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Risk of Ruin — Determinng Optimal Position Size

Most traders ask about optimal position sizing. This should answer most questions. This section is Written by Van Tharp.

Risk of ruin (ROR) has been extensively studied by mathematicians and by traders, and is the basis for most money management systems. The theory is based on a formula that will tell you what the chances are that you, given a historical win ratio and payoff ratio, are likely to go completely bankrupt

and to be ruined. Ideally you want to design a money management system that will protect you from ruin and will give you 0 percent likely (this is not guarantee) chance of going completely bankrupt. The ROR mathematical formula is based on three components:

1. Win ratio. This is based on your percentage of wins and your probability of winning. For example, if your win ratio is 40 percent, you have

40 percent wining trades and 60 percent losing trades.

2. Payoff ratio. Average winning trade dollar amount divided by the average losing trade dollar amount. This is how many dollars you earn compared to one dollar lost—for example, 3 to 1 would mean you earn three dollars for every one dollar you lose.

3. Percent of capital exposed to trading. If you are a novice trader it is recommended that you risk no more than 2 percent of your trading account value on any one trade. Otherwise, you can determine the optimal percent of capital to risk by either referring to a risk-of-ruin table (see Nauzer Balsara’s book, Money Management Strategies for Futures Traders, or Tushar Chande’s book, Beyond Technical Analysis, 2nd ed.) or by using the optimal f formula in this chapter.

Your trading system design and your skills as a trader govern the first two items in the risk of ruin, and your money management system controls the third item. The risk of ruin potential decreases as the payoff ratio increases or the probability of winning increases. The larger the percent of capital risked on each trade, the higher the chances for risk of ruin.

For our purposes, we are assuming that you already have a system that gives you an edge and provides you with a payoff ratio that is better than

1 to 1. You can estimate what your probabilities of ruin are by identifying what your payoff ratio and win ratio are and by referring to the risk-of-ruin

tables found in Tushar Chande’s book and also Nauzer Balsara’s: Tushar Chande, Beyond Technical Analysis, 2nd ed. John Wiley & Sons, 2001, has the following risk-of-ruin tables:

1 percent capital at risk

1.5 percent capital at risk

2 percent capital at risk

Nauzer Balsara, Money Management Strategies for Futures Traders, John Wiley & Sons, 1992, has the following risk-of-ruin tables:

10 percent capital at risk

20 percent capital at risk