Lesson 1 of 6 · 7 min

The Math of Losses

Losses and gains are not symmetrical. An account of 10,000 that falls 50% is left with 5,000. If it then rises 50%, you are not back at the start but at 7,500. To get back to 10,000 you need to earn 5,000 on 5,000, which is a 100% gain. The reason is simple: a percentage loss is taken from the larger amount, while a percentage recovery is taken from the smaller one.

The formula: required gain = 1 / (1 − drop) − 1. Here is what it gives:

• A 10% drop requires an 11.11% gain.
• A 20% drop requires a 25% gain.
• A 30% drop requires a 42.86% gain.
• A 50% drop requires a 100% gain.
• A 70% drop requires a 233.33% gain.
• A 90% drop requires a 900% gain.

Up to about 20% the difference is bearable. Beyond that the curve turns steep, and an account with only 10% left is, in practice, finished. The order doesn't help either: a 20% drop followed by a 20% gain takes 10,000 to 8,000 and then to 9,600, exactly the same as a gain followed by a drop.

A losing streak is not an exception

Assume a streak of 10 losing orders in a row, which happens even to good systems, as you will see in the lesson on expected value. Each loss is applied to what is left, but the difference is still huge.

Now turn the calculation around. Decide how large a drop in your account you can tolerate, say 20%. A streak of 10 losses with 2% risk brings you close to that limit (18.29%), and with 5% it takes you far beyond it. That is how the upper limit of risk per order comes from your tolerance, not from a feeling just before the order. Also plan for a streak longer than ten, because nobody guarantees that this is the worst case.

There is a psychological side too. An account in a 40% drawdown asks you to make calm decisions exactly when it is hardest. That is when people most often raise their risk to recover faster, and that is the road to an even deeper hole. Small risk per order protects not only your money but also the quality of your next decisions.

Try it in the lab: set a drop you can imagine on your own account, then look at the gain it requires. Remember where the number starts to feel uncomfortable. That is the line your system must never reach.