Context Chart

The Maths Every Day Trader Should Know

What does recovering from a loss actually require?

See why the percentage needed to recover grows faster than the drawdown, and why recovery time and losing streaks need their own measurements.

By ContextChart Research · 4 min

Research basis ·

Published

Part 13 of 16Series contents

The climb back starts from a smaller base

Try it yourself

Remaining from 100

80

Gain needed to recover

+25.0%

Recovery gain on remaining balance (%)0 to 950
20% loss → 25.0% gain
0Decline from peak (%)90
  • Gain needed to regain the previous peak
Read the plotted values
Decline from peak (%)Gain needed to regain the previous peak
00
11.01
22.04
33.09
44.17
55.26
66.38
77.53
88.7
99.89
1011.11
1112.36
1213.64
1314.94
1416.28
1517.65
1619.05
1720.48
1821.95
1923.46
2025
2126.58
2228.21
2329.87
2431.58
2533.33
2635.14
2736.99
2838.89
2940.85
3042.86
3144.93
3247.06
3349.25
3451.52
3553.85
3656.25
3758.73
3861.29
3963.93
4066.67
4169.49
4272.41
4375.44
4478.57
4581.82
4685.19
4788.68
4892.31
4996.08
50100
51104.08
52108.33
53112.77
54117.39
55122.22
56127.27
57132.56
58138.1
59143.9
60150
61156.41
62163.16
63170.27
64177.78
65185.71
66194.12
67203.03
68212.5
69222.58
70233.33
71244.83
72257.14
73270.37
74284.62
75300
76316.67
77334.78
78354.55
79376.19
80400
81426.32
82455.56
83488.24
84525
85566.67
86614.29
87669.23
88733.33
89809.09
90900
Move the decline control to trace the curve. A 20% decline needs 25% to recover; a 50% decline needs 100%; a 90% decline needs 900%. The curve describes recovery arithmetic, not the chance of recovery.

The decline is measured against the peak. The recovery is earned on the smaller remaining balance.

Decline during this modelled losing run

9.6%

How likely is that run in an independent-trade model?

At least 5 consecutive losses appear with 38.57% probability under these independent, constant-probability assumptions.

This is not a maximum-drawdown probability. Real skill is estimated, and trades can be dependent. The separate decline control above does not set the loss-run probability.

A constructed example. Change the inputs to explore the relationship; these are not suggested trade settings.

The idea

An account falls from 100 to 80. It has lost 20%. Returning from 80 to 100 requires a 25% gain.

The difference comes from the denominator. The loss was measured against the larger starting amount. Recovery is measured against the smaller amount that remains.

As the drawdown deepens, the recovery requirement grows faster. A 50% loss needs a 100% gain to return to the previous level. These are arithmetic relationships, not predictions about how quickly a trader can recover.

That makes drawdown useful for more than describing discomfort. It shows how much future performance the account now needs before it can exceed its previous peak. Withdrawals during that period can add another demand on the remaining capital.

It also helps separate a losing streak from an account drawdown. Several uninterrupted losses can produce a drawdown, but so can a longer sequence containing small wins and larger losses. Counting only the longest streak misses part of the account's experience.

A drawdown reduces the base from which recovery must happen, and the required percentage gain rises as that base shrinks.

Name the event you care about

An account reaching zero, a missed income payment, a broker liquidation and a daily loss-rule breach are different events. A model must define the event before reporting its probability. The career explorer records unpaid withdrawals; the losing-run example below assumes independent trades. Neither supplies a general real-world ruin rate.

How this experiment works

Change the illustrative percentage decline. Watch both the money remaining and the gain required to return to the starting level.

The consecutive-loss demonstration assumes that the same fraction of current equity is risked each time, and each loss costs exactly the modeled amount. Those assumptions determine the decline. They do not tell us the probability of encountering the sequence.

How we use this

The shared career discussion made recovery and losing runs central questions, rather than footnotes to a growth calculation. Our scenario work distinguishes the deepest equity decline from the longest run of losing trades.

It also keeps sizing policies separate. Reducing size after a decline can soften further losses while slowing recovery if performance subsequently improves. A policy needs to be compared over complete paths, rather than judged only at the moment it reduces exposure.

Show the maths

For a drawdown fraction d below one:

Required recovery gain = d ÷ (1 − d)

For k consecutive full losses at fixed fractional risk f:

Remaining equity fraction = (1 − f) to the power k

The second formula describes a specified sequence. Its likelihood needs a separate probability model. Independent trades, clustered losses, and a fixed number of wins shuffled into different orders produce different run probabilities.

What this does not establish

Neither equation supplies recovery time or a safe risk fraction. Those require assumptions about future performance, costs, dependence, cash flows, and the possibility that an advantage has weakened. These assumptions depend on what the available evidence can support.