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FOREX MONEY MANAGEMENT TOOLS
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Most traders do not know when to correctly add on trading positions. In 1989, Ralph Vince wrote Portfolio Management Formulas: Mathematical Trading Methods for Futures, Options, and Stock Markets (John Wiley & Sons, 1990). This book set the standard for money managers by using a for mula that set the optimal transaction size as a function derived from the ratio of a given transaction's expected return to its associated likely worst case single-trade loss. This concept gives a trader a more precise way to de termine when to add on to positions as the portfolio increases in value. In other words, as a trading account increases in profits, a trader will know when the time is right to increase lot size.

Kelly Formula

Another money management tool used by system traders is the Kelly for mula. John Kelly, an employee for AT&T's Bell Laboratory, originally developed the Kelly criterion formula to assist AT&T with its long distance telephone signal-noise issues. After his method and formula were pub lished as “A New Interpretation of Information Rate” (1956), believe it or not, the gamblers and oddsmakers realized its potential as an optimal bet ting system in horse racing. It enabled gamblers to maximize the size of their bets on consecutive races and was used to help in determining how much to parlay winnings into the next bet. The system is, as you can guess, used by many traders as a money management tool with the same goals in mind: to try to determine how much money to place on the next trade.

There are two basic components to the Kelly formula:

1. Win probability—The probability that any given trade you make will re turn a positive amount.

2. Win/loss ratio—The total positive trade amounts divided by the total negative trade amounts.

Trading Systems: Combining Pivots with Indicators 201

These two factors are then put into Kelly's formula: K = W - [(1 - W)/ R]

where K = Kelly ratio percent value W = Winning probability

R = Win/loss ratio

The theory behind this ratio as it applies to trading can not only help to determine what percent of your total account you could ideally be willing to risk on each trade to maximize your total returns (e.g., if a system shows a Kelly ratio of 0.25 (K ), then you could supposedly risk 25 percent of your account on each trade). In reality, most people would agree that the Kelly ratio provides too high a number for this purpose; so possibly cutting it in half might get you closer to a more reasonable risk level. Another variation of how you can apply the ratio is to effectively compare different trading systems. For example, assume “System 1” wins a lot of the time; but when it loses, it loses big, such as it has a high winning percentage (number of wins versus number of trades) but a low payout ratio (average wins versus average losses). Say “System 2” doesn't win very often; but when it wins, it makes big money. System 2 demonstrates a low winning percentage but a high payout ratio. In order to determine which system is better, the Kelly ratio algorithmically combines both the winning percentages and the pay out ratio to come up with a single number that may be used to “compare” the effectiveness of two very different systems. In order to make that de termination, look for the system that has the highest Kelly ratio. Since the Kelly ratio works from a purely statistical perspective and does not take into account some other factors that someone might deem important, such as the historical max drawdown, it is often just one of a number of things a person will want to look at when comparing systems and criteria in a trad ing method.

The essence of back-testing is to evaluate your methods and to show the strengths and the weaknesses of your system; moreover, it will help you define your goals and expectations for performance. Therefore, back-test ing can help you achieve the highest trading profits with the lowest risks in most trading market conditions.

Sharpe Ratio

The next top classification you need to know, especially if you plan on forming a forex fund, is the term at which all money brokers, banks, and private placement managers look: the Sharpe ratio. This formula was developed by Nobel laureate Bill Sharpe in order to measure risk-adjusted

performance. It is calculated by subtracting the risk-free rate from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns. This is the standard factor used to evaluate the riskto-reward efficiency of investments in order to create efficient portfolios by which almost all registered and professionally managed funds are judged. The formula to calculate the Sharpe ratio [S(I)] is:

S(I) = (r r - R S ) / StdDev(i)

where i = Investment

r r = Expected annual rate of return of investment

R s = Risk-free rate (Treasury bill rate)

StdDev(i) = Standard deviation of r r

Mr. Sharpe is now a professor at Stanford University ; he was one of three economists who received the Nobel Prize in Economics in 1990 for their contributions to what is now called “Modern Portfolio Theory.”

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