Sizing so the bad case is survivable

Two people run the same strategy for ten years. It has a genuine edge; over a long enough run it makes money.

One of them sized every position so that the worst plausible year would cost a fifth of their capital. The other sized so that the worst plausible year would cost all of it. In the eight years where the worst plausible year did not happen, the second one made far more money and looked considerably cleverer.

In year nine it happened.

Why the average is the wrong number when a zero is possible

Suppose an opportunity has a large positive expected return and a small chance of losing everything committed to it. Take it once with a tenth of your capital and the arithmetic is straightforward and favourable.

Now take it repeatedly, each time with everything. The average across all possible futures is still large and rising — but the fraction of futures in which you are still playing shrinks every round, and the enormous average is concentrated in the handful of paths where the bad outcome never landed. On almost every individual path, you are out.

This is not a claim that the odds were misjudged. The odds can be exactly as advertised. What changes is the position size, and position size decides whether the sequence can continue.

Sizing backwards

The habit that follows is to start at the end and work towards the trade.

Write down the worst twelve months you consider genuinely possible for the thing — not the worst you expect, the worst you would not be astonished by. Apply it to the position. Look at what is left. Then ask a specific question: in that state, can I still pay what I owe, meet what I have promised, and act on something else?

If the answer is no, the position is too big. That is the whole method, and it requires no forecast about the asset at all — which is what makes it usable when you have no idea what will happen, which is most of the time.

Two things make the method harder than it sounds. The first is that the worst twelve months you can imagine is reliably milder than the worst twelve months available, because imagination is anchored on what you have personally experienced. The second is that the bad case for the asset tends to arrive together with the bad case for your income, which people almost never model jointly.