## Wednesday, November 25, 2009

### Calculating the risk of ruin

In anticipation of Thanksgiving, I with my gallows sense of humor decided to devote today’s post to the risk of ruin. That is, what are the odds that we will blow out our trading account? There are alternative ways to calculate the risk of ruin. Let me start with a simple formula provided by Nauzer Balsara in Money Management Strategies for Futures Traders (Wiley, 1992). In those cases where the average win equals the average loss, the probability of ruin is the probability of failure divided by the probability of success raised to a power equal to the percent of our account at risk, with the result multiplied by 100. If it’s a tossup whether we win or lose—that is, the probability of winning is 0.50 and the probability of losing is 0.50—and we risk 10% of our capital, the formula reads “(1 raised to the power of 10) * 100.” The probability of ruin is 100%. Ruin is ensured. It is significant to note, as Balsara stresses, that “when the probability of success increases marginally to 0.55, with the same payoff ratio and exposure fraction, the probability of ruin drops dramatically to (0.45/0.55)10” or 13.4%. “Therefore,” he stresses, “it certainly does pay to invest in improving the odds of success for any given trading system.” (p. 15) It also pays, of course, to position size wisely.

If the parameters are the same as in the first example but the payoff ratio is 2 (that is, the average win is twice as large as the average loss) we can still quantify the risk of ruin by means of a mathematical formula. Put in its simplest terms, if we stand only a one in three chance of winning, even though our winners are twice as large as our losers, the risk of ruin is, yet again, certain. Once the payoff ratio exceeds 2, however, we have to turn to simulators (some available at no cost online; Equity Monaco from NeoTicker is one) to calculate the risk of ruin.

These techniques for calculating the risk of ruin assume that we can estimate both the probability of winning and the payoff ratio. That is, they assume that (1) we have a backtest in which we have confidence and (2) we believe that the future will closely resemble the past. It’s leap of faith time.

Moreover, not all trading strategies (and this includes many successful strategies) can be meaningfully quantified. For instance, any strategy that is event-dependent or that relies to any extent on qualitative considerations will resist simple risk:reward calculations, despite what analysts might claim.

But let’s assume that the trader is fairly consistent in his approach and has a track record that spans at least a few months. Another way to calculate the risk of ruin is by using the mean and standard deviation of past returns. David E. Chamness wrote a piece in August 2009 for Futures Magazine that provides some formulas for calculating the risk of ruin this way. He also compares constant position sizing with fixed fractional position sizing and shares an elegant equation for expressing the fixed fractional risk of ruin.