The Risk of Ruin

The mathematical calculations of the risk of ruin are the heart of your money-management rules. These statistical calculations assume that you play the game thousands of times with precisely the same odds. How­ever, your trading situation does not fit this ideal in the real world. Nev­ertheless, you can best understand the hazards of leverage by studying the risk of ruin.

Using certain simplifying assumptions, the risk of ruin estimates the probability of losing all your equity. The goal of money management is to reduce your risk of ruin to, say, less than 1 percent. Here we follow the general approach used by Nauzer Balsara (see bibliography for ref­erence; refer to this excellent book for more details).

There are three variables that influence the risk of ruin: (1) the probability of winning, (2) the payoff ratio (ratio of average winning to average losing trade), and (3) the fraction of capital exposed to trading. Your trading system design governs the first two quantities; your money-management guidelines control the third. The risk of ruin decreases as the payoff ratio increases or the probability of winning increases. It is obvious that the larger the fraction of capital risked on each trade, the higher the risk of ruin.

The estimates here follow Balsara's general simulation strategy to estimate the risk of ruin, except that we used a total of only 1,000 simu­lations (rather than 100,000 simulations) to estimate the probabilities. If

The Risk of Ruin 209

you can go broke in just 1,000 simulations, you probably would not sur­vive 100,000 simulations.

Table 7.1 summarizes the risk of ruin if 1 percent of capital is at risk on each trade with a hard dollar stop. We looked at winning per­centages ranging from 25 to 50 percent, and payoff ranging from 1 to 3. Most trading systems will show about 25 to 50 percent profitable trades.

This range of values is what you would typically see in testing. The 25 percent lower limit for profitable trades is a personal choice. The up­per limit was chosen because the risk of ruin decreases substantially as the winning percentage goes beyond 50 percent. Similarly, it is rela­tively rare to get a payoff ratio greater than 3 when you test one contract per market. Conversely, there is little benefit to trading a system with a payoff ratio less than 1 unless it is very accurate and your transaction costs are small. The smaller bet size of testing (1 percent) is likely to be interesting because Balsara's book does not show risk of ruin for less than 10 percent risked per trade. The results generally agree with his calculations.

These theoretical calculations show that it is not attractive to trade a system with a payoff ratio near 1 unless it has a winning percentage greater than 50 percent. Similarly, the calculations show that if you have a payoff ratio greater than 2.5, then a winning percentage greater than 3 5 percent should reduce your risk to acceptable levels.

Tables 7.2 and 7.3 are for 1.5 and 2 percent of capital risked on each trade, respectively. Note how the risk of ruin increases as the amount risked increases, and decreases as the probability of winning in­creases or payoff ratio increases. These tables show why many traders recommend risking 2 percent per trade with a hard stop.

Table 7.1 Risk of ruin with 1 percent of capital at risk. A 0 probability means the total loss of equity is unlikely, but not impossible.

Probability of Winning(%)			Payoff Ratio
	1.5		2.5	3.0
					3.1
			46.9	0.20
		74.6	0.1
	99.8	0.5
	52.4

210 Ideas for Money Management

Table 7.2 Risk of ruin with 1.5 percent of capital at risk. A 0 probability means the total loss of equity is unlikely, but not impossible.

Probability of Winning(%)			Payoff Ratio
	1.5		2.5	3.0
				88.9
			78.4	1.0
		94.5	0.8
		4.5
	84.2
	1.4

These calculations assume that the payoff ratio and probability of winning are constant. In reality, these numbers keep changing in time, and any estimates you have today will probably change in a few months. Thus, it is better to consider a range of payoff ratios and winning per­centages when you consider your risk of ruin.

Looking at the problem from a different point of view, what would be the "magic" payoff ratios for a 1 percent risk per trade if your win­ning percentages ranged from 25 to 50 percent? The data in Table 7.4, which you can use as a quick reference when you evaluate system testing results, help to answer this question. For example, if the system had a winning percentage of 40 percent, then a payoff ratio above 1.75 would reduce your risk of ruin to manageable levels.

Table 7.3 Risk of ruin with 2 percent of capital at risk. A 0 probability means the total loss of equity is unlikely, but not impossible.