## Saturday, January 16, 2010

### How to Avoid Risk of Ruin in Trading

Here's a nice calculator of risk of ruin for poker players that easily adapts to trading. Risk of ruin represents the odds of losing all of your gambling (or trading) stake.

To adapt the calculator for our needs, instead of estimating win rate and and standard deviation per hour, we will make those daily estimates. So the win rate would represent average profit per day, and the standard deviation would represent a measure of the variability of daily returns.

Let's say that your account total (bankroll) is \$100,000. You are willing to risk 2% of your money in a single day, and 2/3 of your days will fall between losing and making 1% on your capital. You have a modest positive edge that will earn you 10% on your money in a year, which would be \$40 per day on average (\$40 x 250 trading days = \$10,000).

Your risk of ruin in that situation--the risk of losing all your capital--is only .03%. The odds of you losing your money, even if you trade for many years with those parameters, is small.

Now let's say that you become extra aggressive, trade more frequently, and are willing to risk 4% per day, with 2/3 of your days falling between losing and making 2% on your capital. If that increased trading does not pay off for you (i.e., if your edge stays the same), your risk of ruin jumps to 13.53%. That starts to become uncomfortable.

Now let's say that you are prudent, as in the first example, and 2/3 of your trades will fall between making and losing 1% of your capital. Markets change, however, and your edge is cut in half, so that you're only making \$20 per day instead of \$40. Your risk of ruin odds are now 1.83%--not very high, but noticeably higher than in the first example. If your edge is further cut in half to a 2.5% annual return, your risk of ruin jumps to the same 13.53% rate that we saw for the person who overtrades without an additional edge.

The lesson to be learned is that risk of ruin jumps astronomically when one's edge is eroded and when one's variability of returns expand. This is why it's imperative for serious traders to cut their risk (reduce the variability of returns) when they sense that they've lost their feel for markets. It's also why it's imperative for serious traders to risk manage their day to day trading, so that they cap their daily P/L swings relative to the edge they possess.

And the frustrated trader who overtrades when he loses his edge? Risk of ruin, the calculator tells us, jumps to 100%.

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