Guide · Risk and sizing · Stage 2

Position sizing from first principles: size from risk, not conviction

The short answer

Your position size is set by the loss you can afford on the trade, not by how sure you feel about it. Reasoned from the ground up, the first job before compounding is survival, so the size follows from one identity: size equals your risk budget divided by the stop distance per unit. Conviction decides whether to take the trade and where it is wrong, never how large it is, because confidence is poorly calibrated and highest right before the surprises that end accounts.

Almost every sizing guide hands you a formula and moves on. This one derives the discipline instead, because the formula only makes sense once you see the constraint it satisfies. Three ideas do the whole job: you cannot compound an account you have blown up, losses and their recoveries are brutally asymmetric, and the money at risk on a trade is a fixed identity in the stop distance. Put together, they force a conclusion most beginners resist: the feeling of certainty is the one input that must never touch the size.

The first principle is survival

Strip trading down to its base and there is a sequence: you must survive before you can compound, and you must compound before any edge turns into money. The order is not negotiable. A run of good trades means nothing if a single bad one, sized too large, takes the account below the level from which it can realistically come back. Survival is the binding constraint, and everything about sizing is downstream of it.

This reframes the opening question. The instinct is to ask "how much can I make on this trade," which pulls the size upward whenever the idea looks good. The correct question is the inverse: "how much can I lose here without impairing my ability to keep playing." That affordable loss is a number you choose deliberately, in advance, as a small slice of what you hold. Once it is fixed, the size is no longer a matter of opinion. It is whatever makes the loss, if the trade is wrong, land on that pre-chosen figure and no larger.

The regulator's own data is a blunt reminder of why survival, not upside, is the constraint that binds. In a study of individual traders in the equity derivatives segment published in July 2025, SEBI found that 91 percent of individual traders had net losses in FY25, with aggregate net losses of roughly ₹1,05,603 crore. In an environment where most participants lose, the trader whose sizing keeps them solvent through the losing stretches is playing a fundamentally different game from the one chasing the size that feels justified by a good setup.

Same trade, different survivor. Illustrative. The setup and the loss are identical for both traders. The only difference is the fraction staked. Conviction sizing puts the most capital behind the trades that feel surest, which is exactly where a surprise does the most damage; fixed-risk sizing caps the damage of any one trade so the account is still there for the next.

Why conviction is not a sizing input

The intuitive rule, bet more when you are more sure, fails for a specific and well-documented reason: human confidence is not calibrated to outcomes. Overconfidence is, in the decision-science literature, a miscalibration of subjective probability. When people say they are 90 percent certain, the event happens rather less than 90 percent of the time, and the confidence intervals they attach to forecasts are systematically too narrow. The feeling of certainty and the true probability of being right are different quantities, and they diverge most when the task is hard, which describes forecasting a market almost perfectly.

Worse, the miscalibration is not random noise you could average out. Confidence tends to run highest precisely where the exposure to a surprise is greatest: the trade that looks like a certainty is often the crowded, one-sided idea whose failure is most violent. Size on conviction and you are running a rule that loads the maximum capital onto the trades most able to end you. The emotion and the danger move together, so using the emotion as the sizing dial is close to the worst possible design.

Risk-based sizing severs that link on purpose. You risk a fixed small fraction of current equity on every trade, whatever the idea feels like, so the size no longer carries any information about your mood. Conviction is not discarded, it still decides whether the trade is worth taking at all and where the level sits that proves it wrong. What it never does is set the size, because the consequence of letting it, a surprise arriving on the trade you sized largest, is exactly the outcome survival forbids.

Two ways to answer "how large should this be"
Sizing rule	What actually sets the size	Failure mode
Conviction sizing	A feeling of certainty about the trade	Largest capital sits behind the trades most exposed to a surprise; one convincing idea that fails can end the account
Risk sizing	A fixed small fraction of equity and the stop distance	Size never reflects mood; no single trade, however sure it felt, can breach the survival line

The loss and gain asymmetry, made exact

The reason survival dominates is arithmetic, and it is worth seeing precisely rather than as a slogan. When an account falls by some fraction, the gain needed to climb back is calculated on the smaller balance that remains, so it is always larger than the fall, and it grows out of all proportion as the drawdown deepens. Lose 10 percent and you need about 11 percent to recover. Lose half and you need to double what is left. Lose three quarters and you need to quadruple it.

The relationship is a single expression. If the loss fraction is d, the recovery gain g is:

recovery gain g = 1 / (1 − d) − 1

Because the denominator shrinks toward zero as the loss approaches the whole account, the required gain runs away to the point of impossibility. This is the mathematical spine of the whole discipline: a moderate loss is an inconvenience, but a large one is a near-permanent condition, because the gain that would undo it is not one any realistic edge produces. That is why avoiding deep drawdowns is worth more than catching any single large gain, and why a small fixed risk per trade, which keeps drawdowns shallow, protects the base that all future compounding depends on.

The curve is why small losses are cheap and large ones are near-fatal. The gain needed to recover tracks the loss closely at the shallow end and then explodes: a 90 percent loss demands a 900 percent gain, which is why the entire object of sizing is to keep losses in the flat left region of this curve.

Drawdown and the gain required to break even. Exact arithmetic, g = 1 / (1 − d) − 1.
Loss taken	Gain needed to recover	What it means
10%	about 11.1%	Barely worse than the loss; recovered inside normal variation
20%	25%	The gap starts to open
25%	about 33.3%	A third back just to stand still
50%	100%	You must double what is left
75%	300%	A fourfold gain on the remainder
90%	900%	Effectively unrecoverable by any ordinary edge

Deriving the sizing rule from the two statements

Now the formula assembles itself, and it is worth deriving rather than quoting, because once you have derived it you can never be talked into sizing from margin or from a hunch again. It rests on exactly two statements, both of which follow from what we have already established.

Statement one, the risk budget. Survival demands that you risk only a fixed small fraction of your current equity on any trade. Call the fraction f. The money you are willing to lose on this trade, your risk budget R, is therefore your equity E multiplied by f.

Statement two, what a loss actually is. If the trade is wrong and the stop is hit, the loss equals the number of units you hold, the position size S, multiplied by the distance from entry to stop per unit, D. That is simply what a stop-out costs: size times the per-unit move against you.

These two describe the same quantity. The money you are willing to lose is the loss you take when stopped, so set them equal and solve for the only unknown, the size:

risk budget: R = E × f loss if stopped: R = S × D therefore: S = (E × f) / D

Everything the trade involves enters through this one identity. The instrument, the entry price, the volatility, the technical level you chose, none of them size the trade directly; they matter only through the stop distance D and the equity E. The size S is an output, computed last, never a round number you decide first and rationalise afterward. Read the identity and the discipline is obvious: a wider stop forces a smaller size for the same risk, a larger account permits a larger size, and the fraction f is the single dial that governs how aggressive the whole system is.

Three steps, and the size falls out at the end. The affordable loss and the stop distance are the only two inputs. Dividing one by the other gives the size directly, which is why a disciplined trader can state their size the moment they know their stop, with no reference at all to how good the trade feels.

An illustrative worked example

Take round, invented numbers purely to watch the identity resolve. Suppose an account holds ₹5,00,000 of equity, the trader has decided to risk a fixed 1 percent per trade, and a technical level places the stop ₹8 below a planned entry near a price of ₹500. The risk budget is ₹5,00,000 multiplied by 0.01, which is ₹5,000. The stop distance is ₹8 per unit. The size is therefore ₹5,000 divided by ₹8, which is 625 units. If the trade is wrong and the stop fills at the level, the loss is 625 multiplied by ₹8, which is exactly the ₹5,000 chosen in advance. Nothing about how promising the setup looked entered the calculation, and that is the point.

Illustrative only. Every figure above is invented to demonstrate the arithmetic of the size identity. It describes no actual trade, instrument, or outcome, and no result, win rate, or return is implied. The position-sizing calculator performs exactly this arithmetic for figures you enter yourself.

Why the fraction must be small, and where ruin sets the ceiling

The derivation fixes the shape of the rule but leaves one number open: how small should the fraction f be. First principles answer the direction without hand-waving. Losses arrive in clusters, not politely spaced out, so the fraction has to be small enough that a realistic run of consecutive losing trades still leaves the account in the flat, recoverable region of the drawdown curve. If a losing streak of a plausible length would push you toward the steep right-hand side of that curve, the fraction is too large, full stop.

The fixed-fractional method, risking a constant fraction of current equity, has a property that makes this work in your favour: as the account shrinks, the same fraction stakes fewer rupees, so the losses automatically taper and the account resists being driven to zero. That is precisely why it is the conservative default that dramatically lowers the probability of ruin, and why small fractions on the order of one or two percent are so widely used. But the exact safe ceiling is not a first-principles constant. It depends on the variance of the strategy, and turning it into a number is the job of the risk-of-ruin math, which shows how the probability of eventually blowing up depends jointly on your edge, your variance, and the fraction you risk. Sizing and ruin are the same question asked from two ends.

There is a second constraint that first principles cannot see but reality imposes: you cannot always place the exact size the identity returns. In Indian derivatives, contracts trade in fixed lot sizes, so the tradable size jumps in discrete steps and the smallest possible position may already risk more than your budget allows. That lot-size floor is where a clean identity meets a hard market constraint, and the practical India method is built around exactly that friction. Reasoning about capital at risk from the stop, rather than from the margin an instrument happens to require, is the same upstream judgement that the method we teach is built around.

Where the reasoning is abused. The commonest way to defeat this whole framework is to size from the margin instead of the stop. In a leveraged instrument the margin is a small fraction of the exposure, so a size that looks modest against the margin can risk many times your intended budget once the stop distance is counted. Always run the identity on the loss taken if the stop is hit, then confirm the exposure and its margin are ones you can actually hold. If the smallest tradable size breaks the budget, the honest move is to pass on the trade, not to widen the risk to fit.

What follows once size is set by risk

Reasoned from the base, position sizing turns out to be a survival tool wearing the costume of an optimisation problem. It is not the lever that makes money; the edge does that, and the edge lives upstream in the analysis that decides whether a trade is worth taking and where it is wrong. What sizing does is guarantee you are still holding the account when the edge pays out, by refusing to let any single trade, however sure it felt, breach the line past which recovery is a fantasy.

That is the entire argument in one line: size from the loss you can afford, because the affordable loss is the only input that keeps you in the game, and the game is the only place the edge can ever work. Conviction picks the fights. Risk sets the stakes. Keep the two jobs separate and the arithmetic of survival is on your side.

Common Questions

Frequently asked questions

What is the first principle of position sizing?

Survival. Before you can compound an account you have to still hold it, and one large enough loss ends the game permanently. So the first question is not how much you can make on a trade, it is how much you can lose without impairing your ability to keep trading. The affordable loss is the input; the position size is what the affordable loss and the stop distance produce together. Everything downstream, the instrument, the price, the target, feeds through that.

Why should position size not be based on conviction?

Because confidence is not calibrated to outcomes, and it tends to peak exactly when a surprise is most likely. If you size up when a trade feels sure, you place the most capital at risk right before the trades most able to hurt you, and a single one can end the account. Risk-based sizing removes the feeling from the decision: you risk a fixed small fraction of equity on every trade regardless of how good the idea looks, so no one trade, however convincing, can ruin you.

Why does a 50 percent loss need a 100 percent gain to recover?

Because the recovery gain is calculated on the smaller balance left after the loss. A 50 percent loss halves the account, and doubling what remains, a 100 percent gain, only returns it to the start. The general relationship is recovery gain equals one divided by one minus the loss fraction, minus one. It rises far faster than the loss itself: 10 percent needs about 11 percent, 25 percent needs about 33 percent, 50 percent needs 100 percent, 75 percent needs 300 percent.

How do you derive the position-sizing formula?

Start from two statements. First, risk a fixed fraction f of current equity on the trade, so the money at risk is equity multiplied by f. Second, the loss if the stop is hit equals the position size multiplied by the stop distance per unit. Set the two equal, because the money at risk is the loss you take when stopped, and solve for size: size equals equity multiplied by f, divided by the stop distance per unit. Size is an output, not a starting guess.

What fraction of equity should you risk per trade?

First principles fix the direction, not a magic number: the fraction has to be small enough that a realistic run of consecutive losses cannot take the account into the region where recovery becomes impractical. Small fixed fractions such as one or two percent are common defaults because they keep the worst plausible losing streak survivable. The exact ceiling is a risk-of-ruin question that depends on the variance of the strategy, which is why sizing and the probability of ruin have to be reasoned together.

Why does avoiding large drawdowns matter more than catching large gains?

Because losses and the gains needed to undo them are asymmetric. A small drawdown is recovered by a slightly larger gain, but a large drawdown demands a gain so large it is unrealistic: 75 percent lost needs 300 percent back, 90 percent lost needs 900 percent. A missed gain costs you an opportunity; a large loss damages the base that every future gain compounds on. Protecting the compounding base is worth more than any single upside you might catch.

Does risk-based sizing mean ignoring conviction entirely?

Conviction still decides whether to take the trade and where the idea is wrong, which sets the stop. What it must not do is set the size directly. The reasoning is one of consequence, not disrespect: since confidence is poorly calibrated and highest before surprises, letting it move the size concentrates capital exactly where it is most dangerous. Keeping the risk fraction fixed lets you act on good ideas without any single one being able to end you.

How does position sizing relate to leverage in Indian derivatives?

The size identity is written in terms of the loss taken if the stop is hit, not the margin posted. In leveraged instruments the margin is a small fraction of the exposure, so reasoning from margin badly understates the money at risk and produces sizes far too large. Size from the stop distance and the affordable loss, then check that the resulting exposure and its margin are ones you can hold. The lot-size floor in Indian derivatives complicates this, which the practical India guide covers.

Is the worked example in this guide a real result?

No. Every number in the worked example is illustrative and chosen to show how the size identity resolves, not to describe any actual trade, instrument, or outcome. The arithmetic of the drawdown-recovery table is exact and verifiable because it is pure mathematics, but no performance, win rate, or return is claimed anywhere. This is an educational explanation of a reasoning method, not a recommendation or a record of results.

Where the facts come from

Sources

SEBI, individual traders in the equity derivatives segment. The study published in July 2025 reported that 91 percent of individual traders had net losses in FY25, with aggregate net losses of roughly ₹1,05,603 crore, the cited basis for treating survival as the binding constraint. sebi.gov.in
Drawdown-recovery arithmetic. The recovery-gain relationship g = 1 / (1 − d) − 1 is elementary algebra; the tabulated values (50 percent needs 100 percent, 75 percent needs 300 percent, 90 percent needs 900 percent) are exact and independently verifiable.
Fixed-fractional sizing. The method of risking a constant fraction of current equity per trade, and its property of tapering losses as equity falls to reduce the risk of ruin, is set out in Ralph Vince, Portfolio Management Formulas, and is standard in the money-management literature.
Overconfidence and miscalibration. The finding that subjective confidence is systematically miscalibrated, with stated certainty exceeding realised accuracy and intervals set too narrow, is a well-established result in the judgement-and-decision-making literature on the overconfidence effect.

Educational note. This guide explains the reasoning behind position sizing. It is not a recommendation to trade or invest, and it is not investment advice. Illustrative figures are labelled illustrative and describe no actual result. Bharath Shiksha is an educational publisher, not a SEBI-registered investment adviser or research analyst.