2. Risk of ruin: not making it to the end alive

Risk 3: Drawdown and ruin

A strategy with a positive edge makes money over the long run. The sentence is true and it is dangerous, because it leaves out the condition holding it up: you have to still be there when that long run arrives. Risk of ruin is the probability that you will not be, and it is perfectly compatible with being right.

Having an edge is not having a guarantee

Imagine a system that is right 55% of the time, with the gain and the loss the same size on every trade. The edge is obvious: for every hundred trades you expect fifty-five hits and forty-five misses. Nobody doubts that this system, repeated enough times, produces a profit.

Now two traders run it. The first divides his capital into twenty equal bets, that is, he risks 5% on each one. The second divides it into five, 20% per trade. Same strategy, same edge, same hit rate.

In the classic gambler's ruin setup, with equal-sized bets and symmetrical payoffs, the probability of going broke before the edge asserts itself is the ratio of the probability of missing to the probability of hitting, raised to the number of bets that fit into your capital. With 45 over 55 the ratio comes to 0.818. Raised to the power of five it gives 37%. Raised to the power of twenty it gives 1.8%.

Read that slowly: the same system ruins one in every three traders who bet 20% and fewer than two in every hundred who bet 5%. There is no difference in talent, in analysis or in structural luck between the two. Only in size.

The three levers

What ruin depends on, ordered by how much of it you control:

• The relative size of the bet. It is the dominant lever and the only one you control completely. It appears as an exponent, so its effect is not proportional, it is explosive.
• The size of the edge. Take the same capital in twenty bets, but suppose the real edge was not 55 against 45 but 51 against 49. The ratio goes from 0.818 to 0.961, and raised to the power of twenty that gives a 45% probability of ruin. Four points less of edge turn a 2% risk into the toss of a coin.
• The number of trades. Time does not dilute the risk, it accumulates it. The longer the horizon, the closer your probability of ruin gets to that limiting value. Trading a lot does not save you; it exposes you to more chances of meeting the bad run that knocks you out.

There is an uncomfortable asymmetry in that list: the edge is what you think you know and the size is what you decide. And as you have just seen, a moderate error in estimating the edge is paid for with a probability of ruin multiplied by twenty-five: from 1.8% to 45%.

Practical ruin arrives long before the mathematical kind

All of the above calculates the probability of reaching zero. No real investor reaches zero, and that is why a lot of people wrongly conclude that risk of ruin is a casino game with no application. Exactly the opposite is true: your ruin barrier is not at zero, it is much higher up, and you do not know exactly where.

The trader who divided his capital into twenty bets and slept soundly with a 1.8% risk would probably quit if he lost 40%. That point is his effective ruin, because from there on he stops running the strategy, which amounts to not having one. And since his barrier sits where he still holds the capital of twelve bets, he has only eight bets of cushion before he reaches it: 0.818 raised to the power of eight gives 20%. His true risk was not 1.8%, it was eleven times greater.

The professional version of the same problem goes by another name: clients. A manager with a solid strategy who goes through two bad years and a 35% fall does not lose his own capital, he loses other people's. The redemptions arrive close to the worst moment, assets shrink, the fees do not cover the running costs and the vehicle is wound up, often weeks before the strategy recovers. Marcos López de Prado insists on this point when he writes about why most quantitative funds fail: the problem is almost never that the idea did not work, it is that nobody funded the wait.

Surviving is a precondition, not a virtue

It is worth separating two questions that tend to get muddled. One is what happens on average to a thousand investors following the same strategy. The other is what happens to one particular investor over time. If some of those thousand are knocked out along the way, the group average describes a result no individual experiences. Your path does not average with anybody else's: if you are out, you are out.

That is why the first question to ask of any strategy is not how much it returns, but how much has to go wrong, and for how long, before you can no longer run it.

Real case: when being right was not enough

Long-Term Capital Management was born in 1994 with two Nobel laureates on its board and delivered net returns above 40% a year in 1995 and 1996. In 1998, after the Russian default, it lost around 90% of its capital in a matter of months, some 4.6 billion dollars, and a consortium of banks coordinated by the Federal Reserve Bank of New York had to take the portfolio on with an injection of the order of 3.6 billion.

The detail almost nobody mentions is the one that matters here: a good part of those positions ended up converging, more or less as the models had predicted, and whoever inherited them got the money back. The fund was not entirely wrong about the direction. It was wrong about the size, and that is why it did not make it alive to the moment when it was right.