When Contract Granularity Will Not Let You Size Correctly
Position sizing formulas return continuous numbers. Markets trade in discrete units. On a large account the gap between the two is negligible, because rounding one contract off a position of forty changes very little. On a small account the gap is the whole problem, and no amount of care with the arithmetic makes it go away.
When the Calculation Returns a Fraction
Work through the division with a small account and a wide stop and the answer will frequently be less than one contract. There is no way to take that trade at the intended risk. The instrument does not offer a fractional unit, so the position is either one, which risks more than the plan allows, or zero, which is not a position.
This is not an edge case for accounts starting small. It is the normal case on any session where the range is wider than usual, which is to say on a meaningful share of sessions. The method works perfectly and then hands back an answer the market will not accept.
Rounding Up Costs More Than It Looks
Rounding a fractional answer up to one contract is the path of least resistance, and it is worth being precise about what it does. If the calculation asked for a little over half a contract, taking one nearly doubles the intended risk on that trade. Repeated across the sessions where it happens, the actual average risk drifts well above the stated one.
The distribution is the sharper issue. The trades that force the rounding are the ones with the widest stops, which are the volatile sessions. So the overshoot lands specifically where the rule is most likely to be tested, and the account carries excess risk in exactly the conditions it was sized to survive.
Rounding Down Means Not Trading
Rounding down is correct in principle. Rounding down to zero means the trade does not happen, and if that occurs on a large share of sessions, the strategy being run is no longer the strategy that was tested. The filter is now the account size rather than the rules, and it removes wide range sessions selectively.
Whether that hurts depends on the rule. If wide range days were unprofitable anyway, the accidental filter is doing something useful by accident. If they were where the rule made its money, the small account is systematically excluded from the trades that mattered, and its results will not resemble the test for reasons that have nothing to do with the rules themselves.
The Options That Are Real
Smaller contract denominations are the direct answer where they exist. A product carrying a fraction of the notional of its full sized sibling turns a coarse ladder into a finer one, and finer ladders round more accurately. Brokers offering fractional share exposure have the same effect for the same reason.
Choosing an instrument whose typical range fits the account is the other real option, and the less popular one, since it usually means trading something less prominent. There is also the passive answer, which is to accept the ceiling and let the account grow until granularity stops binding. That is slower and it is not a failure. It is the recognition that some sizing problems are account size problems wearing a different label.
What Does Not Help
Widening the risk limit until the arithmetic returns a whole number is the tempting non-answer. It resolves the rounding by moving the constraint the rounding was enforcing, which leaves the position where it was and removes the thing that made it disciplined.
Tightening the stop until the size works is the same manoeuvre in another direction, and it is worse, because stop placement is answering a different question entirely. A stop sitting where the trade is genuinely invalidated is not negotiable against a sizing constraint. If the two cannot be satisfied at once, the trade is unavailable at this account size, and saying so plainly is more useful than adjusting inputs until the spreadsheet cooperates.