Kelly Criterion Calculator

Enter win probability and win/loss ratio to get full and fractional Kelly position size recommendations.

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Recommended Sizing Model Half-Kelly (16.25%)

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Trade Parameters

Historical Win Rate (W) info 55%

Presets:

Average Loss (Risk)

Baseline stop-out loss (1R)

Average Win (Reward)

Expected profit at take-profit

Trading Account Equity / Bankroll

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Computed Payoff Ratio (R) Reward-to-Risk Factor

1 : 2.00 Positive Expectancy

K% = W - [(1 - W) / R]

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Kelly Growth Curve & Allocation Simulator

Geometric Capital Growth Rate vs. Risk Fraction Size (%)

RECOMMENDED: Half-Kelly (16.25%)

Half Kelly: 75% Growth, 50% Less Drawdown

Full Kelly: Mathematical Maxima

Overbetting: Deterministic Wealth Ruin

Geometric Growth +3.25% per trade compound

Volatility Drag Low (0.41) Half-Kelly smoothed

Ruin Probability < 0.01% under disciplined stops

Peak Growth Fraction 32.50% critical turning point

Optimal Position Sizing Tiers

Allocations dynamically adjusted for $50,000 Equity

Full Kelly (Aggressive)

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32.50% ($16,250)

Theoretical maximum geometric compound rate. High variance with significant 40-50% drawdown risk.

warning Drawdown Risk: Severe

Half Kelly (Recommended)

STANDARD

16.25% ($8,125)

Standard: captures 75% of maximum growth with 50% less volatility and drastically smoothed drawdowns.

verified Optimal Balance: High Sharpe

Quarter Kelly (Conservative)

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8.13% ($4,063)

Capital preservation mode: minimal drawdown, buffer against estimation errors in win probability or choppy markets.

shield Drawdown: Ultra Low (<10%)

Expected Value (EV)

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+$65.00 (+0.65 R)

Average statistical edge generated per transaction. Positive expectancy confirms Kelly sizing eligibility.

trending_up Positive Mathematical Edge

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Quantitative Sizing Sensitivity Matrix

Full Kelly sizing fractions (%) modeled across variable win probabilities and payoff ratios. Current profile highlighted.

Formula: ƒ* = W - ((1 - W) / R)

Win Rate (W) \ R:R (R)	1 : 1.00 (Even)	1 : 1.50	1 : 2.00	1 : 2.50	1 : 3.00	1 : 4.00
40.0% Win Rate	-20.0% (No Edge)	0.00%	10.00%	16.00%	20.00%	25.00%
45.0% Win Rate	-10.0% (No Edge)	8.33%	17.50%	23.00%	26.67%	31.25%
50.0% Win Rate	0.00% (Breakeven)	16.67%	25.00%	30.00%	33.33%	37.50%
55.0% Win Rate (Active)	10.00%	25.00%	32.50% ★	37.00%	40.00%	43.75%
60.0% Win Rate	20.00%	33.33%	40.00%	44.00%	46.67%	50.00%
65.0% Win Rate	30.00%	41.67%	47.50%	51.00%	53.33%	56.25%

★ Indicates your current calculator parameters (W=55%, R=2.0). Negative values signify zero statistical edge (do not allocate capital).

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Quantitative Foundations

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula that calculates the statistically optimal percentage of capital to risk on a single trade to maximize long-term wealth growth while avoiding mathematical ruin.

The Standard Formula

K% = W - [ (1 - W) ÷ R ]

K% (Kelly Fraction): Optimal % of equity to risk on trade.

W (Win Probability): Historical win frequency (0.0 to 1.0).

1 - W (Loss Rate): Historical loss frequency.

R (Win/Loss Payoff Ratio): Average Win $ ÷ Average Loss $.

assignment_turned_in Step-by-Step Worked Example

Suppose your systematic trend-following strategy demonstrates a 55% win rate, an average winner of $200.00, and an average stop-loss loss of $100.00:

Determine Payoff Ratio (R):
R = Average Win ÷ Average Loss = $200 ÷ $100 = 2.00
Compute Loss Probability (L):
L = 1 - W = 1 - 0.55 = 0.45 (45%)
Calculate the Risk-Reward Drag:
Drag = (1 - W) ÷ R = 0.45 ÷ 2.0 = 0.225 (22.5%)
Calculate Optimal Full Kelly (K%):
K% = 0.55 - 0.225 = 0.325 = 32.50% of bankroll

Why Institutional Desks Use Half or Quarter Kelly

While Full Kelly guarantees maximum theoretical geometric asset expansion asymptotically, it assumes exact knowledge of future probability distributions. In real financial markets:

Parameter Estimation Error: Backtested win rates are noisy estimates. If true win rate drops from 55% to 48%, Full Kelly transforms a winning system into an account-destroying drawdown machine.
Volatility Dampening: Half Kelly captures 75% of peak geometric growth while cutting portfolio variance and drawdowns by over 50%.
Psychological Execution: Full Kelly often subjects traders to rolling 50-70% drawdowns. Fractional Kelly preserves mental capital and operational endurance.

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Quantitative Risk FAQs

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Rule of Thumb: When in doubt, trade Quarter-Kelly. If your edge is real, geometric growth will compound smoothly. If your edge is overstated, you will avoid irreversible capital impairment.

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