Guide · Risk and position sizing

Risk of ruin, explained and calculated

The short answer

Risk of ruin is the probability that a run of trades drives your equity down to a floor, such as zero or a level at which you stop, before it can compound. It depends on three things: the fraction of capital you risk per trade, your win rate, and your reward-to-risk ratio. Its defining, counterintuitive property is that a system with a genuine positive edge can still be near-certain to blow up if the per-trade risk is too high, because ruin is decided by the path equity takes, not only by where the average trade expects it to end.

Expectancy answers a question about the destination: over many trades, which way does equity drift. Risk of ruin answers a question about the journey: does a bad enough stretch arrive first and end the game. These are different questions, and conflating them is the most expensive mistake in retail sizing. This page is the reasoning behind the site's live calculators, the narrative for why the number on the screen moves. It teaches the actual mathematics: the gambler's ruin relationship, the Kelly criterion and why practitioners bet a fraction of it, and why risking a constant percentage of equity behaves so differently from risking a constant number of rupees. Every specific figure here is an illustrative model output, labelled as such, tied to assumed inputs, and never a claim about any real strategy or any student's results.

Why a positive edge is not enough

Start with the trap, because it drives everything else. Imagine a system that, over a long horizon, is expected to make money: on average each trade adds a small positive amount to equity. Intuition says such a system cannot go broke, that you simply wait for the average to assert itself. The mathematics disagrees. The average is a statement about a very long run. Ruin is a statement about the worst stretch inside that run, and a losing streak that is entirely ordinary for your win rate can be fatal if each loss removes a large slice of capital.

The mechanism is the asymmetry of a percentage loss. Lose 50 percent of an account and you do not need 50 percent to get back, you need 100 percent, because you are now compounding off a smaller base. Lose 80 percent and you need 400 percent. Push the per-trade risk high enough and a handful of consecutive losses, which probability guarantees will eventually occur, opens a hole that the edge can no longer fill within any horizon that matters. The edge sets the drift; the size sets whether you live long enough to collect it.

The curve is convex, and that is the whole point. With the edge held constant, doubling the risk per trade does not double the danger, it raises it far faster, because the number of capital units protecting you shrinks and that number lives in an exponent. The flat region on the left is where disciplined sizing lives; the cliff on the right is where confident traders with real edges still blow up. Illustrative.

The gambler's ruin formula

The classical model comes from gambler's ruin. Treat each trade as an independent bet of the same size, with a known probability of winning and a fixed payoff. Under those assumptions, the probability of eventually being wiped out has a clean closed form. For the fixed-fractional case commonly quoted in trading, the risk of ruin is approximately:

ROR ≈ ( (1 − A) / (1 + A) ) ^ C

where the two ingredients are:

A is the per-trade edge, expressed as a signed fraction. For a simple even-money bet it is just the win rate minus the loss rate. When wins and losses differ in size, a common form is A = (W × R − L) / (W × R + L), where W is the win rate, L = 1 − W is the loss rate, and R is the reward-to-risk ratio.
C is the number of risk units of capital you hold before you hit the floor. If you risk a constant 1 percent of equity per trade, you hold roughly 100 units; risk 5 percent and you hold 20; risk 10 percent and you hold 10. In short, C ≈ 100 / (risk percent).

Two structural facts fall straight out of this expression, and they are worth more than any single computed value. First, the base (1 − A)/(1 + A) is a number between 0 and 1 for any positive edge, so raising it to a higher power drives ruin toward zero. That means every extra unit of capital you keep in reserve, by risking less per trade, cuts ruin geometrically. Second, because C is the exponent and scales inversely with your risk percentage, shrinking the per-trade risk is a lever on the exponent, which is why its effect is so violent. The even-money version of this relationship is the standard textbook form of gambler's ruin; the reward-weighted edge is the adaptation traders use when their winners and losers are not the same size.

Read the formula as a shape, not an oracle. The value of the gambler's ruin expression is the direction it points: more edge and more units both push ruin down, and size is the strongest lever because it moves the exponent. The precise decimal it returns for a given input is a property of an idealised model, not a forecast of your account. Treat it as illustrative.

A worked illustration

To see the exponent bite, hold a single hypothetical edge fixed and vary only the size. Assume a modelled system with a 50 percent win rate and winners twice the size of losers, a reward-to-risk of 2. Then the reward-weighted edge is A = (0.50 × 2 − 0.50) / (0.50 × 2 + 0.50) = 0.50 / 1.50 ≈ 0.33. The base becomes (1 − 0.33)/(1 + 0.33) ≈ 0.503. Now walk the size up and watch the exponent do the work.

Illustrative model. One fixed edge (win rate 50 percent, reward-to-risk 2, so base of about 0.503), varying only the risk taken per trade. Figures are outputs of a simplified gambler's ruin model, not results of any real or offered strategy.
Risk per trade	Units of capital (C)	Modelled risk of ruin	What it means
1%	about 100	vanishingly small	Ruin from losses alone is negligible over any realistic horizon
2%	about 50	extremely small	Still deep safety margin, larger drawdowns become plausible
5%	about 20	small but real	Orders of magnitude riskier than 1 percent, though still low
10%	about 10	meaningful	A run of ten or so losses is now within reach and would gut the account
25%	about 4	severe	Only a handful of losers separates the account from the floor

The edge never changed. Only the size did. Yet modelled ruin travels from a rounding error to a serious threat, because C collapsed from 100 to 4 and it sits in the exponent. This is the arithmetic behind a rule that risk-first desks treat as close to sacred: cap the per-trade risk at a small, constant fraction of equity, and do it regardless of how convincing the current trade feels. The size is doing work that conviction cannot, and it is doing it in the one place, the exponent, where small changes have outsized consequences.

The Kelly criterion, and why practitioners bet less than it

If ruin punishes oversizing, what is the right size? The sharpest answer is the Kelly criterion, published by J. L. Kelly Jr in 1956. Kelly asks a specific question: which fixed fraction of capital, bet every time, maximises the long-run growth rate of the account. Its answer, in the simplest formulation, is that the optimal fraction equals the edge divided by the odds. For a bet with probability p of winning at net odds b to one, the growth-optimal fraction is f* = (b × p − q) / b, where q = 1 − p.

Kelly is elegant, but full Kelly is not what disciplined traders bet, for two connected reasons. The first is the shape of the growth curve. Growth rises as the fraction climbs toward f*, peaks there, then falls as you bet more, and crosses back below zero at roughly twice the Kelly fraction. Past f* you are taking more risk to earn less growth, which is the definition of a bad trade. Betting above full Kelly is therefore strictly dominated: it raises variance and ruin while lowering the very growth it was supposed to buy.

Half Kelly keeps most of the growth for a fraction of the pain. Because the curve is flat near its peak but the variance keeps rising with size, moving from full to half Kelly sacrifices only a modest slice of growth while cutting the swings substantially. Everything to the right of the peak is worse on both axes. Illustrative.

The second reason is deeper and specific to trading: your edge is estimated, not known. Kelly assumes you feed it the true probabilities. In markets you infer them from a finite backtest that is almost always flattering, curve-fit to some degree, and unstable across regimes. If your real edge is smaller than your estimate, then the fraction you believed was full Kelly is quietly above true Kelly, which puts you on the wrong side of the peak without knowing it. Fractional Kelly, betting a half or a quarter of the computed fraction, is the standard defence. It is not timidity, it is a margin of safety sized to the honest uncertainty in every backtest.

Illustrative and qualitative. The growth-versus-drawdown tradeoff across fractional Kelly choices, for a fixed edge. Directions are model-general, magnitudes are schematic, not measured, and not a promise of any outcome.
Sizing choice	Long-run growth	Depth of drawdowns	Sensitivity to a wrong edge estimate
Full Kelly	Maximum, in theory	Severe, frequent large swings	High, tips into overbetting if edge is overstated
Half Kelly	Most of the maximum retained	Much shallower than full	Forgiving, absorbs moderate estimation error
Quarter Kelly	Lower, but still positive	Gentle, easiest to hold through	Very forgiving
Above full Kelly	Falls, then negative past ~2x	Extreme, ruin rises sharply	Dangerous, strictly worse on both axes

Fixed-fractional versus fixed-rupee sizing

There is a second sizing decision hiding underneath the fraction, and it changes whether ruin is even reachable. It is the choice between risking a constant percentage of current equity and risking a constant rupee amount, and the two behave in fundamentally different ways during a losing run.

Fixed-fractional sizing risks the same percentage of whatever the account is worth right now. As equity falls, the rupee risk falls with it automatically. Each loss removes only a slice of what remains, never the whole, so the balance approaches zero without ever mathematically reaching it from losses alone. This built-in brake is a real protection, but it is not comfort: a bad run still produces a deep percentage drawdown, and the same shrinking that prevents ruin also slows the recovery, because you are now risking less in rupee terms just when you need to claw back.

Fixed-rupee sizing risks the same absolute amount every trade, whatever the balance. Early on that feels stable. In a drawdown it becomes corrosive: a constant rupee loss is a growing percentage of a shrinking account, so each successive loss bites harder, and a long enough streak can drive the balance to zero outright. The method that felt steady in calm markets is the one that can actually ruin you in a bad one.

Illustrative comparison of the two sizing regimes through a losing run. Behaviour is model-general; it is not a recommendation of either method or a claim about results.
Property	Fixed-fractional (percent of equity)	Fixed-rupee (constant amount)
Risk as equity falls	Shrinks automatically	Stays constant, so grows as a share
Can losses alone reach zero?	No, only approaches it	Yes, a long streak can
Behaviour in a drawdown	Self-braking, but recovery is slower	Self-accelerating downward
Behaviour in a winning run	Compounds, risk grows with equity	Linear, risk stays flat
Main weakness	Deep percentage drawdowns remain	True ruin is possible

Two accounts can run the identical entries and exits, differ only in this choice, and end a rough patch in completely different places: one bruised but alive on a percentage rule, the other at zero on a rupee rule. The site's drawdown-recovery calculator makes the recovery asymmetry concrete, showing how much larger the gain must be than the loss that preceded it, which is exactly why the self-braking property of percentage sizing matters so much.

Path dependence, seen directly

The cleanest way to feel why sizing dominates is to hold the edge and the sizing fixed, then simply re-run the same system many times. Because each sequence draws its wins and losses in a different order, the equity curves fan out. Most cluster and survive. A tail, produced by nothing more exotic than an unlucky early ordering of ordinary losses, drifts down and touches the floor. Same edge, same rules, different path, different fate. Ruin is the size of that unlucky tail.

Ruin is the weight of the lower tail. Nothing distinguishes the ruined paths except the order in which ordinary wins and losses arrived early. A resampling or Monte Carlo view like this is why risk-first practitioners judge a system by the spread of its outcomes, not by a single backtest equity curve, which is only one path out of the many that could have happened. Illustrative.

Why the real number is worse than the model

The gambler's ruin formula is a floor on danger, not a ceiling, because its three assumptions all fail in the direction that understates risk. Naming them is what separates using the number from being fooled by it.

Your edge is estimated, not known. The win rate and reward-to-risk you feed the formula come from a finite, backward-looking sample that selection and curve-fitting tend to flatter. If the true edge is smaller, every ruin figure computed from the optimistic one is too low. Feeding the conservative end of your uncertainty into the inputs, rather than the point estimate, is the honest adjustment.

Trades are not independent. Markets move in regimes, so losses cluster rather than arriving like independent coin flips. Clustering fattens the tail beyond what the formula's independence assumption admits, which means the true probability of a ruinous streak is higher than the clean model says.

Discipline drifts under pressure. The formula assumes you keep sizing to plan. Deep in a drawdown, the pull to increase size and win it back is strongest exactly when doing so is most dangerous, and that behavioural drift converts a survivable stretch into a ruinous one. It is a large part of why institutional desks hard-wire sizing limits and automatic stops rather than trusting judgement under stress.

What the math argues for. Taken together, these three gaps point one way: toward humility and small size, not toward any promised outcome. The formula does not tell you a system will make money at 1 percent risk. It tells you that oversizing can convert even a good system into a near-certain loss, and that a conservative fraction buys survival, which is the only state in which an edge can ever pay off. Survival is a precondition, not a return.

Where this fits, and what it means for you

Risk of ruin belongs to the sizing layer of trading, the step between having an idea worth acting on and deciding how much of the account rides on it. It cannot manufacture an edge, and no amount of clever sizing rescues a system with no edge at all. What it does is decide whether a real edge survives long enough to compound, and that is a question every serious approach has to answer before it worries about returns. Building the edge itself, the analysis that produces an entry worth taking and a level that genuinely invalidates it, is the upstream work that the method we teach is built around; sizing is how you make sure a run of bad luck never takes that work off the table.

In the curriculum this sits within Stage 3, where risk and capital preservation are treated before any discussion of scaling up. The sequence is deliberate: read charts, define an edge, then learn the mathematics of surviving it, in that order, because reversing them is how confident traders with genuine skill still end up at zero. The SEBI evidence below is the sober backdrop to all of it.

Use the live calculators

This page is the reasoning; the tools do the arithmetic. Work them together: derive an edge, turn it into a size, and see what a drawdown at that size would demand to recover.

Position-sizing calculator: turn a stop distance and a chosen risk percentage into a concrete position size, the C in the formula above.
Expectancy calculator: turn a win rate and reward-to-risk into an edge per trade, the A the ruin math depends on.
Drawdown-recovery calculator: see the loss-versus-recovery asymmetry that makes deep drawdowns so hard to climb out of.
All calculators: the full set, including compound returns and R-multiples.

Frequently asked questions

What is risk of ruin in trading?

Risk of ruin is the probability that a sequence of trades drives your equity down to a pre-set floor, such as zero or a level at which you stop, before it compounds. It is a function of three inputs: how much of your capital you risk on each trade, your win rate, and your reward-to-risk ratio. It is not the same as your average return. A system with a genuine positive edge can still carry a high risk of ruin if the per-trade risk is large, because ruin depends on the path equity takes, not only on where it is expected to end up.

How is risk of ruin calculated?

For a simplified model of independent, equal-sized bets, the fixed-fractional risk of ruin is approximately ((1 minus A) divided by (1 plus A)), raised to the power C, where A is the per-trade edge as a signed fraction and C is the number of risk units of capital you hold before hitting the floor. C equals one hundred divided by your risk percentage per trade. Because C sits in the exponent, ruin falls roughly geometrically as either the edge or the number of units rises. Real trading breaks the model's assumptions, so treat any single number as illustrative, not a promise.

Can a strategy with a positive edge still go to zero?

Yes, and this is the central lesson of the mathematics. Expectancy tells you where equity is expected to drift over many trades. Ruin is about whether a bad enough run arrives before that drift takes hold. If you risk a large fraction of capital per trade, a short losing streak that is entirely normal for your win rate can cut equity so deeply that recovery becomes arithmetically implausible. A positive edge sized too aggressively can therefore be near-certain to blow up. The fix is not a better edge, it is a smaller per-trade risk.

What is the Kelly criterion?

The Kelly criterion, published by J. L. Kelly Jr in 1956, gives the bet fraction that maximises the long-run growth rate of capital. In its simplest form the optimal fraction equals the edge divided by the odds. Betting the full Kelly fraction grows capital fastest in theory but produces severe swings. Betting above full Kelly is strictly worse: it raises variance and risk of ruin while lowering growth. Because real edges are estimated with error, most practitioners deliberately bet a fraction of Kelly, commonly half or a quarter, trading a little growth for a large reduction in drawdown.

Why do traders use fractional Kelly instead of full Kelly?

Full Kelly assumes you know your edge exactly. In trading you never do, you estimate win rate and reward-to-risk from a finite sample that is usually optimistic. If your true edge is smaller than you think, full Kelly quietly becomes overbetting, which lowers growth and raises ruin. Half Kelly keeps roughly three-quarters of the theoretical growth rate while cutting the size of drawdowns substantially, and quarter Kelly is gentler still. Fractional Kelly is best understood as a margin of safety against the estimation error baked into every backtest.

What is the difference between fixed-fractional and fixed-rupee position sizing?

Fixed-fractional sizing risks a constant percentage of current equity on each trade, so the rupee amount shrinks automatically as the account falls. Mathematically it cannot reach exactly zero from losses alone, because each loss removes only a fraction of what remains, though it can still fall into a deep drawdown that is painful and slow to recover. Fixed-rupee sizing risks the same absolute amount every trade regardless of equity, so a losing run removes a rising share of a shrinking account and can drive it to zero. Percentage sizing builds a natural brake that rupee sizing lacks.

How much should I risk per trade to keep risk of ruin low?

There is no universal number, and no honest source can promise you a safe one, because your true edge is unknown and your discipline under stress is uncertain. What the mathematics shows is direction, not a guarantee: for a fixed positive edge, cutting the per-trade risk fraction lowers modelled ruin sharply, because the number of capital units you hold rises and it sits in the exponent. This is why risk-first frameworks favour small, constant per-trade risk and treat the exact figure as a conservative choice, sized well below what aggressive math might tolerate, rather than a target to maximise.

Why is the real risk of ruin usually higher than the formula suggests?

The textbook formula assumes independent trades, a constant edge and a known win rate. Real trading violates all three. Your edge is estimated from a limited sample and is often optimistic, so the true edge may be smaller. Losses cluster because market regimes shift, which fattens the tail beyond what an independence assumption captures. And discipline can drift under drawdown, when the temptation to increase size to recover is strongest. Each of these pushes actual ruin above the modelled figure, which is one more reason to treat the formula as a floor on danger, not a ceiling.

Do the calculators on this site compute risk of ruin?

The free calculators handle the components that feed the ruin picture. The position-sizing calculator turns a stop distance and a risk percentage into a size. The expectancy calculator turns a win rate and reward-to-risk into an edge per trade. The drawdown-recovery calculator shows the asymmetry of losses, that a large drawdown needs a disproportionately larger gain to recover. This article is the narrative that explains why those numbers move the way they do, and why sizing, not edge alone, decides survival.

Where the facts come from

The Kelly criterion. J. L. Kelly Jr, A New Interpretation of Information Rate, Bell System Technical Journal, 1956, the original derivation of the growth-optimal bet fraction and the result that overbetting lowers growth. ieeexplore.ieee.org
Gambler's ruin. The classical fixed-fractional risk-of-ruin relationship, where ruin probability falls geometrically as the edge and the number of capital units rise, follows from standard gambler's ruin theory. en.wikipedia.org
SEBI evidence on retail outcomes. SEBI's study of individual traders in the equity derivatives segment, released July 2025, reported that about 91 percent of individual traders incurred net losses in FY25, with aggregate net losses of about ₹1,05,603 crore, up roughly 41 percent from ₹74,812 crore in FY24. Cited as context on why survival, not aggressive sizing, is the prior question. sebi.gov.in

Educational note. This guide explains the mathematics of risk of ruin and position sizing. Every numerical example is an illustrative output of a simplified model, tied to assumed inputs, not a result of any real, past, or offered strategy, and not a projection of any outcome. It is not a recommendation to trade or invest, and it is not investment advice. Bharath Shiksha is an educational publisher, not a SEBI-registered investment adviser or research analyst.