Drawdown maths and the risk of ruin

Losses and gains are not symmetric, losing streaks are longer than intuition suggests, and both facts are pure arithmetic that you can check.

The recovery asymmetry

Lose ten percent and you need eleven percent to get back. Lose fifty and you need one hundred. Lose ninety and you need nine hundred.

The practical consequence is that avoiding the deep drawdown is worth vastly more than catching the large gain. This is the single most counterintuitive fact in investing, and it is not an opinion.

Losing streaks are longer than you expect

Suppose your approach wins half the time. The chance of five consecutive losses is one in thirty two. That sounds remote until you notice that across a hundred trades, a run of five or worse is close to certain, and a run of seven happens regularly.

• 50 percent win rate: expect a run of 7 losses within a few hundred trades.
• 40 percent win rate: expect runs of 10 or more. Entirely normal, and it feels exactly like the approach has stopped working.
• 60 percent win rate: still expect runs of 5 or 6. A good strategy does not spare you this.

Now combine the two facts. If you risk ten percent of capital per position and hit a run of seven, you are down more than half, requiring a double to recover, while in the psychological state a seven loss streak produces. That is how accounts end, and note that nothing in this scenario required a bad strategy.

Risk of ruin, informally

Risk of ruin is the probability that a losing sequence takes you below the point of recovery, given your win rate, your average win against your average loss, and your size per position. Two of those you only partly control. The third you control completely.

Why crypto makes this sharper

• Individual assets genuinely go to zero, not to a distressed valuation. Position sizing must assume total loss is possible for anything outside the largest few.
• Eighty percent drawdowns are normal, not exceptional. Bitcoin has done it more than once. Altcoins routinely do ninety five percent. A portfolio sized for equity market volatility is dramatically oversized here.
• Leverage liquidates rather than margin calls. There is no phone call and no grace period. A position at ten times leverage is closed by a ten percent move against you.
• Correlation rises exactly when you need it not to. In a crash almost everything falls together, so a portfolio of twelve tokens is often one position wearing twelve costumes.

What to actually do

1. Decide the maximum you would accept losing in total. Not per position, in aggregate. This number governs everything else.
2. Size so that the worst plausible outcome on any single holding is survivable. For anything speculative, assume zero and check the total is acceptable.
3. Assume correlation of one within crypto when calculating your worst case. Diversifying across ten tokens does not divide the risk by ten.
4. Set the maximum drawdown at which you stop and reassess, in advance and in writing. Twenty to twenty five percent is a common and defensible level.
5. Treat leverage as a size multiplier, not a separate thing. Five thousand at three times leverage is a fifteen thousand position.
6. Never increase size to recover a loss. This is the specific behaviour that converts a drawdown into a ruin, and it feels rational at the time.

Common questions

How much should I risk per trade in crypto?

Small enough that a realistic losing streak leaves you trading. Risking one percent means twenty consecutive losses cost about eighteen percent. Risking twenty percent means seven losses effectively end you, with the same strategy.

Why is a 50 percent loss so serious?

Because recovering requires a 100 percent gain. The asymmetry grows steeply: 75 percent down needs 300 percent, and 90 percent down needs 900 percent.

What is risk of ruin?

The probability that a losing sequence takes you below the point of recovery. It depends on win rate, the ratio of average win to average loss, and position size. Size is the input you fully control.