Learn/ Risk/ Lesson 03

Risk · Lesson 03 7 min read Beginner

The arithmetic of a drawdown

Losses and gains are not symmetric, and the asymmetry gets worse the deeper you go. This one piece of arithmetic explains why position sizing is not a cautious habit but a structural requirement.

Why it is not symmetric

Lose 20% of your capital and you need 25% to get back. Lose 50% and you need 100%. The reason is that the loss is taken on the larger number and the recovery has to be earned on the smaller one.

Start with ₹1,00,000. Lose half and you hold ₹50,000. To return to ₹1,00,000 you must double what is left. Nothing about that is unfair or surprising — it is simply how percentages work — but almost nobody carries it in their head while deciding how much to risk.

The recovery curve

Gain required to recover a given drawdownIllustrative
Flat, then vertical. Up to about 20% the curve is nearly linear and the damage is proportionate. Past 50% it turns almost straight up — each further percentage point of loss costs disproportionately more to undo.

The practical reading is that drawdowns have a character change somewhere around a third of capital. Below it, recovery is a matter of ordinary trading. Above it, recovery requires performance you have never demonstrated, under conditions worse than any you have traded in.

A 10% drawdown is a bad month. A 50% drawdown is a different career.

The same method, three sizes

Here is the part that makes this concrete. Below are the equity curves from one identical sequence of 100 trades — same entries, same exits, same 43 wins and 57 losses, same two-to-one reward-to-risk. The only difference is how much was risked on each.

8% and 3% per tradeIllustrative
The 8% line finishes higher — and fell 76% on the way. Around trade 40 there is a run of nine consecutive losses, which is entirely ordinary at a 43% hit rate. The larger size turns that ordinary streak into an account that has lost three-quarters of itself.
The same trades at 1%Illustrative
The identical losing streak barely registers. The worst point is a 16% dip. Same method, same trades, same order — only the size changed.

Be honest about what this comparison shows. Larger size did produce a larger final number. The argument for smaller size is not that it earns more. It is that the 76% path is one almost nobody actually completes:

  • At that depth, most people stop trading the method entirely — usually at the bottom.
  • Leveraged positions attract margin calls, which force the exit whatever you intended.
  • The recovery from 76% requires a 317% gain, from a smaller base, with confidence in ruins.

The curve on paper is not the curve you would have lived through.

What a drawdown actually costs

Three costs, only one of which is money.

  1. The arithmetic cost. The recovery curve above. Known, computable, and the smallest of the three.
  2. The time cost. Capital spent climbing back is capital not compounding. A year recovering is a year of returns you never collect.
  3. The behavioural cost. The largest. Deep drawdowns make people abandon a working method, or double up to recover faster — and both decisions get made at the worst possible moment.
Common mistake

Deciding position size from confidence in the trade. Confidence has no relationship to outcome, and the trades people feel most certain about are not measurably more likely to work. Size comes from your capital and your stop distance — both of which you can check — not from how the setup feels.

Read it yourself

Practice
  1. You are down 30%. What gain returns you to breakeven?
  2. You risk 5% per trade. How many consecutive losses take you down 40%?
  3. Given a 43% hit rate, how unusual is a run of nine losses in a hundred trades?
Show answers

1. About 43%. Not 30 — the recovery is always larger than the loss, and the gap widens with depth.

2. Ten. Each loss compounds on what is left, so 0.95 to the power of ten is about 0.60. Ten losses in a row at a 43% hit rate is unlikely but entirely possible, and a 40% hole needs 67% to climb out of.

3. Not unusual at all — expect it. With a 57% chance of losing any given trade, a nine-loss run has better than an even chance of appearing somewhere in a hundred trades. That is why it is in the chart above. The streak is not the tail risk; the size you meet it with is.

Terms used

Drawdown
The fall from a peak in equity to the trough that follows, as a percentage.
Maximum drawdown
The deepest such fall over a period. The number that decides survivability.
Recovery factor
The gain required to return to the previous peak.
Equity curve
Account value plotted over trades or time.
Losing streak
Consecutive losses. Ordinary, frequent, and the thing sizing exists to survive.

Practise this on your own charts

The Risk track works through 5 lessons like this one, each built around a drawn example and an exercise you complete yourself.

See the Risk track