Kelly Criterion Position Sizing: Formula Limits and Why Traders Use Half-Kelly

Kelly criterion position sizing is a formula for working out how big a bet or trade should be when you genuinely have an edge, so that your capital compounds as fast as possible over the long run. For Indian retail traders, the value isn’t in “bet 31% of the account because the formula said so.” It’s in understanding what the formula does, seeing why full Kelly is almost always too aggressive, and then using half-Kelly or a capped fractional Kelly inside the same 1–3% risk-per-trade discipline that brokers and risk guides already teach. Below we work through the formula with rupee examples, set it against fixed fractional 1% risk, and show how Zerodha Varsity blends Kelly with percentage-risk caps.

If you’re putting together a wider risk framework, begin with our pillar on risk management in trading and come back here for the Kelly-specific maths. Every trade P&L figure below comes from published educational examples, or from simple arithmetic on those figures. None of it is a live market recommendation.

What Is the Kelly Criterion?

John Larry Kelly Jr., a researcher at Bell Labs, described the criterion in 1956. Wikipedia’s Kelly criterion page explains the idea as sizing a sequence of bets so that you maximise the long-term expected value of the logarithm of wealth, which works out to the same thing as maximising long-term expected geometric growth. Gamblers picked it up first, and traders followed, because a mathematically consistent answer to “how much should I risk?” is hard to come by.

Zerodha Varsity’s Kelly’s Criterion chapter puts the same idea in an Indian trading setting. Kelly, in their framing, estimates the best fraction of trading capital to expose when you have information and an edge on the next trade. Varsity also points out that John Kelly came up with it at AT&T’s Bell Laboratories in the 1950s while working on telecom noise problems. Professional gamblers adapted it for bet sizing, and stock-market practitioners came after them.

Two warnings come attached to the formula. One, Wikipedia stresses that Kelly holds perfectly only when outcome probabilities are fully known, and in markets they almost never are. Two, risk-averse strategies deliberately invest less than full Kelly. That’s the reason half-Kelly and quarter-Kelly turn up so often in real use.

Kelly answers “what size maximises long-run growth if your edge is known.” Markets almost never give you a known edge, so fractional Kelly is the version traders can live with.

Kelly Criterion Position Sizing Formula Traders Actually Use

Varsity gives the version traders can actually work with:

Kelly % = W − [(1 − W) / R]

Where:

• W = winning probability (number of winning trades ÷ total trades)
• R = win/loss ratio (average gain on winning trades ÷ average loss on losing trades)

An R above 1 is what you want, Varsity says, since it means your average gains are bigger than your average losses. What comes out is a percentage, the Kelly percent, which the original school of thought reads as the share of capital to put on the next similar trade.

Wikipedia’s more general binary form is f = p/l − q/g. Here p is the win probability, q = 1 − p is the loss probability, g is the fractional gain on a win and l is the fractional loss on a loss. If a losing bet wipes out the whole stake (l = 1) and the payoff odds are even, this collapses toward the familiar edge-over-odds results. But if you’re an active trader who thinks of risk as “rupees lost if the stop hits,” Varsity’s W and R form is the one you’ll pull straight out of a trade log.

There’s a subtle point in a CFA Institute Enterprising Investor note by Alon Bochman, CFA. The popular W − [(1 − W)/R] form fits bets where the downside is losing the entire amount wagered. When a loss is only part of the position, as with a stop loss that doesn’t wipe out the account, a magnitude-aware form, Kelly % = W/A − (1 − W)/B, can point to a different allocation. For retail sizing, the cleanest takeaway is this: treat Kelly as a guide to how much of a risk budget you’ve already fixed should be used. It isn’t a licence to put 30% of your brokerage balance into a single futures lot.

Worked Rupee Example From Varsity’s Trade Log

Varsity uses an illustrative 10-trade log on one stock, Tata Motors in their case. Here are the results in INR:

Working from that table, Varsity gets:

• W = 6 / 10 = 0.6 (60% win rate)
• Average gain = average of the six wins = ₹4,532
• Average loss = average of the four losses = ₹3,274
• R = 4,532 / 3,274 = 1.384
• Kelly % = 0.6 − (0.4 / 1.384) = 0.31, or 31%

So on an 11th similar trade, full Kelly says put roughly 31% of capital to work. Plenty of beginners read that as “throw nearly a third of the account at this setup.” Varsity flags straight away why that reading is dangerous.

Turning 31% into half-Kelly and a risk budget

Say your trading capital is ₹5,00,000, the same figure Varsity uses for its percentage-risk example in that chapter.

• Full Kelly (31%) → about ₹1,55,000 of capital exposure on the next trade.
• Half-Kelly (15.5%) → about ₹77,500 of capital exposure.
• Quarter-Kelly (7.75%) → about ₹38,750 of capital exposure.

Half-Kelly is still a big commitment for a retail futures or options account once you add margin, slippage and a run of losses. Which is why Varsity doesn’t stop at the raw Kelly percent.

Why Full Kelly Is Too Aggressive for Retail Traders

Varsity’s main objection is blunt. A system with “great accuracy” can still throw up a Kelly percent of 70%, which would mean exposing 70% of capital, and there’s still a 30% chance of losing that big chunk in one shot. Wikipedia adds that betting above the Kelly amount raises the risk of ruin, and that gamblers bet less than full Kelly to cut ruin probability, smooth out volatility and leave room for model error. Then there’s the human side: deep drawdowns make full Kelly very hard to stick with.

Recovery maths says the same thing from the other direction. In Varsity’s position sizing chapter for active traders, a ₹1,00,000 account that drops 5% needs about 5.3% to get back to where it was. A 10% loss needs about 11.1%. A 60% loss needs a 150% gain on whatever’s left. Full Kelly makes it more likely you end up in that hole. Our explainer on recovery trauma in trading goes through the same arithmetic for small accounts.

Wikipedia’s classic biased-coin example shows how far theory and behaviour can drift apart. With a coin that lands heads 60% of the time on even-money bets, Kelly says bet 20% of your bankroll on each toss. Yet in a study summarised on the same page, many participants still went bust or bet badly despite a clear edge. Knowing the formula is one thing; following it under stress is another.

Full Kelly maximises growth on paper; half-Kelly and a hard risk cap maximise the chance you are still solvent when your edge estimate turns out to be optimistic.

Half-Kelly and Fractional Kelly in Practice

Wikipedia keeps the terms simple. A full Kelly bet uses the Kelly fraction, half-Kelly uses half that size, and quarter-Kelly a quarter. You give up some long-run growth, and in return you get gentler drawdowns and more slack for errors in your estimates of W and R.

Varsity’s practical tweak is more useful still for Indian retail traders. Keep the percentage-risk method as the outer limit, and let Kelly scale only within it:

• Set a maximum risk budget. Varsity’s worked illustration uses “up to 5%” of capital as a flexible ceiling for this Kelly overlay, while noting separately that many professionals stay within 1–3% risk per trade.
• If Kelly % is 30%, expose 30% of that 5% ceiling → 1.5% of capital at risk.
• If Kelly % is 70%, expose 70% of 5% → 3.5% of capital at risk.

Run the 31% Varsity example through a 5% ceiling on ₹5,00,000 and you get:

• Risk budget used = 0.31 × 5% = 1.55% of capital ≈ ₹7,750 maximum loss if the stop hits.
• Half of that Kelly reading inside the same ceiling comes to about 0.78% of capital ≈ ₹3,875.

That’s the spirit of half-Kelly, without pretending you know your live win rate to three decimal places.

Percentage Risk Example: Stops First, Size Second

Before getting to Kelly, Varsity shows percentage risk using an intraday Tata Motors futures setup (illustrative prices from their chapter):

• Entry near ₹393.65, stop at ₹390, target at least ₹400
• Stop distance ₹3.65; reward distance ₹6.35; reward-to-risk about 1.7
• Lot size 1,500; margin about ₹73,500 per lot in their example
• Capital ₹5,00,000; risk cap 1.5% → max loss ₹7,500
• Loss per lot if stopped = 3.65 × 1,500 = ₹5,475
• Lots allowed = 7,500 / 5,475 ≈ 1.36 → take 1 lot

Varsity sets that against buying six lots simply because 5,00,000 / 73,500 ≈ 6.8. Six lots would put about ₹32,850 at risk, roughly 6.57% of capital, well past the 1–3% professional rule of thumb they quote. Kelly doesn’t replace this stop-based arithmetic. All it does is help you decide whether today’s edge deserves the bottom or the top of your risk band. For how targets and stops relate, see our guide on risk reward ratio in trading.

Kelly vs Fixed Fractional 1% Risk

Fixed fractional position sizing holds risk almost constant, say 1% of current equity on every trade, however “good” a setup feels. On ₹5,00,000, 1% risk means ₹5,000 per trade. Shares or lots = rupee risk ÷ stop distance.

Here’s how it stacks up against Kelly:

For most Indian retail swing and positional traders, fixed fractional at 0.5–1% is the everyday default. Kelly is more of a research tool: run it on a closed set of at least several dozen trades before you let it push risk toward 1.5–2%. If you’re still working out how big an account needs to be before swing trading makes sense, read how much capital for swing trading in India.

How This Fits Common Indian Broker Guidance

In the Kelly chapter, Varsity’s own rule of thumb is that professional traders don’t risk more than 1% to 3% of capital on any one trade, and its percentage-risk example uses 1.5%. That sits well with the fixed fractional habit many Indian broker education desks teach beginners. Pick a small percentage, divide by the stop, and only after that look at margin or lot size.

Where retail accounts usually go wrong isn’t the formula. It’s skipping the stop, treating available margin as position size, or sizing up after losses (the gambler’s fallacy, which Varsity covers in its earlier position-sizing chapter). Kelly can’t fix a missing stop. Used properly, it only adjusts a risk percentage you’ve already capped.

A practical sequence that stays within broker-style advice:

1. Write down the stop first, and know the rupee loss per share or per lot.
2. Cap risk at 1% by default (or 1.5% only once your log is stable).
3. Work out Kelly % from your own closed trades (W and R), never from a win rate someone is marketing to you.
4. Use half-Kelly or Varsity’s “Kelly × risk ceiling” rule so the final risk stays within 1–3%.
5. If Kelly comes out negative, your numbers don’t show a positive expectation. Size goes to zero, not to “one small lot anyway.”

Limits and Failure Modes You Must Respect

Sample size. Ten trades, as in Varsity’s teaching example, are enough to show the algebra and nowhere near enough to trust a live Kelly percent. Win rate and average win/loss swing around a lot early in a system’s life.

Changing markets. W and R measured during a trending Nifty can fall apart when the index goes sideways. Both Wikipedia and the CFA note stress that probabilities are estimates, not constants.

Correlated bets. Three long positions in bank stocks aren’t three independent Kelly bets. Treat correlated risk as a single bucket.

Options and asymmetric payoffs. Buying options can cost you most of the premium, which is close to the “lose the whole amount risked” case. Selling options can lose many times the premium you collected. Use the real average win and average loss from your options log, and don’t borrow R from your equity swing trades.

Overbetting past Kelly. Wikipedia states plainly that betting more than Kelly raises ruin risk. If your spreadsheet says 12% and you take 25% “because conviction is high,” you’ve stopped doing Kelly. That’s just discretionary oversizing.

A Simple Checklist Before You Use Kelly Criterion Position Sizing

• Do I have a written strategy with a stop decided in advance?
• Do I have enough closed trades to estimate W and R honestly?
• Is my full Kelly percent so high that even half-Kelly goes past 2–3% risk?
• Have I converted Kelly into rupee risk, and then into shares or lots using the stop distance?
• Am I staying inside the framework laid out in our risk management in trading pillar?

If any answer is no, stick with fixed fractional 1% until the whole process feels boring. Boring position sizing is a good thing.

The Bottom Line

Kelly criterion position sizing gives Indian traders a principled link between edge (win rate and payoff ratio) and size. Varsity’s formula, Kelly % = W − [(1 − W)/R], came out at 31% on their published 10-trade illustration. They soften that full-Kelly reading right away by folding Kelly into a percentage-risk ceiling, so exposure stays in the low single digits of capital. Wikipedia’s history and the half-Kelly habit explain why: full Kelly assumes you know the odds and asks you to sit through painful drawdowns. For retail accounts, the version that survives real brokerage statements is half-Kelly or Kelly-scaled risk inside a 1–3% cap, alongside fixed fractional habits.

Use Kelly to ask sharper questions about sizing, not as permission to pile the account into one idea. Size from the stop, cap the damage, and only then let a verified edge nudge you from 1% toward 1.5%. Never from 1% toward 31%.