In 2003, this author lost 35% of his account trading commodities with a profitable long-term trend-following system. The resulting emotion? Fear. I dreaded how much worse it might get and thought my system could be broken. I wondered how likely it was that I would lose half of my account and wanted to calculate the odds of further losses.
The first risk of ruin equation below was derived with the help of a Monte Carlo simulation. Then Colorado State University professors Dr. Sanjay Ramchander and Dr. Hong Miao recommended a more complete formula published by D.R. Cox and H.D. Miller in “The Theory of Stochastic Processes.” Their formula to calculate risk of ruin was written for insurance companies, but it also applies to traders.
An insurance company is ruined when it loses its capital. A gambler is ruined when he loses all his money. A hedge fund may have to stop trading when it loses a specific percentage of its starting capital. Even with a good system, a trader may decide to stop trading after losing some large fraction of his account.
Few traders know how to calculate risk of ruin. Many traders talk about maximum drawdown, as if there is a maximum limit. Obviously, once the “maximum” drawdown has happened, further losses are still possible. The maximum drawdown is merely the point at which the bad luck ended in some historical data set. The maximum observed drawdown will continue to increase the longer the game is played.
Suppose an experimenter flips a coin 1,000 times and observes a string of bad luck consisting of 10 tails in a row. Is this the maximum possible number of consecutive tails? No.
If the experiment continues for one million flips, a string of 20 consecutive tails is likely. There is no fixed limit to the maximum number of consecutive tails, or consecutive losses, or maximum drawdown.
The maximum drawdown will usually be much larger than the worst string of consecutive losses. After a string of losses is interrupted by a win, losses may resume. Bear markets have rallies and then sink to new lows. In a similar vein, the path to ruin is rarely a straight line. The following equations account for all possible paths to ruin.