Kelly Position Sizing

Simple Kelly for a stock trade

Use when you have a view on win probability and typical win versus loss size for a discrete trade or strategy.

Portfolio size capital

Total capital you are willing to risk across this strategy.

Win probability p

percent

Probability the trade ends as a winner on your sizing horizon.

Average gain when right upside

percent

Typical percentage gain on winning trades in this strategy.

Average loss when wrong downside

percent

Typical percentage loss on losing trades (use positive number).

Kelly assumes repeated, independent trades with similar characteristics. Many practitioners scale down to half or quarter Kelly to reduce volatility.

Portfolio level Kelly (mean variance)

Approximate Kelly fraction using expected return and volatility of a stock or basket relative to the risk free rate. Based on continuous time Kelly under lognormal assumptions.

Portfolio size capital

Total capital available for the strategy or asset.

Expected annual return mu

percent

Forward looking expected return for the asset or strategy.

Risk free rate r

percent

Yield on short dated risk free instruments in your base currency.

Annual volatility sigma

percent

Annualized standard deviation of returns for the asset or strategy.

Kelly fraction is approximately (mu minus r) divided by sigma squared. Estimation error and fat tails argue for sizing well below full Kelly.

Trade level Kelly output

single trade mode

Kelly fraction

Optimal fraction of capital per trade under your assumptions.

Position size (full Kelly)

Dollar amount at full Kelly position sizing.

Position size (quarter Kelly)

Dollar amount at quarter Kelly, a common risk managed compromise.

0% 25% 50% 75% 100%+

Suggested portfolio allocation (quarter Kelly): -

Provide realistic inputs to see Kelly sizing.

Portfolio level Kelly output

mean variance mode

Kelly leverage or allocation

Fraction of capital or leverage suggested by mean variance Kelly formula.

Position at full Kelly

Dollar exposure implied at full Kelly, given your portfolio size.

Provide expected return and volatility to compute portfolio level Kelly sizing.

Important: Kelly sizing is mathematically elegant but assumes repeatable edges, independence and no model error. Real markets are messier. Many portfolio managers use a fraction of Kelly to avoid extreme drawdowns.