Sizing A New Trade From Scratch

You have an idea you believe in. How many shares?

The instinct almost everyone starts with is to work backwards from the profit: "if this goes 20 percent I want to make $300k, so I need $1.5m." That reasoning produces sizes that are indistinguishable from wishful thinking, because nothing in it is a constraint. Sizing works the other way round. You ask what stops you — how much you can afford to lose, how much the market will let you buy and sell, what the house allows, how sure you actually are — and you take the smallest answer.

Four ceilings

Every new trade has four independent limits on its size, and they are genuinely independent: one can be enormous while another is tiny.

The risk budget. How many dollars are you willing to hand back if you are wrong? Most desks express this as a fraction of book equity per trade — 20 to 30 basis points is common — so a $50m book allows roughly $125k of loss on any single idea.

Liquidity. Can you build it and, much more importantly, get out of it? Sizing against average daily volume is not about being polite to the market, it is about whether your exit is a decision or an announcement.

House limits. Single-name concentration caps, sector caps, financing headroom, borrow availability. These are hard numbers you do not negotiate intraday.

Conviction. A discount applied to whatever survives the first three. A thesis with one of three legs confirmed does not get the same size as one with all three.

The one piece of arithmetic

Only the first ceiling needs a formula. Let $R$ be the dollars you are prepared to lose on the trade and $d$ be the distance to your invalidation level, expressed as a fraction of the entry price. Then the largest notional you may hold is

$$N = \frac{R}{d} .$$

In plain English: if you will accept losing $125,000 and you will be out after a 10 percent adverse move, you can hold $1.25m, because 10 percent of $1.25m is exactly the loss you accepted. Note what this does — it makes a wider stop mean a smaller position, which is the opposite of what traders do when they widen a stop to "give the trade room".

Worked example: a liquid large-cap

The book is $50m, the per-trade risk budget is 25 basis points, so $R = 125{,}000$. You want to buy XYZ at $42; your thesis is wrong below $38.30, so $d = 3.70 / 42.00 = 0.088$, an 8.8 percent stop.

• Risk-budget ceiling: $N = 125{,}000 / 0.088 = 1{,}420{,}000$, about $1.42m.
• Liquidity ceiling: XYZ trades $95m a day; at 10 percent participation you could build $9.5m in a session. Nowhere near binding.
• Concentration cap: 4 percent of a $50m book is $2.0m. Not binding.
• Conviction: one of three thesis legs has confirmed, so you take half. $1.42\text{m} \times 0.5 = 710{,}000$.

You buy $710k, about 16,900 shares. Sanity check: if the stop triggers at $38.30 you lose $16{,}900 \times 3.70 = 62{,}530$, roughly $63k — half your budget, exactly as intended.

Worked example: an illiquid small-cap

Same book, same $125k budget. ABC trades at $18 with $6m of average daily volume. Your invalidation is $15.80, so $d = 2.20 / 18.00 = 0.122$.

• Risk-budget ceiling: $125{,}000 / 0.122 = 1{,}024{,}000$, about $1.02m.
• Concentration cap: still $2.0m. Not binding.
• Exit liquidity: you want to be able to leave in one session at 15 percent of volume, so $0.15 \times 6{,}000{,}000 = 900{,}000$.
• Stress haircut: in the market you would actually be exiting into, volume halves. Apply 50 percent and the honest exit ceiling is $450,000.

So you buy $450k, about 25,000 shares. If the stop hits, you lose $25{,}000 \times 2.20 = 55{,}000$, well inside the $125k you were allowed to risk. That gap is not a mistake to be corrected. It is the market telling you this idea cannot carry a full-sized bet, and topping the position up to $1.02m would simply convert an exit decision into an exit problem.

The ceilings move after you put the trade on

None of these four numbers is fixed. Volatility doubles and the same stop distance now gets hit by ordinary noise, so the risk-budget ceiling falls. The stock has a bad earnings print and average volume drops by a third, so the exit ceiling falls. The book grows and the concentration cap rises. Your thesis confirms and the conviction discount goes away.

This is why the calculation belongs in a note you keep, not in your head at the moment of entry. Write down all four ceilings and which one bound, then reread it at the weekly review. When a position that was sized on a $900k liquidity ceiling is sitting in a name now trading $3m a day, you are over-sized without having bought a single extra share, and the only way to notice is to have written down why the original number was what it was.