What is the Kelly formula for stocks?

For a stock or portfolio, the Kelly fraction is approximately the expected return above the risk-free rate divided by the variance of returns. An asset expected to earn 6% above cash with 20% volatility gives 0.06 ÷ 0.04 = 1.5, or 150% of capital. That is why full Kelly on real estimates often implies leverage, and why practitioners usually bet a fraction of it.

Why use half Kelly instead of full Kelly?

Because the inputs are estimates. Full Kelly is optimal only when the edge and the risk are known exactly; overestimate the edge or underestimate the risk and you overbet, which lowers long-run growth and deepens drawdowns. Half Kelly keeps roughly three quarters of the growth rate with half the volatility, a trade-off many practitioners prefer.

How has Kelly weighting done in Opulence Alpha's Golden Tickets?

Through the week that closed on 21 September 2026, the Kelly-weighted basket was down 12.10% and the equal-weight basket, holding the same names, was up 29.17%, both gross of costs; Kelly rose in 16 of 38 weeks and equal weight in 22. Every week of both baskets is published on the ledger.

FAQ · Kelly criterion

What is the Kelly criterion?

Reviewed against the platform's code on Sep 26, 2026

The Kelly criterion is a rule for sizing a bet or an investment position so that capital grows as fast as possible over the long run. For a simple bet it stakes the edge divided by the odds; for an investment it is roughly the expected return above the risk-free rate divided by the variance of returns.

Why it matters

Choosing good ideas is half the problem; deciding how much to put in each is the other half. Betting too little wastes part of an edge. Betting too much is more dangerous: above the Kelly amount, long-run growth falls while risk keeps rising, and at about twice the Kelly amount the growth rate above cash falls to roughly zero, even though every bet has a positive expected value.

How it works

The Kelly (1956) rule stakes the fraction of capital that maximises the expected logarithm of wealth; for a bet with win probability p and net odds b, that is f = p − (1 − p)/b. For continuously traded assets the equivalent is approximately (μ − r)/σ². Because μ and σ are estimates, and overstating the edge or understating the risk leads to overbetting, practitioners often use fractional Kelly: half-Kelly keeps about three quarters of the growth rate with half the volatility (MacLean, Thorp & Ziemba, 2010).

How Opulence Alpha applies it

Opulence Alpha publishes a Kelly-weighted Golden Ticket basket beside Equal and Conviction baskets that hold the same ten names each week, so the gap between them prices the sizing rule alone. Each name's weight is its forecast edge divided by the square of its estimated uncertainty, which has a floor, and the weights are then rescaled to fill the basket. That rescaling cancels the half-Kelly multiplier, so Kelly changes how the basket is split between names, not how much is at risk. Results are gross of costs, with no position limits.

Kelly against Equal, every week on the ledger →

Related concepts

Conformal predictionConformal prediction turns any forecast into intervals with a stated coverage, sized by the model's measured errors on held-out data, not by an assumption.Probabilistic forecastingProbabilistic forecasting publishes a distribution of possible returns, with calibrated intervals, instead of one expected number — so a position can be sized from its uncertainty.Refutation LedgerA Refutation Ledger is a public record of what happened after investment decisions — including failures, faults and changes — kept so a process can be judged on all of its outcomes.

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Questions

What is the Kelly formula for stocks?: For a stock or portfolio, the Kelly fraction is approximately the expected return above the risk-free rate divided by the variance of returns. An asset expected to earn 6% above cash with 20% volatility gives 0.06 ÷ 0.04 = 1.5, or 150% of capital. That is why full Kelly on real estimates often implies leverage, and why practitioners usually bet a fraction of it.
Why use half Kelly instead of full Kelly?: Because the inputs are estimates. Full Kelly is optimal only when the edge and the risk are known exactly; overestimate the edge or underestimate the risk and you overbet, which lowers long-run growth and deepens drawdowns. Half Kelly keeps roughly three quarters of the growth rate with half the volatility, a trade-off many practitioners prefer.
How has Kelly weighting done in Opulence Alpha's Golden Tickets?: Through the week that closed on 21 September 2026, the Kelly-weighted basket was down 12.10% and the equal-weight basket, holding the same names, was up 29.17%, both gross of costs; Kelly rose in 16 of 38 weeks and equal weight in 22. Every week of both baskets is published on the ledger.

References

Kelly, J. L. (1956). A New Interpretation of Information Rate. Bell System Technical Journal.
Thorp, E. O. (2006). The Kelly Criterion in Blackjack, Sports Betting and the Stock Market. In Handbook of Asset and Liability Management, Vol. 1. Elsevier.
MacLean, L. C., Thorp, E. O. & Ziemba, W. T. (2010). Long-term capital growth: the good and bad properties of the Kelly and fractional Kelly capital growth criteria. Quantitative Finance.

Educational content about research methods. Not investment advice.