The Kelly criterion is a formula that tells you what fraction of your capital to put into a trade, given how often you expect to win and how much you win or lose when you do. It is not a signal and it does not pick trades. It answers one question: how big should this position be? Used with honest inputs and a safety margin, it keeps you from betting too little on a real edge and, more importantly, from betting so much that one bad run ends the account.
This guide covers the formula, two worked examples (one with stocks, one with an options spread), why almost everyone trades a fraction of full Kelly, and the specific ways the math fails in live markets.
TL;DR
- Kelly sizing is f* = (bp − q) / b: win probability p, loss probability q, and payoff ratio b. The result is the share of capital to risk.
- The formula assumes you know your odds exactly. You never do, so the realistic move is to trade a fraction of it, commonly half or a quarter.
- For options, apply Kelly to the maximum loss of a defined-risk trade. A negative result means the trade has no edge at your estimated odds, so skip it.
- Small errors in your win-rate estimate can swing the output enormously. Use journal data, and treat Kelly as a ceiling, not a target.
- Kelly is a sizing tool only. It ignores correlation between positions and your personal limits.
Table of Contents
- What the Kelly criterion does
- The Kelly formula, step by step
- Applying Kelly to options trades
- Where your win probability comes from
- Full Kelly versus fractional Kelly
- What Kelly assumes, and where it breaks
- Adjusting Kelly for changing markets
- A practical Kelly workflow for options traders
- Our perspective
- Get the inputs before the open
- FAQ
- Sources
What the Kelly criterion does
John L. Kelly Jr. published the idea in 1956 in the context of information theory. In trading terms, it finds the bet size that maximizes the long-run growth rate of your capital. Investopedia describes it as a formula for the optimal fraction of capital to allocate to an investment or wager. Edward Thorp's paper on blackjack, sports betting and the stock market frames the goal more precisely: maximize the expected value of the logarithm of wealth over a repeated sequence of bets.
That logarithm matters. Because growth compounds, a 50% loss needs a 100% gain to recover. Betting too much hurts more than betting too little helps, and Kelly is the point where those two forces balance over many repetitions.
One academic treatment calls the approach myopic: it optimizes each period from your current capital, yet it remains sound for maximizing long-run growth. In practice that means the formula resizes every time your account changes, risking more after wins and less after losses.
The Kelly formula, step by step
For a trade with two outcomes, a win or a loss, the formula is:
f* = (bp − q) / b
- f* is the fraction of capital to risk
- p is the probability of winning
- q is the probability of losing, which equals 1 − p
- b is the net payoff per dollar risked, so your average win divided by your average loss
Investopedia gives an equivalent form built from your track record: Kelly % = W − (1 − W) / R, where W is your historical win percentage and R is your win/loss ratio.
There is also a version for assets with normally distributed returns, where the fraction is the excess return divided by the variance. That one suits portfolio allocation across assets more than single trades, so this article stays with the binary form that fits individual trade ideas.
Worked example with a stock trade
Say your journal shows a 55% win rate, and your average winner is 1.2 times your average loser.
- p = 0.55, q = 0.45, b = 1.2
- bp = 0.66, so bp − q = 0.21
- f* = 0.21 / 1.2 = 0.175, or 17.5% of capital
Risking 17.5% of your account on every trade would produce violent swings even with a genuine edge. Half Kelly is 8.75% and quarter Kelly is about 4.4%. Most traders find even those numbers uncomfortable, which is the first clue that Kelly is an upper limit rather than a recommendation.
Applying Kelly to options trades
Options complicate the inputs in three ways: payoffs are asymmetric, outcomes are not truly binary, and time decay changes the odds as expiration nears. The cleanest workaround is to use defined-risk structures and reduce each trade to a simplified two-outcome bet: the maximum loss and the profit target you actually plan to take.
Worked example with an iron condor
Suppose an iron condor has a $500 maximum loss and a $200 profit target. Then b = 200 / 500 = 0.4. The result depends heavily on the win probability you assign:
| Estimated win probability | Full Kelly (f*) | Quarter Kelly |
|---|---|---|
| 70% | −2.5% (no trade) | none |
| 72% | 2.0% | 0.5% |
| 75% | 12.5% | 3.1% |
| 80% | 28.0% | 7.0% |
The break-even point is a win probability of about 71.4%. Below it, f* is negative and the formula says there is no edge. Between 70% and 75%, the recommended size goes from nothing to 12.5% of capital. That is the whole problem in one table: when payoffs are lopsided, a few points of estimation error flip the decision.
Now turn a percentage into contracts. With a $50,000 account and quarter Kelly at 75% (3.1%), you would risk about $1,560. At $500 maximum loss per spread, that rounds down to three contracts. Always round down.
If you want the mechanics of sizing around max loss in more detail, our guide to position sizing for options traders covers the formulas and the typical 0.5% to 1% per-trade range. To check the numbers behind each leg before you size, use the profit and loss calculation workflow.
Buying versus selling premium
The two sides of the market behave differently under Kelly. Long options often have a low win rate and a large payoff ratio. Short premium strategies have a high win rate and a small payoff ratio, with a tail that can exceed your model. If you size a naked short position as though the modeled loss were the real loss, Kelly will tell you to bet too much. Stick to defined-risk spreads when you use Kelly on credit trades, and read our beginner's guide to buying versus selling options if you are still choosing a side.
Where your win probability comes from
The formula is only as good as p and b. There are two practical sources.
Your own trade journal. This is the sturdier source. Log every trade with entry, exit, size and result, and compute win rate and average win versus average loss for each strategy separately. A hundred or more trades per strategy is a reasonable minimum before the numbers mean much; with twenty trades, a 60% win rate is mostly noise. Mixing strategies in one pool will blur the result, because a covered call and a long call do not share one payoff profile. A useful companion read on why win rate alone misleads is this piece on win rate versus expectancy in a trade journal, since Kelly needs both the hit rate and the size of wins relative to losses.
Option pricing. Delta is a rough stand-in for the chance that an option finishes in the money. A 20-delta short strike implies something near an 80% chance of expiring out of the money. It is only a proxy, because implied volatility usually prices in a premium over what is later realized, and a defined-risk trade that you manage early does not behave like a hold-to-expiration bet. Our article on choosing delta before the open explains how to use it as a starting point.
Whichever source you use, round your probability estimate down. Overestimating your edge is the costly direction.
Full Kelly versus fractional Kelly
Full Kelly uses the raw output of the formula. Fractional Kelly multiplies it by a factor, usually one half or one quarter. Three reasons to use a fraction:
- Your inputs are estimates. Research on Kelly investing points to great sensitivity to parameter estimates, especially the expected return, which makes the strategy dangerous when those estimates are wrong.
- Drawdowns at full Kelly are deep. Thorp's analysis of the mathematics shows that betting a fraction gives up a modest share of growth in exchange for a large cut in volatility. Half Kelly is the common middle ground.
- Overbetting is asymmetric. Betting more than the true Kelly amount reduces growth faster than betting less by the same margin, and at roughly double Kelly the long-run growth rate falls to zero. Since your estimate of Kelly can easily be off by that much, a fraction keeps you on the safe side of the curve.
A simple rule: if you have fewer than 100 logged trades for a strategy, start at quarter Kelly or lower. As your sample grows and the numbers hold, you can move toward half Kelly. Never go above it.
What Kelly assumes, and where it breaks
The criterion is elegant and fragile. Know these limits before you put it to work.
It assumes you know the odds. In a casino the probabilities are fixed. In markets they are estimates. The CFA Institute's Financial Analysts Journal notes that Kelly offers a logical baseline for allocation, but is often misused in finance because market probabilities are not fixed, known quantities.
It sizes one bet at a time. Investopedia stresses that Kelly is a position-sizing tool, not a standalone strategy, and that it lacks any consideration of diversification. Five Kelly-sized trades on correlated tech names are really one large trade. If you hold several positions at once, cap total risk across them, not only per trade.
It assumes you can always exit. Gaps, halts and thin option markets mean your real loss can exceed the planned loss. Regulatory filings from U.S. advisers note that exchanges may suspend trading or impose limits in emergencies, which can make it impossible to close positions. Defined-risk structures soften this problem; they do not remove it.
It ignores your life. Kelly maximizes growth, not sleep. It does not know that you need the capital for a tax bill or payroll. If you trade around other income or business obligations, set aside the money you cannot lose first. Our guide to options trading around business cash flow walks through how to do that.
Adjusting Kelly for changing markets
A static fraction treats a calm market and a panic as the same. Practitioner research on dynamic sizing suggests that a fractional-Kelly framework should reflect confidence, market regime and survivability. Here is a simple way to do that without building a model:
- Cut the fraction when volatility spikes. If the VIX jumps or your recent results drift from your journal averages, drop from half to quarter Kelly until things settle.
- Cut it when you are less sure. A new strategy with a thin sample gets a smaller fraction than one with 200 trades behind it.
- Cap the result. Many traders set a hard ceiling per trade, such as the 0.5% to 1% range, and let Kelly only pull them lower. Then Kelly serves as a veto, not a license to go bigger.
- Recompute on a schedule. Update win rate and payoff ratio monthly or quarterly from the journal, not after every trade.
Before you size anything, you also need clear rules on when to enter and exit; otherwise your journal data is inconsistent and your p and b are meaningless. We cover this in turning entry and exit rules into orders.
A practical Kelly workflow for options traders
- Pick one strategy, for example short put spreads on liquid index ETFs.
- Pull your last 100 or more trades of that type and compute win rate, average win and average loss.
- Calculate f* using the formula. If it is zero or negative, stop: your data shows no edge.
- Multiply by 0.25 or 0.5, based on how much data you have and how stable the numbers are.
- Apply your hard cap, and compare against total portfolio risk across open positions.
- Convert to contracts using the maximum loss per spread, rounded down.
- Re-run the numbers on a fixed schedule, and again after any large drawdown.
Our perspective
We built Morningoptions around a simple belief: the idea is only half the trade, and the size is the other half. Plenty of active traders with day jobs or businesses to run get the setup roughly right and then lose it all on sizing. Kelly is useful to them for one reason: it forces you to write down an edge in numbers. If you cannot state your win rate and your payoff, you do not have a sizing method, you have a feeling.
That is why our daily briefings pair each contract idea with entry and exit levels and a bear case. Those give you concrete inputs: where you are wrong, what the loss looks like, and what a reasonable target is. That gives you a defined maximum loss and a payoff ratio to plug into your own sizing rules. We would not tell anyone to run full Kelly on any idea, ours included. Treat the formula as a ceiling, keep your per-trade risk small, and let your journal decide whether the edge is real.
— Customer
Get the inputs before the open
Sizing works best when the setup is defined before the market opens. Morningoptions delivers ranked, specific contract ideas with entry and exit levels and a bear case, so the maximum loss and target are visible before you size. The free plan gives you limited daily trade ideas. Pro is $89 per month, or $742 per year, and adds full briefings, the lunchtime scanner and the AI chat scanner for researching tickers on demand.
See the plans on the Morningoptions home page and start with the free briefing.
FAQ
Can I use the Kelly criterion for options?
Yes, with care. Reduce each trade to a maximum loss and a profit target, estimate the win probability, and apply the formula to the capital at risk. Stick to defined-risk structures, because undefined losses on short premium can far exceed any modeled estimate, which makes Kelly overstate the size.
What does a negative Kelly result mean?
It means that at your estimated odds and payoff, the trade has no positive expected edge, so the formula says to bet nothing. In the iron condor example above, any win probability below roughly 71.4% gives a negative result. Skip the trade or look for a better price.
Is half Kelly or quarter Kelly better?
Neither is universally right. Quarter Kelly suits a small sample or an unproven strategy, while half Kelly fits a large, stable track record. Because your inputs are estimates, fractional sizing gives a margin of safety against errors in your win rate and payoff ratio.
How many trades do I need before trusting my win rate?
A common benchmark is at least 100 trades per strategy. Below that, results are dominated by luck, and Kelly will amplify the noise. Track each strategy separately and recompute regularly.
Does Kelly replace a stop-loss or a risk limit?
No. It only decides size. You still need an exit plan, a cap on total portfolio risk, and rules for correlated positions.
This article is educational and is not personalized financial advice. If you are unsure how much of your capital you can afford to risk, talk to a licensed financial adviser.
Sources
- Kelly Criterion Explained, Investopedia
- The Kelly Criterion in Blackjack, Sports Betting, and the Stock Market, Edward O. Thorp
- Using the Kelly Criterion for Investing, Ziemba and colleagues
- Concentrated Investing, CFA Institute Financial Analysts Journal
- Investment adviser brochure (ADV Part 2A), SEC Investment Adviser Public Disclosure
- The Kelly Criterion in Financial Markets, Atlas Peak Research
- Win rate versus expectancy in your trade journal