How it unfolds, step by step
The setup
On this chart the drawdown runs from 5% up to 70%, and the line is the gain required on the remaining balance to return to the starting figure.
What happens next
Up to about 20% the two numbers are close enough that the difference looks like a rounding detail. Past 30% they separate quickly, and past 50% the required gain runs away entirely.
What it means — and does not
Nothing in this depends on markets or on skill. It is division. The arithmetic rewards not being in the steep part of the curve far more than it rewards being good at climbing out of it. A rule about the largest acceptable loss is doing more work than any rule about gains.
- Gain needed to recover (%)
- A doubling · 100
The gain required to undo a loss, against the size of that loss. The two are equal nowhere, and separate fast past 30%.
Show the underlying data
| Drawdown taken, % | Gain needed to recover (%) |
|---|---|
| 5 | 5.3 |
| 10 | 11.1 |
| 15 | 17.6 |
| 20 | 25 |
| 25 | 33.3 |
| 30 | 42.9 |
| 33 | 49.3 |
| 40 | 66.7 |
| 45 | 81.8 |
| 50 | 100 |
| 55 | 122.2 |
| 60 | 150 |
| 65 | 185.7 |
| 70 | 233.3 |
What this does not establish
The arithmetic itself cannot fail. It is a definition. What can be wrong is the assumption that a is a percentage of a fixed base. Capital added or withdrawn mid-way changes what the percentage is being measured against. A figure quoted without saying which base it uses is not comparable to another one. The level to check is the base, not the shape of the curve.
Things to check
4What percentage of capital is at stake, as a percentage rather than in rupees?
What gain would be needed to undo it, and is that gain plausible?
Is the drawdown measured against the starting balance or the peak? They differ.
Remember: a definition drawn as a curve. It says nothing about any market.
Common mistakes
2Assuming a 20% loss is undone by a 20% gain. It needs 25%.
Comparing two drawdown figures without checking whether both are measured from the same base.
A balance falls 20%. What gain on what is left returns it to where it started?
- 20%
- 25%
- Slightly under 20%, because of compounding
Show the answer
B. 25%
The gain is earned on the smaller amount that remains, so it must be larger than the fall: 0.20 divided by 0.80 is 0.25. The gap widens the further the balance has fallen, which is why the size of the worst loss carries more weight than the size of an average gain.
Frequently asked
3What is the formula?
Required gain = loss divided by (1 − loss), with both as decimals. A 0.33 loss gives 0.33 ÷ 0.67, which is 0.49, a little under 50%.
Why is it not symmetric?
Because the gain is earned on what is left, which is smaller than what was there before. The bigger the loss, the smaller the base the recovery has to work from.
Does this mean small losses are safe?
It means small losses are cheaper to undo than large ones, which is arithmetic. It says nothing about whether any particular loss should be taken.