Kelly Criterion and Position Sizing
Bell Labs to blackjack to portfolios — sizing for long-run log-utility growth
In 1956, John Kelly Jr. published a paper in the Bell System Technical Journal titled 'A New Interpretation of Information Rate.' The paper was nominally about telecommunications — specifically, the optimal channel capacity of an information channel — but it contained a side observation that became one of the most consequential ideas in quantitative finance.
Kelly showed that for a sequence of repeated bets with positive expected value, there is a specific bet-size fraction that maximizes the long-run growth rate of the bettor's wealth. The fraction — the Kelly fraction — is computed from the bet's edge and odds and has the property that no other constant fraction produces faster long-run growth. Edward Thorp, then a mathematics professor at MIT, picked up Kelly's framework in the late 1950s for blackjack — his 1962 book *Beat the Dealer* introduced both card-counting and Kelly-criterion bet sizing to a popular audience.
That is the opening. Finishing a lesson is where it stops being interesting and starts being useful: the full lesson runs to 8 sections and ends with 6 practice questions. A free account is what opens the rest, and the other 255 lessons in the Academy with it. No card.
What this lesson covers
- 1The Kelly fraction for equity-like investments
- 2When Kelly applies and when it does not
- 3Kelly Position Sizer
- 4Kelly fraction in the discrete and continuous cases
- 5Kelly fractions for representative bets
- 6Edward Thorp's Princeton/Newport Partners — Kelly applied to markets, 1969-1988
- 7Where to see this on the platform
- 8Summary