Drawdown recovery calculator

How much gain do you need to recover a loss?

The gain needed to get back to a previous high is gain = L / (1 - L), where L is the loss as a decimal of the peak. A 25% loss needs 0.25 / 0.75 = 33.33%.

The reason is that the gain is worked out on a smaller balance than the loss was. With the default figures, $10,000 falls 25% to $7,500. Getting back to $10,000 means adding $2,500 to $7,500, and $2,500 is a third of $7,500. The money lost and the money to regain are equal; the percentages are not, because they are measured from different starting points.

The curve in the result plots this for every loss up to 80% and beyond, against a dashed line where the gain equals the loss. The gap between them widens faster and faster as the loss grows.

Drawdown recovery table

Each row shows the gain needed for a loss, and the whole periods the climb takes at an assumed 2% gain per period, the calculator's default. The table under the result redoes the last column at whatever rate you enter.

Up to about 10%, the gain needed is only a little larger than the loss. From there the gap opens quickly: a 50% loss needs the account to double, and a 90% loss needs it to grow tenfold. The number of periods grows more slowly than the gain needed, because compounding works on the recovery too, but it still more than triples between a 20% and a 60% loss.

How long does it take to recover from a drawdown?

If the account gains a steady r per period, the number of periods to recover is n = ln(1 / (1 - L)) / ln(1 + r). For a 25% loss at 2% a month, n = ln(1.3333) / ln(1.02) = 0.2877 / 0.0198 = 14.53 months. The peak is only passed at the end of a whole month, so the calculator reports 15: after 14 months $7,500 has grown to $9,896.09, and after 15 it is $10,094.01.

The assumed rate changes the time a great deal:

The rate here is an assumption you choose for the arithmetic. No account gains the same percentage every period; some periods lose, and each loss along the way lengthens the climb.

How do you calculate drawdown from a peak and a trough?

A drawdown is measured from the highest value an account reached to the lowest value after it: drawdown = (peak - trough) / peak. Choose From a peak and trough and enter both values.

The default account peaked at $20,000 and later fell to $14,000. The drawdown is $6,000 / $20,000 = 30%, and the gain needed to return to $20,000 is 0.30 / 0.70 = 42.86%. At an assumed 2% a month that is 18.01 months, so the peak is passed in month 19: after 18 months the value is $19,995.45, just short, and after 19 it is $20,395.36.

The trough is the lowest point after the peak, not the lowest point ever. If the account later sets a new high and falls again, that is a new drawdown measured from the new peak. Money added or withdrawn during the fall changes the figures, so measure from values that exclude deposits and withdrawals where you can.

Why a gain of the same percentage is not enough

A fall of L followed by a rise of L leaves (1 - L) x (1 + L) = 1 - L squared of where you started. The shortfall is small for small moves and large for big ones:

• Down 10%, then up 10%: 99% of the peak. $10,000 becomes $9,000, then $9,900.
• Down 20%, then up 20%: 96% of the peak.
• Down 25%, then up 25%: 93.75% of the peak.
• Down 30%, then up 30%: 91% of the peak.
• Down 50%, then up 50%: 75% of the peak.

The order does not matter: up 25% then down 25% also ends at 93.75%. The metric under the result shows this figure for whatever loss you enter.

Worked examples in pounds, euros and dirhams

The percentages are the same in every currency; only the amounts change, and nothing is converted.

In the pound example, £9,000 has to come back on a base of £41,000. After 13 months at 1.5% the account stands at £49,755.65, still below the peak, which is why the count rounds up to 14.

What a run of losing trades does to the account

Losses compound downward the same way gains compound upward. Losing a fixed share of the current balance on several trades in a row gives a drawdown of 1 - (1 - loss per trade) raised to the number of losses:

• Ten losses of 1% each: 1 - 0.99^10 = 9.56% down, needing a 10.57% gain to recover.
• Ten losses of 2% each: 18.29% down, needing 22.39%.
• Three losses of 10% each: 72.9% of the balance is left, a 27.1% drawdown, needing 37.17%.

Enter a drawdown worked out this way as the loss percentage to see the recovery time. The share of the account risked on each trade is set in the position size calculator, and the average result per trade in the trading expectancy calculator.

How to calculate drawdown recovery in Excel

With the loss as a decimal in A2 (0.25), the gain needed is =A2/(1-A2), which returns 0.3333; format it as a percentage.

For the time to recover, Microsoft documents NPER(rate, pmt, pv, [fv], [type]). Enter the present value as a negative number and the target as a positive one. The recovery is the number of periods for 75 to grow to 100 with no payments: =NPER(0.02,0,-75,100) returns 14.53, which you round up to 15 whole periods. In general, =NPER(rate,0,-(1-A2),1) gives the periods for any loss in A2. From a peak in B2 and a trough in C2, the drawdown is =(B2-C2)/B2.

Common mistakes and what the calculator leaves out

• Adding percentages. A 25% loss and a 25% gain do not cancel; the account ends at 93.75%.
• Measuring from the wrong point. Drawdown runs from the highest value before the fall, not from the starting balance or the most recent value.
• Reading the recovery time as a schedule. The rate per period is a figure you choose, and real periods vary and can lose.
• Ignoring deposits. Money added during a drawdown lifts the balance without any gain, so the recovery looks shorter than the trading alone made it.

The calculator leaves out costs, tax, money added or withdrawn, and the variation in returns from one period to the next. For a sequence of gaining and losing periods, see the trading compounding calculator.

Glossary

Drawdown: the fall from a peak to a later low, as a percentage of the peak. Peak: the highest value before the fall. Trough: the lowest value after that peak. Maximum drawdown: the largest such fall over a period of records. Recovery gain: the percentage rise from the trough needed to get back to the peak. Recovery period: the number of periods that rise takes at an assumed rate.

Frequently asked questions

Courses for trading through losing periods

Sources and review