial advice. The value of investments may go down as well as up, and past performance is not a guide to future results.
