# Kelly Criterion Calculator - Position Sizing by Edge Source: https://theoptionsbench.com/position-sizing/ > Plain-text mirror for AI/LLM ingestion. Canonical HTML page: https://theoptionsbench.com/position-sizing/ --- Kelly criterion - key facts The Kelly criterion turns your win rate and average win/loss into the position size that maximises long-run growth - most traders bet a fraction of it to cut volatility. Full Kelly f* = p - (1 - p) ÷ b, where p = win rate and b = average win ÷ average loss. Half / Quarter Kelly f* ÷ 2 or f* ÷ 4 - the common choices; far less drawdown for most of the growth. Payoff ratio (b) Average win ÷ average loss - your reward-to-risk per trade. No edge If p - (1 - p) ÷ b ≤ 0, Kelly says bet nothing - there is no positive edge. Caution Full Kelly is volatile and assumes a stable win rate and payoff; size down when unsure. Want the full explanation? Read Position Sizing for Options Trading . ## How to use this calculator - Enter your win rate as a percentage, from your own closed trades or a realistic backtest. - Enter your average win and average loss in dollars, net of fees. - Enter your account size. - Read the result: Full, Half, and Quarter Kelly stakes as a percent of the account and in dollars, plus your expectancy and payoff ratio. - Scan the win-rate sensitivity table to see how the stake changes if your edge is better or worse than you assumed. **What it tells you:** how large a position your edge justifies - and why most traders stake a fraction of the Full Kelly figure. ## How this calculator works The Kelly Criterion answers one question: given an edge, what fraction of your capital should you risk on each trade to grow it fastest over the long run? The formula is **f* = p - (1 - p) ÷ b**, where **p** is your win rate as a decimal and **b** is your payoff ratio - average win divided by average loss. Multiply the result by your account size for the dollar stake. The calculator shows Full Kelly alongside **Half** and **Quarter Kelly**, because Full Kelly is rarely what you actually want to trade. It also reports your **expectancy** - the expected profit or loss per trade - and your payoff ratio, so you can see at a glance whether you have an edge at all. If expectancy is zero or negative, there is no edge to size and the calculator says so. ## Why fractional Kelly Full Kelly maximises growth only if your inputs are exactly right. They never are - win rates wander and a few large losses can warp your average. Worse, Full Kelly is punishingly volatile: drawdowns of 50% or more are normal at the optimal fraction. Betting half of Kelly captures about three-quarters of the growth with roughly half the volatility, which is why Half and Quarter Kelly are the practical default. When in doubt, size down. And remember the formula sizes a single, independent bet. Several correlated positions - a basket of bullish premium-selling trades, say - behave like one bigger position, so the safe total is well below the sum of their individual Kelly sizes. ## Worked example A fixed, hypothetical illustration - not live market data. Suppose a strategy wins 60% of the time, with an average win of $200 against an average loss of $100, on a $10,000 account. - Payoff ratio: $200 ÷ $100 = 2 : 1. - Full Kelly: 0.60 - 0.40 ÷ 2 = 40% -> $4,000. - Half Kelly: 20% -> $2,000. Quarter Kelly: 10% -> $1,000. - Expectancy: 0.60 × $200 - 0.40 × $100 = +$80 per trade - a genuine edge. Forty percent of the account on one trade is far too aggressive for most people; the Half or Quarter Kelly figure is the realistic takeaway. ## ⚠ Common mistakes - Trusting Full Kelly. It assumes a perfect edge estimate and swings violently - almost everyone should trade a fraction of it. - Overstating your edge. Optimistic win rates and payoff ratios inflate the size; use conservative, fee-adjusted numbers from real trades. - Ignoring correlation. Sizing several correlated positions each at Kelly stacks one big bet - size the cluster, not each leg. - Applying it to undefined-risk trades. Kelly assumes a known loss per trade; a naked option with an open-ended loss breaks that assumption. - Forgetting it is a ceiling. Kelly is the most you should risk for growth, not a target you must hit. Found this useful? Get the bi-weekly email Strategy breakdowns, the edge cases these calculators surface, and trades worth watching - free, no noise. Join the free email -> ## Frequently asked questions What is the Kelly Criterion? The Kelly Criterion is a formula for the bet size that maximises the long-run growth rate of your capital, given a known edge. It balances growth against risk of ruin: bet too little and you leave growth on the table, bet too much and volatility - and the chance of a deep drawdown - climbs sharply. It is widely used as a position-sizing reference in trading and gambling. How is the Kelly percentage calculated? Full Kelly fraction = p - (1 - p) ÷ b, where p is your win probability (win rate) and b is your payoff ratio (average win ÷ average loss). For example, a 60% win rate with a 2:1 average win/loss gives 0.60 - 0.40 ÷ 2 = 0.40, or 40% of the account. Half and Quarter Kelly are simply that figure divided by two and four. Why use Half or Quarter Kelly instead of Full Kelly? Full Kelly is the growth-optimal size only if your win rate and payoff ratio are exactly right - and in real trading they never are. Overestimating your edge makes Full Kelly bet too much, and Full Kelly already produces large swings. Most practitioners use Half or Quarter Kelly, which keeps the bulk of the growth with a fraction of the volatility and a wide margin for input error. What does "no edge" mean here? If the formula returns zero or a negative number, your inputs imply a non-positive expectancy - over many trades you would not make money - so Kelly recommends no position at all. This happens whenever the win rate is too low for the payoff ratio (for example, a 40% win rate at 1:1). Fix the edge before sizing the bet. How do I estimate win rate and average win/loss for options? Use your own closed-trade history for the same strategy and setup, or a realistic backtest. Be conservative: count commissions and slippage, and lean toward a lower win rate and a lower payoff ratio than your best-case numbers. Garbage in, garbage out - Kelly is only as good as the edge estimate you feed it. Does Kelly account for several positions at once? No. The basic formula sizes a single, independent bet. If you hold many correlated positions - for example several bullish premium-selling trades - they effectively act as one larger bet, so you should size well below what single-trade Kelly suggests. Treat the output as a per-idea ceiling, not a portfolio rule.