should I round up or down when position sizing gives a fraction of a share

Round down, because rounding up takes more risk than the rule you wrote permits. The breach is largest exactly where the formula was least precise: at 34 shares one extra share adds about 3% to the position, at two shares it adds 50%. Rounding down can only ever leave you under your own limit, which is the direction a constraint is supposed to fail in.

the fixed number of units in which a derivatives contract must be traded is called the

Lot size. The exchange fixes it for each futures and options contract and there is nothing smaller — you can hold one lot or two, never one and a half. That makes the quantity step in derivatives far coarser than the one-share step in the cash market, so a rule that rounds neatly on shares may not be expressible at all in a contract.

how much does one extra share change my risk

By 1/n of the position, where n is the share count the formula returned — every share carries the same rupee risk, so adding one changes total risk by exactly one share’s worth. At 34 shares that is about 3%; at eight shares 12.5%; at two shares 50%. The same sizing rule is therefore precise on one trade and close to a coin toss on the next, purely because of what the share costs.

what does it mean when the position sizing formula returns less than one share

It means that at your stop distance, a single share risks more rupees than your rule allows, so the trade is outside what the account can express — the answer is zero, not one. A ₹60,000 account risking 1% has ₹600 to lose, and one share with a ₹1,900 stop distance would risk more than three times that. Treating those as absences rather than trades also matters when testing a system, because they were never available to take.

how big is the position if I risk 1 percent with a 3 percent stop

Position value equals the risk budget divided by the stop distance expressed as a fraction of price — so ₹4,000 of risk with a 3% stop buys roughly ₹1,33,000 of stock, whatever the share costs. Widen the stop to 10% and the same ₹4,000 of risk buys only about ₹40,000. Tight stops therefore produce surprisingly large holdings, which is where impact cost and concentration bite rather than where the loss does.

Position sizing, rounding and lot size

The account holds ₹4,00,000 and the rule, written down months ago and followed since, risks 1% of it on any single idea — ₹4,000. On Tuesday evening the scan produces three candidates. The first is a share at ₹3,850 with a sensible stop ₹117 below; the calculator says 34.19 shares and you buy 34, and the arithmetic is so nearly exact that you never think about it again. The third is a share quoted at ₹18,400 with a stop ₹1,900 below. The calculator says 2.1 shares. You buy three, because two feels like nothing, and in that one keystroke you have taken 43% more risk than your rule permits — on the trade where you were least paying attention.

Position sizing is taught, correctly, as a formula: risk budget divided by risk per share. What the formula returns is a real number, and what the exchange sells is an integer. Between them sits a rounding step nobody writes into their rules, and its effect is not uniform — it is trivial when the answer is large and violent when the answer is small.

Because every share carries the same risk, adding or dropping one share changes the position’s risk by exactly one share’s worth. As a fraction of the position, that is 1/n, where n is the number of shares. The arithmetic is trivial and its consequences are not.

Largest rounding error in risk ≈ 1 ÷ n

n: The number of shares the sizing formula returned, before rounding

Example: At 34 shares one share is about 3% of the position. At 8 shares it is 12.5%. At 2 shares it is 50%. The same sizing rule is precise on one trade and approximate on the next, purely because of what the share costs.

Think of it like this

Tiling two rooms

The same 2×2 foot tiles line both rooms. The hall takes about 41 tiles, so cutting one to fit changes almost nothing about the job. The bathroom takes about two and a half, so the decision to lay two or three is a decision about a large fraction of the floor, and no amount of care with the measuring tape improves it — the tile is simply large relative to the room.

In the market

A sizing formula is a measuring tape. A share is a tile. On a low-priced share with a tight stop the tile is small and the fit is near-exact. On a high-priced share with a wide stop the tile is a large part of the position, and the rounding decision matters more than the precision of the formula that produced it.

Worked example

One risk rule, four situations

A ₹4,00,000 account risking 1% — ₹4,000 — per trade

Share at ₹3,850, stop ₹117 awayActual risk ₹3,978, or 0.99% of the account. Rounding cost you almost nothing4,000 ÷ 117 = 34.19 → 34 shares

But look at what you now holdNearly a third of the account in one name. A tight stop always produces a large holding — the risk rule was satisfied and the exposure rule, if you have one, may not be34 × ₹3,850 = ₹1,30,900

Share at ₹9.40, stop ₹0.45 awayActual risk ₹3,999.60. Rounding is invisible at this share count — but the position is ₹83,547, and 8,888 shares in a name that trades three lakh shares a day is about 3% of a day’s volume4,000 ÷ 0.45 = 8,888.9 → 8,888 shares

Share at ₹18,400, stop ₹1,900 awayActual risk ₹3,800, or 0.95%. Taking three instead would risk ₹5,700 — 1.43% of the account, from a single share4,000 ÷ 1,900 = 2.11 → 2 shares

The same share, in a ₹60,000 account risking 1%The rule does not permit the trade at all. One share risks ₹1,900, which is 3.2% of that account, and puts 31% of it into one position600 ÷ 1,900 = 0.32 → 0 shares

Four trades under one rule, and the rule behaved four different ways. It was near-exact at 34 shares and at 8,888; it became a coin toss between 0.95% and 1.43% at two shares; and at a smaller account size it silently removed a candidate from the universe altogether. None of that is in the formula. All of it is in the fact that the quantity axis, like the price axis, moves in steps — and the step is one share, whose size in rupees is whatever the market happens to charge for it.

Loading interactive demo…

Move the price and the stop distance and watch the share count. The interesting region is where it drops into single figures.

In derivatives there is no rounding at all

In the cash market the smallest step is one share, which is usually small enough to be a nuisance rather than an obstacle. In derivatives the smallest step is one contract, and the Lot size is fixed by the exchange in a specification revised from time to time. There is nothing below it. If one lot carries more risk than your rule permits at your stop distance, you have exactly two options: take a position larger than your rule, or do not take the trade.

What the two markets let you choose

Cash market

The step is one share, so the sizing formula can usually be honoured to within a few per cent.
The step becomes coarse when the share is expensive or the account is small, and the coarseness is 1/n.
A candidate that cannot be sized is simply skipped, and the skip is quiet.
The binding constraint is often exposure, not risk — a tight stop produces a very large holding.

Derivatives

The step is one lot, fixed by the exchange, and there is nothing smaller.
If one lot exceeds your risk budget, the rule cannot be honoured at any quantity.
Skipping is the correct response and it feels like being excluded, which is why it rarely happens.
The margin figure is not the risk figure, so the account can look comfortable while the rule is being broken.

What this does to your universe, and therefore to your backtest

Follow the fourth line of the worked example one step further. If a ₹60,000 account cannot size the ₹18,400 share, then it cannot size any share where the stop distance in rupees exceeds its whole risk budget — which in practice removes most high-priced names from a small account entirely. The account’s real universe is not the universe it scanned. It is the subset it could have transacted, and that subset is skewed towards lower-priced shares.

The skew compounds with the previous lesson. Low-priced shares are also where the tick is a large percentage of price, so the names a small account can size are disproportionately the names where its entries and stops get rounded hardest.
A [[Backtest]] run across the full universe assumed positions the account could never have held. Not because of survivorship or costs, both of which get discussed, but because the sizing step would have returned zero and the trade would not have happened.
The fix is to filter before you test, not after. Apply the sizing rule as a screen: for each candidate on each historical date, would the rule have returned at least one unit? The trades where it returns zero are not losses, and they are not wins either — they are absences, and leaving them in inflates the sample with trades that were never available.
And the universe changes as the account grows. A rule that was untestable at ₹60,000 becomes testable at ₹6,00,000, which means the same written system is a different system at different account sizes. That is worth knowing before you conclude that a strategy stopped working.

◆ Your call

The sizing formula returns 1.4 shares

A ₹1,20,000 account, a 1% risk rule, and a candidate quoted at ₹22,000 whose sensible stop sits ₹850 below the entry. The formula returns 1.41 shares. The setup is the cleanest one on the list this week.

Simple bhasha mein

Halwai 2.1 plate nahi banata

Halwai per-plate hisaab rakhta hai. Aapka budget 2.1 plate ka nikla — ab do lo ya teen, beech mein kuch nahi milta. Share bhi aise hi poore milte hain. 4 lakh ke account pe 1% rule matlab ₹4,000 ka risk. Share ₹18,400 ka, stop ₹1,900 neeche — formula bola 2.11 share. Do liye toh risk ₹3,800 (0.95%, rule ke andar). Teen liye toh risk ₹5,700 — yaani 1.43%, aur aapka 1% ka rule ek hi share ki wajah se toot gaya. Jab formula 34 share bolta hai, tab ek share upar-neeche se kuch nahi bigadta; jab do bolta hai, tab ek share aadha position hai. Isiliye hamesha neeche round karo — aur agar ginti paanch se kam aa rahi hai, toh trade ka size aapka analysis nahi, calculator ki rounding tay kar rahi hai.

What to remember

The sizing formula returns a real number; the market sells integers, and the gap is rounding you never wrote down.
The rounding error in risk is about 1/n — invisible at 34 shares, decisive at two.
Always round down, and treat a share count below about five as a signal that granularity is now governing the trade.
In derivatives one lot is the floor. If a lot exceeds your risk budget, the rule cannot be honoured at any size.
Your account size silently selects your universe, so apply the sizing rule as a screen inside the backtest rather than after it.

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Common questions

Short, direct answers to what people ask about this topic.

should I round up or down when position sizing gives a fraction of a share: Round down, because rounding up takes more risk than the rule you wrote permits. The breach is largest exactly where the formula was least precise: at 34 shares one extra share adds about 3% to the position, at two shares it adds 50%. Rounding down can only ever leave you under your own limit, which is the direction a constraint is supposed to fail in.
the fixed number of units in which a derivatives contract must be traded is called the: Lot size. The exchange fixes it for each futures and options contract and there is nothing smaller — you can hold one lot or two, never one and a half. That makes the quantity step in derivatives far coarser than the one-share step in the cash market, so a rule that rounds neatly on shares may not be expressible at all in a contract.
how much does one extra share change my risk: By 1/n of the position, where n is the share count the formula returned — every share carries the same rupee risk, so adding one changes total risk by exactly one share’s worth. At 34 shares that is about 3%; at eight shares 12.5%; at two shares 50%. The same sizing rule is therefore precise on one trade and close to a coin toss on the next, purely because of what the share costs.
what does it mean when the position sizing formula returns less than one share: It means that at your stop distance, a single share risks more rupees than your rule allows, so the trade is outside what the account can express — the answer is zero, not one. A ₹60,000 account risking 1% has ₹600 to lose, and one share with a ₹1,900 stop distance would risk more than three times that. Treating those as absences rather than trades also matters when testing a system, because they were never available to take.
how big is the position if I risk 1 percent with a 3 percent stop: Position value equals the risk budget divided by the stop distance expressed as a fraction of price — so ₹4,000 of risk with a 3% stop buys roughly ₹1,33,000 of stock, whatever the share costs. Widen the stop to 10% and the same ₹4,000 of risk buys only about ₹40,000. Tight stops therefore produce surprisingly large holdings, which is where impact cost and concentration bite rather than where the loss does.