Payoff Ratio

The Risk of Ruin 211

Table 7.4 Payoff ratio needed for negligible risk of ruin with a 1 percent hard stop

Note the nonlinear nature of these relationships. For example, consider a payoff ratio of 1.5 and winning percentage of 40 percent. If you now change your risk per trade from 1 percent to 2 percent, the risk of ruin increases disproportionately from 0.5 to 9.2 percent (see Tables 7.1 and 7.3). Hence, there is little incentive to overleverage an account and consistently bet much more than 2 percent per trade. You. should also notice the benefits of modifying system design to improve the pay­off ratio, or probability of winning, or both. The main advantage is that you can then increase the fraction of capital allocated to the system without unduly increasing risk.

These calculations do not mean you cannot vary bet size from trade to trade based on other information. For example, as Table 7.4 shows, if your probability of winning is greater than 50 percent and the payoff ratio is greater than 1, then the risk of ruin is very small. Thus, if you can find a mechanism to identify extraordinary opportunities, you can vary bet size. Such variations could significantly improve your over­all results. See the section on identifying extraordinary opportunities in chapter 4.

In summary, the risk-of-ruin calculations show that there is little incentive to overtrade an account by regularly betting, say, 10 percent or more of account equity. A bet size of 1 to 2 percent of account equity is a more prudent choice. However, because the risk of ruin calculations assume that the probability of winning and payoff ratio are constants, and in actual trading, the probability of winning and payoff ratio vary from trade to trade, these risk-of-ruin results should be used only as general guidelines. They can be used to increase exposure for extraordi­nary opportunities.