Position Sizing in Ticks and Kelly

Course 31 of 60 in the futures hub. Kelly hands you a percent of the account, and your broker wants a contract count. I'd use half of it at most, and less again if the trade will sit through the overnight session.

Contracts From Ruin Math

Kelly is a formula from betting math. Give it your win rate and how big your winners are compared with your losers, and it hands back the fraction of your account to risk on each trade so the account grows fastest over a long run. It sounds like exactly what a trader wants. The trouble starts when people read the answer as permission to size up to whatever the platform will carry.

Futures make it harder in a specific way. The formula speaks in percent of equity, while your broker speaks in contracts, ticks and margin. Until you've turned one into the other, the Kelly number is a slogan. Forex traders can run the same arithmetic in lots and pips, and the forex course does it that way.

1. What Kelly is answering

Here's the formula in plain terms. Call your win rate p, and your average winner divided by your average loser b. Kelly says risk f = p minus (1 minus p) divided by b. A system that wins 55% of the time with winners 1.2 times the size of its losers comes out at 0.55 minus 0.45 / 1.2, which is 0.175. That's 17.5% of the account on one trade.

That number answers one narrow question: on a bet repeated many times with known odds, what fraction grows the bankroll fastest? It assumes the odds are known and never change. It knows nothing about a gap on the Sunday reopen, a margin increase from your broker, or how sure you feel. Those land on you anyway, so I treat the formula as a ceiling and work out the real size underneath it, starting with the margin calculator.

2. Why half-Kelly

Full Kelly grows fastest on paper and hands you drawdowns most people can't sit through. Half-Kelly gives up some of that growth for a much calmer ride, and between the two I'd take half every time. Even half can be a big number, though. Here's what it looks like on a mid-sized account.

Half of 17.5% is 8.75%. On $20,850 that's 0.0875 x $20,850 = $1,824.38, call it $1,824, at risk on one trade. A 1% rule on the same account allows $208.50. I use whichever is smaller.

Look at the gap between those two numbers. The formula says risk nearly nine times what a plain 1% rule would allow. If my win rate estimate were spot on and the market never changed character, the bigger number might be right. Neither is true for me, so $208.50 is where I'd stop.

In my notebook Kelly only ever lowers the size. I check the dollar figure in the risk calculator before I think about contracts at all.

3. Convert to contracts

Now turn the dollars into contracts. Divide what you're allowed to lose by the dollar cost of your stop, and round down. Say the stop on ES is 8 points. ES ticks are 0.25 points at $12.50, so 8 points is 32 ticks and $400 a contract. $208.50 divided by $400 is 0.52, which rounds down to zero.

Zero is an answer. It means the stop is too wide for this account in the full-size contract. The Micro E-mini is a tenth of the size at $1.25 a tick, so the same 32-tick stop costs $40 and $208.50 covers five of them. Half-Kelly here says four full ES ($1,824 / $400 is 4.56, rounded down) on a twenty-thousand-dollar account. Don't celebrate that. Go back to your win rate, because something in it is off.

4. ETH haircut

ETH means extended trading hours, the part of the day outside the regular U.S. session. A stop I sized during the U.S. day isn't one I'd trust in those hours.

So if a position will be held through those hours, I cut the fraction before converting it. Halve it, run the division again, and accept the smaller count. The order matters. Size first and haircut later, and you end up arguing with yourself about closing one contract at a bad price.

5. When Kelly is a pass

Run the formula on a 45% win rate with the same 1.2 payoff and you get 0.45 minus 0.55 / 1.2, about minus 0.008. A negative answer means the expected value is below zero and the right size is nothing. Plenty of systems that feel good sit right around that line, and a lucky stretch in a short record can hide which side you're on.

I'd also leave the formula alone when the market just changed under me: a new contract, new hours, a margin change, or a strategy I've traded for a month. Numbers lifted from someone's blog aren't an estimate of anything. If you came here from the seasonality lesson, the same caution applies there, since a pattern from a handful of years is a small sample too.

6. Where people go wrong with it

The big one is treating Kelly as permission. A platform will let you hold four ES on a small account, and a formula fed optimistic numbers will sign off on it. Another is copying a size from someone on a stream whose account, stop and win rate you know nothing about. Costs matter too: commissions and slippage shave your average winner, which lowers b, which lowers the Kelly answer, sometimes below zero.

The next lesson, on sizing from ATR, comes at the stop distance from the volatility side. Kelly says how much of the account to put up. ATR says how far away the stop needs to be, and you need both before the order goes in.

Your win rate is an estimate

Every input to Kelly comes from your own trade record, and most records are short. Forty trades at a 55% win rate could easily be a 45% system that had a decent month. Nothing on the screen tells you which. That's the real reason to stay well under the formula: you're plugging in a guess and getting back a number with three decimal places.

What I do is keep the journal going, re-run the numbers every month or so, and let the fraction move slowly. If the win rate drifts down, the size drops before I've decided anything. If it drifts up, I wait for a lot more trades before believing it.

Sizing rules worth keeping

• Work out the Kelly fraction, halve it, and never let it go above your 1% cap.
• Convert dollars to contracts by dividing by the stop's dollar cost, then round down.
• Zero full-size contracts means micros or no trade.
• Cut the fraction first if you'll hold through the overnight hours.
• A negative Kelly result means the trade doesn't get made.

On this account and this stop that's five micros, and I'd take five micros I can sit through over four ES I can't. Educational only. Not a recommendation to buy, sell, or hold any contract or pair.