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Risk Management Formulas

The core risk-management formulas every systematic trader should know, each with its variables, a worked Indian-market example in rupees, and its caveats.

Risk Formulas: Risk management is arithmetic applied before entry, not a feeling applied after a loss. The essential formulas are: risk per trade (a fixed fraction of equity you are willing to lose), position size (that rupee risk divided by the per-unit stop distance), portfolio heat (the sum of open risk across all positions), the Kelly fraction (the theoretically growth-optimal bet size), risk of ruin (the probability of hitting a capital floor), drawdown recovery (the gain needed to erase a decline), and the R-multiple (outcome measured in units of risk). Together they answer one question: how much to bet so that a normal string of losses cannot end you. The Kelly and risk-of-ruin figures in particular depend on stable, accurately estimated edge, which live markets rarely provide — so practitioners trade well below the mathematically optimal size.

These formulas convert a trading decision into a defensible position size. All examples use round, illustrative Indian-market numbers — capital of about five lakh rupees, Nifty around 25,000, a lot size of 75 — and are for education only, never a recommendation. For concepts behind the maths see Position sizing, Risk per trade, and Risk of ruin.

Risk per trade

Decide, before entry, the maximum you will lose if the trade hits its stop. It is normally a small fixed fraction of current equity.

ItemDetail
FormulaRupee risk (1R) = Equity × risk fraction
VariablesEquity = current account value; risk fraction = fraction risked per trade (e.g. 0.01 for 1%).
Worked exampleEquity ₹5,00,000 × 1% = ₹5,000 maximum loss on the trade. This ₹5,000 is one unit of risk, “1R”.
CaveatsThe realised loss can exceed 1R on a gap or slippage; the fraction should be based on live equity, not the starting figure.

Position size

Turn the rupee risk into a quantity using the distance to your stop. This is the formula that keeps every trade's downside equal.

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FormulaQuantity = (Equity × risk fraction) / (stop distance per unit × point value)
VariablesStop distance = points between entry and stop; point value = rupees per point per unit (per share = 1; per Nifty index point = lot size).
Worked exampleRisk ₹5,000. Nifty futures, stop 50 points away, lot 75 → risk per lot = 50 × 75 = ₹3,750. Lots = 5,000 / 3,750 ≈ 1.33 → round down to 1 lot.
CaveatsLot-based instruments force rounding, so actual risk rarely equals target exactly; always round down. Margin, not risk, may become the binding constraint.

Round down, never up

When the formula gives 1.33 lots, take 1, not 2. Rounding up silently increases your risk beyond the fraction you chose. Over many trades, consistently rounding up is how a disciplined 1% rule quietly becomes a 2% rule. A position-sizing calculator can automate the rounding.

Portfolio heat

Per-trade risk is not enough; correlated positions can all lose together. Portfolio heat is the total open risk across the book.

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FormulaHeat = Σ (open risk of each position) / Equity
VariablesOpen risk of a position = current distance to its stop × quantity × point value.
Worked exampleFour open trades each risking ₹5,000 = ₹20,000 open risk on ₹5,00,000 = 4% heat. A cap of, say, 6% would block a fifth full-size trade.
CaveatsSumming risk assumes independence; correlated positions (e.g. several Bank Nifty longs) can lose simultaneously, so effective heat is higher than the sum suggests. See Portfolio heat and diversification.

Kelly fraction

The Kelly criterion gives the bet fraction that maximises long-run growth for a known edge. It is a ceiling to stay well beneath, not a target.

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Formulaf* = W − (1 − W) / R, where R = avg win / avg loss (payoff ratio), W = win probability.
VariablesW = probability of a win; R = ratio of average win size to average loss size.
Worked exampleW = 0.55, avg win ₹8,000, avg loss ₹5,000 → R = 1.6. f* = 0.55 − 0.45/1.6 = 0.55 − 0.281 = 0.269, i.e. full Kelly ≈ 27% of equity per trade.
CaveatsFull Kelly is far too aggressive in practice — drawdowns are brutal and the inputs W and R are estimated with error. Practitioners use a fraction (half- or quarter-Kelly). A misestimated edge can make Kelly recommend a ruinous size. See Kelly calculator.

Why nobody bets full Kelly

Full Kelly maximises growth only if your win rate and payoff ratio are exactly right and constant — which they never are. Over-betting relative to your true edge causes growth to collapse and drawdowns to balloon. Because live edges drift and are estimated from limited data, most systematic traders bet a small fraction of Kelly, treating the formula as an upper bound.

Risk of ruin

Risk of ruin estimates the probability that a run of losses drives equity down to a defined floor before the edge plays out.

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Formula (simple model)For fixed-fraction, even-payoff bets: RoR ≈ ((1 − edge) / (1 + edge))^(units of capital), where edge = 2W − 1.
Variablesedge = expected fraction won per bet; units of capital = equity divided by the amount risked per trade.
Worked exampleW = 0.55 → edge = 0.10. Risking ₹5,000 of ₹5,00,000 gives 100 units. RoR ≈ (0.90/1.10)^100, a vanishingly small number — whereas risking ₹50,000 (10 units) gives (0.818)^10 ≈ 13%.
CaveatsThis closed form assumes fixed payoffs, a constant edge, and independent trades — none strictly true. It is a comparative guide (smaller bets, lower ruin), not a precise probability. See Risk-of-ruin calculator.

Drawdown recovery

Losses and the gains needed to undo them are asymmetric, and the asymmetry worsens sharply as drawdowns deepen.

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FormulaGain to recover = 1 / (1 − D) − 1, where D = fractional drawdown.
VariablesD = drawdown as a fraction of the peak (e.g. 0.20 for a 20% decline).
Worked exampleA 20% drawdown (₹5,00,000 → ₹4,00,000) needs 1/0.80 − 1 = 25% gain to get back. A 50% drawdown needs a 100% gain; a 90% loss needs a 900% gain.
CaveatsThis is why deep drawdowns are so dangerous — recovery cost is non-linear. It also explains why controlling maximum drawdown matters as much as raising returns.
DrawdownGain needed to recover
10%11.1%
20%25%
33%50%
50%100%
75%300%

R-multiple

Expressing every outcome in units of the amount risked makes trades of different sizes directly comparable and gives a size-independent measure of edge.

ItemDetail
FormulaR-multiple = trade P&L / initial risk (1R). Expectancy (in R) = mean of all R-multiples.
Variables1R = the rupee amount risked at entry; trade P&L = realised profit or loss.
Worked exampleRisked ₹5,000; trade made ₹15,000 → +3R. Over 100 trades averaging +0.25R, expected profit ≈ 100 × 0.25 × ₹5,000 = ₹1,25,000, before costs, illustratively.
CaveatsR assumes the initial risk was actually honoured; a stop that slips makes the realised loss more than 1R, distorting the statistics. Past expectancy does not guarantee future results.

How these fit together

Risk per trade sets 1R. Position size spends 1R across the stop distance. Portfolio heat caps how many 1R bets can be open at once. Kelly and risk of ruin tell you whether your chosen fraction is survivable. Drawdown recovery shows the cost of getting it wrong, and the R-multiple measures the result. Used together they make sizing a calculation, not a guess. See also Capital allocation and Stop-loss concepts.

Frequently asked questions

How do I calculate position size from risk?
Divide the rupee amount you are willing to risk by the per-unit loss at your stop. If you risk 5,000 rupees on Nifty futures with a 50-point stop and a lot size of 75, the risk per lot is 50 × 75 = 3,750 rupees, so 5,000 / 3,750 ≈ 1.33 lots, which you round down to 1 lot.
What is a sensible risk-per-trade fraction?
Many systematic traders risk a small fixed fraction of equity per trade, commonly cited around 0.5% to 2%, so that a normal losing streak does no lasting damage. This is a widely used heuristic for reasoning about survivability, not a rule or a recommendation, and the right figure depends on your strategy, edge, and tolerance.
What is portfolio heat?
Portfolio heat is the total open risk across all your positions, expressed as a fraction of equity. If four trades each risk 5,000 rupees on a 5,00,000-rupee account, heat is 20,000 / 5,00,000 = 4%. Capping heat prevents correlated positions from combining into a single oversized bet.
What is the Kelly criterion?
The Kelly criterion gives the bet fraction that maximises long-run growth for a known edge: f* = W − (1 − W)/R, where W is win probability and R is the payoff ratio. It is a theoretical ceiling; because real edges are uncertain and full Kelly produces severe drawdowns, practitioners bet a fraction of it.
Why do traders use a fraction of Kelly rather than full Kelly?
Full Kelly is optimal only if your win rate and payoff ratio are known exactly and stay constant, which never happens live. Overestimating your edge makes full Kelly over-bet, collapsing growth and producing brutal drawdowns. Half- or quarter-Kelly sacrifices a little theoretical growth for far more robustness to estimation error.
What is risk of ruin?
Risk of ruin is the probability that a run of losses reduces your capital to a defined floor before your edge can compound. It falls sharply as you risk less per trade: risking 1% of capital gives a far lower ruin probability than risking 10%, all else equal. It is a comparative guide, not an exact prediction.
Why does a 50% drawdown need a 100% gain to recover?
Because gains compound on a reduced base. Losing 50% of 5,00,000 leaves 2,50,000, and getting back to 5,00,000 from there requires doubling — a 100% gain. The recovery formula 1/(1−D) − 1 shows the cost rises non-linearly, which is why limiting maximum drawdown is so important.
What is an R-multiple in risk terms?
An R-multiple expresses a trade's result as a multiple of the amount risked at entry (1R). Risking 5,000 rupees and making 15,000 is a +3R trade. Averaging the R-multiples of many trades gives expectancy in R, a size-independent measure of edge you can compare across strategies.
Do these formulas guarantee I won't lose money?
No. They are tools to size positions so that a normal sequence of losses is survivable and comparable across trades. They cannot create an edge, protect against gaps or slippage beyond your stop, or predict the future. Every figure here assumes your inputs are accurate, which live markets constantly challenge.
Should risk be based on starting capital or current equity?
On current equity. Basing the risk fraction on live equity means position sizes shrink automatically during drawdowns and grow as the account recovers, which dampens losses when you are struggling. Sizing off a fixed starting figure keeps risking the same rupees even as the account falls, increasing effective risk.

Last reviewed 11 July 2026. Educational content only — not investment advice.

Educational content only — not investment advice. See our Risk Disclosure and Methodology.