Loss from peak
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Free Tool
Drawdown Recovery Calculator
A loss and its recovery are not symmetric. Lose 50 percent and you do not need 50 percent back, you need 100 percent, because the gain is measured against the smaller capital that survived. Enter a drawdown depth and this tool returns the exact gain required to reach the prior peak, the recovery multiple, the rupee hole on an optional account value, and, on your own assumed return, how long the climb takes. Then it plots the convex recovery curve against the 1 to 1 line, so the widening asymmetry is impossible to miss.
The first rule of compounding is not losing. You cannot out-earn a deep drawdown; you can only avoid it, because the gain required to recover curves upward without bound.
Arithmetic, not a forecast. The required gain and the recovery multiple are exact and depend only on the drawdown depth you enter. The time to recover uses a return per period that you supply as an assumption; it is arithmetic on that assumption, not a forecast, and no return is implied or achievable by using this tool. The teaching point is the shape of recovery, not any level of return you should expect.
Drawdown depth
Presets
The loss from your peak, as a positive percent. Must be above 0 and below 100.
Optional. Your assumption for the recovery rate, not a rate the tool can produce. Used only for time to recover.
Optional. Used to show the rupee hole and the rupee gain required.
Gain required to recover
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Recovery multiple
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Time to recover
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Rupee hole to fill
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The asymmetry, in one line
Capital surviving
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Gain required
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Gain minus loss (the penalty)
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The recovery curve against the 1 to 1 line
The straight line is the naive expectation, a loss recovered by an equal gain. The curve is the truth: the gain actually required. Your drawdown is marked, and the vertical gap between curve and line at that point is the asymmetry you are paying.
Your drawdown, step by step
| Quantity | Value |
|---|
Time to recover at nearby rates
| Assumed return / period | Periods |
|---|
Periods to climb back, from ln(1 divided by (1 minus d)) divided by ln(1 plus r). Each rate is an assumption you might use, not a return this or any tool can deliver.
Flags to read before trusting the recovery number
The recovery arithmetic is fixed and unforgiving, so the leverage is entirely upstream, in never letting the drawdown get deep. That means sizing every position from a real stop and holding hard risk limits so an ordinary losing streak stays shallow enough to recover from. That discipline, capping the depth rather than hoping to out-earn it, is what the method we teach is built around, because the account you keep is the one you did not blow a hole in.
The one principle
A loss and its recovery are not symmetric. The loss is measured against the capital you had; the recovery is measured against the smaller capital that survived, so the gain required is always larger than the loss and it grows without bound. A 50 percent loss needs a 100 percent gain, a 75 percent loss needs 300 percent, a 90 percent loss needs 900 percent. This convexity is the mathematical reason the first job of a trader is not losing: because you cannot realistically out-earn a deep drawdown, the entire game is capping how deep it can go.
This is the most expensive fact in trading, and it is arithmetic, not opinion. The SEBI FY25 finding that over 91 percent of individual derivatives traders were net loss-making, with aggregate net losses near 1,05,603 crore rupees, is in large part this asymmetry playing out at scale: positions sized too large for the stop turn an ordinary losing streak into a drawdown deep enough that the required recovery gain is a return almost nobody sustains. The account does not fail because the trader could not find gains; it fails because the hole demanded a gain the market never owes anyone.
The math, derived
Read it from the capital that survives. A drawdown of fraction d leaves you holding one minus d of the peak. To get back to the peak, that survivor must grow by the gain g that closes the gap. The condition is forced:
surviving capital = peak × (1 − d)
recover: surviving × (1 + g) = peak
so (1 + g) = 1 ÷ (1 − d)
the recovery multiple: the factor the survivor must be multiplied by
g = d ÷ (1 − d)
the required gain, always larger than d for any d above 0
recover: surviving × (1 + g) = peak
so (1 + g) = 1 ÷ (1 − d)
the recovery multiple: the factor the survivor must be multiplied by
g = d ÷ (1 − d)
the required gain, always larger than d for any d above 0
Worked on a 25 percent drawdown: the survivor is 0.75 of the peak, the recovery multiple is 1 divided by 0.75, about 1.333, and the required gain is 0.25 divided by 0.75, about 33.3 percent. Not 25. The extra 8.3 points is the penalty for having divided by a smaller base. Push d to 0.50 and the survivor halves, the multiple is 2, and the required gain is exactly 100 percent. Push d to 0.90 and the survivor is a tenth, the multiple is 10, and the required gain is 900 percent. The loss uses the old, larger denominator and the recovery uses the new, smaller one, and that single mismatch is the whole asymmetry.
time to recover at rate r per period:
(1 + r)t = 1 ÷ (1 − d)
t = ln( 1 ÷ (1 − d) ) ÷ ln( 1 + r )
r is YOUR assumption; t is arithmetic on it, not a forecast
(1 + r)t = 1 ÷ (1 − d)
t = ln( 1 ÷ (1 − d) ) ÷ ln( 1 + r )
r is YOUR assumption; t is arithmetic on it, not a forecast
The time identity just asks how many periods of compounding at r it takes to reach the recovery multiple. At an assumed 12 percent per period, a 50 percent drawdown needs about 6.1 periods and a 75 percent drawdown about 12.2, because the deeper hole demands a larger multiple and the log of that multiple grows. The rate is an assumption you provide; the tool does not know and cannot promise it.
Why avoiding the loss beats recovering it. Cutting the drawdown in half more than halves the required gain, because g grows faster than d. Halving a 50 percent drawdown to 25 percent takes the required recovery from 100 percent down to 33.3 percent, a two-thirds reduction in the gain you must find. Prevention has convex payoff; recovery has convex cost. That is the same fact read from both ends, and it is why a risk manager spends effort capping depth rather than planning heroic comebacks.
The asymmetry, drawn
Plot the gain required against the depth of the loss and lay the naive 1 to 1 line beneath it. At shallow losses the two nearly touch: down 10 needs up 11.1. As the loss deepens the curve peels away and climbs toward the vertical, because the surviving base is vanishing. The gap between the curve and the line at any depth is the penalty the arithmetic charges for that drawdown.
Loss against recovery, side by side
Set four drawdowns next to the gains they demand and the asymmetry stops being abstract. At ten percent the two bars are almost level. By fifty percent the recovery bar is twice the loss. By seventy-five percent it is four times the loss, and the shape is accelerating, not steadying.
Reference: the full recovery ladder
The complete asymmetry from a shallow dent to a near-total loss, with the required gain, the recovery multiple, and the number of periods to climb back at a stated assumed return of 12 percent per period. Read the required gain as exact arithmetic and the time column as arithmetic on that single assumption, not a return anyone should expect. This is the table the tool above computes for whatever depth you enter.
| Drawdown suffered | Gain required to recover | Recovery multiple | Periods at assumed 12% / period | What it means |
|---|---|---|---|---|
| −5% | +5.3% | 1.05x | 0.5 | A scratch. Recovery barely exceeds the loss. |
| −10% | +11.1% | 1.11x | 0.9 | A mild dent, quickly repaired. |
| −15% | +17.6% | 1.18x | 1.4 | Still linear-looking; the gap is opening. |
| −20% | +25.0% | 1.25x | 2.0 | The recovery is already a quarter above the loss. |
| −25% | +33.3% | 1.33x | 2.5 | A third more than the loss, just to get flat. |
| −33.3% | +50.0% | 1.50x | 3.6 | Half your survivors' next job is repair. |
| −40% | +66.7% | 1.67x | 4.5 | The curve is bending hard now. |
| −50% | +100.0% | 2.00x | 6.1 | You must double the survivors to undo one halving. |
| −60% | +150.0% | 2.50x | 8.1 | A one-and-a-half-times gain merely to break even. |
| −75% | +300.0% | 4.00x | 12.2 | A near-terminal hole; recovery may never come. |
| −90% | +900.0% | 10.00x | 20.3 | Effectively unrecoverable within a normal horizon. |
Trace the acceleration in the required-gain column. From minus 40 to minus 50 percent the required gain jumps 33 points, from 66.7 to 100. From minus 80 to minus 90 it would jump 500 points. The loss deepens in even steps while the recovery requirement explodes, and the periods column shows the same story in time: at an assumed 12 percent, a mild drawdown is undone in a period or two, but a 90 percent loss needs roughly twenty periods of flawless compounding just to reach the starting line.
Failure modes: where the clean number still misleads
The recovery identity is exact, but the identity is not the whole story of getting an account whole again. Five things break the tidy number in practice, and each one makes the real recovery harder than the arithmetic suggests.
1. Position sizing set the depth, and you cannot undo it after the fact. The single variable that governs how far a losing streak can drag the account is the size of each bet. Risking 1 percent, ten straight losses cost about 10 percent and need roughly an 11 percent recovery. Risking 5 percent, the same streak costs about 40 percent and needs a 67 percent recovery. Depth is decided upstream by sizing; by the time you are reading the recovery number, the expensive choice has already been made. The companion position sizing calculator is where that choice actually lives.
2. Deep drawdowns are where discipline collapses. The arithmetic assumes you keep executing the same process on the way down, but the psychology of a large drawdown pushes the opposite way. People abandon a working system at its worst point, or double up to get even faster, precisely when the recovery math is most hostile and a further loss is least affordable. Increasing risk after losses is a martingale, and it turns a survivable drawdown into a terminal one, because a larger bet on a shrunken base is exactly the move the geometry punishes hardest.
3. Withdrawals make recovery path dependent. For an untouched balance the recovery depends only on the depth of the loss. The moment you take money out, order and timing start to matter: selling units to fund a withdrawal while the account is down locks in part of the loss and shrinks the base the required gain has to act on. An account being drawn down during a deep drawdown can fail to recover even when the underlying method eventually does. The compound returns calculator shows this sequence-of-returns effect directly.
4. Account drawdown is not strategy drawdown. A backtest reports a strategy's peak-to-trough on its own equity curve, with no deposits, no withdrawals and no leverage layered on. Your account adds all three. A method in a modest 12 percent drawdown can sit inside an account that is far deeper in the hole because of over-leverage or capital added at the peak. Feed the recovery identity the drawdown that actually governs your capital, not the gentler backtest figure that never carried your real position sizes or cash flows.
5. Chasing a bigger return to climb out usually makes it worse. The instinct in a deep hole is to reach for a higher return, but a bigger target almost always means bigger swings, and under compounding, larger swings lower the return you actually keep through volatility drag. So the very move meant to speed the recovery can slow it, while raising the risk of a fresh drawdown from an already weakened base. You cannot out-earn a deep drawdown by taking more risk; that is the trap the arithmetic sets, and the only reliable exit is to have never been that deep.
Common Questions
Frequently Asked Questions
Why does a 50 percent loss need a 100 percent gain to recover?
+Because the gain is measured against the smaller capital that survives the loss, not against the capital you started with. A 50 percent loss on 1,00,000 leaves 50,000. To rebuild 50,000 back to 1,00,000 you must double it, which is a 100 percent gain on the reduced base. The general rule is that the required gain equals the drawdown divided by one minus the drawdown: 0.50 divided by 0.50 is 1.00, or 100 percent. The loss and the recovery use different denominators, and that mismatch is the entire source of the asymmetry. It is arithmetic, not psychology, and it holds for any account of any size.
What is the formula for the gain needed to recover a drawdown?
+For a drawdown of fraction d, expressed as a decimal, the gain required to return to the prior peak is g equals d divided by one minus d. Down 10 percent needs 0.10 divided by 0.90, about 11.1 percent. Down 25 percent needs 0.25 divided by 0.75, about 33.3 percent. Down 50 percent needs 0.50 divided by 0.50, exactly 100 percent. Down 90 percent needs 0.90 divided by 0.10, exactly 900 percent. Equivalently the recovery multiple is one divided by one minus d, so the surviving capital must be multiplied by that factor to get back to whole. The required gain is exact and depends only on the depth of the loss.
How long does it take to recover from a drawdown?
+That depends on the return you can earn while climbing back, which is an assumption, not something any tool can supply. If you compound at a rate r per period, the number of periods to recover a drawdown d is the natural log of one divided by one minus d, divided by the natural log of one plus r. At an assumed 12 percent per period, a 25 percent drawdown takes about 2.5 periods, a 50 percent drawdown about 6.1, and a 75 percent drawdown about 12.2. This calculator computes the time from whatever return you enter and labels it clearly as resting on your assumption. It is arithmetic on that assumption, not a forecast, and no return is implied or achievable by using it.
Why is the recovery curve convex rather than a straight line?
+Because the denominator in the required-gain formula, one minus d, shrinks as the loss deepens, and dividing by a shrinking number grows without bound. Near shallow losses the required gain is only slightly larger than the loss: down 10 needs up 11.1, close to a straight line. As d approaches 1, one minus d approaches zero and the required gain heads to infinity, so the curve bends sharply upward. Between the two, each extra percent of drawdown costs progressively more in required gain: the step from 40 to 50 percent adds 33 points of required gain, but the step from 80 to 90 percent adds 500. Convexity is why deep drawdowns are not merely worse, they are disproportionately worse.
What is the difference between account drawdown and strategy drawdown?
+Strategy drawdown is the peak-to-trough decline of a method measured on its own equity curve, before you add or remove money. Account drawdown is what your actual balance does, which is affected by deposits, withdrawals, position sizing and leverage layered on top. They can differ sharply. A strategy in a modest 12 percent drawdown can leave an account in a far deeper hole if the trader was over-leveraged or added capital at the peak and is now compounding the loss on a larger base. The recovery identity applies to whichever figure you feed it, so it matters that you measure the drawdown that actually governs your capital, not the gentler backtest number that never had your withdrawals in it.
Why do withdrawals make a drawdown harder to recover?
+Because taking money out during a drawdown removes the very capital that would have compounded the recovery, and it does so at the worst possible price. This is path dependence: for an untouched balance the recovery depends only on the depth of the loss, but once you withdraw, the order and timing of losses change the endpoint. Selling units to fund a withdrawal while the account is down locks in part of the loss and shrinks the base that the required gain has to act on, so the same percentage recovery now returns you to a lower level. An account being drawn down during a deep drawdown can fail to recover at all, even if the underlying strategy eventually does, which is why withdrawal policy belongs in any honest recovery plan.
How does position sizing limit how deep a drawdown can go?
+Position sizing caps the loss per trade, which caps how far a losing streak can drag the account, which is the whole game because the required gain explodes with depth. Risking a fixed fraction of the account, say 1 percent, means ten straight losses cost roughly 10 percent and need about an 11 percent gain to recover, which is survivable. Risking 5 percent turns the same ten-loss streak into roughly a 40 percent drawdown needing a 67 percent gain, which is not. A fixed-fractional model also shrinks the rupee bet automatically as the account falls, which is the property that keeps ordinary streaks from becoming terminal. Depth is set upstream by the size of each bet, so avoiding a deep drawdown is far cheaper than recovering from one.
Can you out-earn a deep drawdown with a higher return?
+Not in any practical sense, because the required gain grows faster than any sustainable return can close it. A 90 percent drawdown needs a 900 percent gain, a tenfold return, merely to get back to where you started; at an assumed 12 percent per period that is about twenty periods of flawless compounding just to break even. The deeper the hole, the more the arithmetic runs against you, and reaching for a bigger return usually means bigger swings, which under compounding drag can lower the return you actually keep. This is the sense in which you cannot out-earn a deep drawdown, you can only avoid it. The leverage is entirely on the prevention side, in the position sizing and the risk limits that stop the drawdown getting deep in the first place.
Is this drawdown recovery calculator a prediction of returns?
+No. The required gain and the recovery multiple are exact arithmetic that follow only from the drawdown depth you enter; they say nothing about whether you will earn that gain. The time to recover is computed from a return per period that you supply as an assumption, and it is arithmetic on that assumption, not a forecast, with no return implied or achievable by using the tool. The point of the page is not any ending figure but the mechanism it exposes: that recovery is convex in the size of the loss, so capital preservation dominates return-chasing. Nothing here is a recommendation to trade or advice; Bharath Shiksha is an educational publisher, not a SEBI-registered investment adviser or research analyst.
Where the facts come from
Sources
- The drawdown-recovery identity. The gain required to recover a loss of fraction d is d divided by one minus d, equivalently the recovery multiple is one divided by one minus d. This is an exact algebraic result, not an estimate: a 50 percent loss needs a 100 percent gain, a 75 percent loss needs 300 percent, a 90 percent loss needs 900 percent. Standard in the drawdown and capital-preservation literature. Reproduced on the companion compound returns tool.
- The FY25 loss base rate. SEBI study on the profit and loss of individual traders in the equity derivatives segment: over 91 percent net loss-making in FY25, with aggregate net losses of about 1,05,603 crore rupees, up roughly 41 percent from about 74,812 crore in FY24, across the top 13 brokers and around 96 lakh unique traders. sebi.gov.in
- Time to recover. The number of periods to recover a drawdown d while compounding at a rate r per period is the natural log of one divided by one minus d, divided by the natural log of one plus r, a direct rearrangement of the compounding relation. The rate r on this page is treated throughout as a user-supplied assumption, never a projected or implied return.
Educational note. The required gain and recovery multiple are exact arithmetic that depend only on the drawdown depth you enter. The time to recover depends entirely on an assumed return you supply; it is arithmetic on that assumption, not a forecast, and no return is implied or achievable by using this tool. The reference table is a mathematical model, not a prediction of any strategy or account. Nothing here is a recommendation to trade or to buy or sell any security, and it is not investment advice. Bharath Shiksha is an educational publisher, not a SEBI-registered investment adviser or research analyst.