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# Single Market Factor №1 Optimal f

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In his 1990 book titled Portfolio Management Formulas, Ralph Vince popularized a formula known as optimal f. The theory behind this method is that:

• There is a "correct" amount of capital to apply to any contract using a particular trading approach.
• Trading using the "correct" amount of capital will maximize the profitability experienced without sustaining a total loss of capital.
• Trading with less than the suggested amount of capital will likely result in a total loss of capital.
• Trading with more than the suggested amount of capital will result in an exponential decrease in the percentage return compared to using the "correct" amount.

In brief, using a listing of actual and/or hypothetical trades generated by trading one market using a given approach, a calculation is performed and a value is arrived at between .01 and 1.00. The largest losing trade within the listing of trades is then divided by this value to arrive at the suggested amount of capital with which to trade one contract.

As an example, if the largest losing trade within a particular trade listing was \$2,000 and the optimal f value turns out to be 0.40, then the suggested capital amount would be \$5,000 (\$2,000 / 0.4). According to this theory, if you were only going to trade one contract of this one market using this one trading approach, then you should place \$5,000 into your trading account. If future results mirror past results your percentage rate of return will be maximized by trading with \$5,000. Also, according to the theory, if you trade with less than \$5,000 you will likely "tap out" and if you trade with more than \$5,000 you may trade profitably. However, your rate of return will be far inferior than if you had traded with \$5,000. Needless to say this is a bold theory.

This approach makes the assumption that future trading results will be similar to past results. If future results are far inferior to past results then the end result using optimal f can be disastrous. However, in testing using trading systems that have a positive expectation, and for which future results were similar to past results, optimal f has definitely shown the ability to increase profits exponentially compared to simply trading a preset number of contracts. Unfortunately, the reality of the situation is that using optimal f to trade one market is generally not practical. The big problem with a strict usage of optimal f is that it does not consider drawdowns in its analysis. The only measure of risk that is used is the single largest losing trade. While the case can be made that this is statistically correct, the fact of the matter is that using this method alone will invariably result in large percentage drawdowns at some point in time. Because the drawdowns that can result on a single market basis can be huge in percentage terms, most traders will not adhere to this approach long enough to enjoy the expected benefits. However, the good news is that this method can be very useful when applied across a portfolio of markets.

## Calculating Optimal f

The method for calculating optimal f is fairly complex; however, the following example should give you enough information to utilize this method if you so desire. In order to calculate optimal fyou need a trade listing for a given market containing at least 30 trades. This approach uses an iterative process to arrive at a value of/between .01 and 1 that maximizes a variable known as the Terminal Wealth Relative (TWR) for a given set of trades. The profit or loss for each individual trade is divided by the largest losing trade. Then the negative of this ratio is multiplied by a factor, known as /, and added to 1 to arrive at a return value, referred to as holding-period return (HPR). The formula for one trade is:

PR = (-(profit or loss on trade x) / largest losing trade) HPR on trade x = 1 + [f times (PR)]

This process is repeated for all trades in the trade listing. The HPR values for all trades are then added together to arrive at another value known as the TRW. The value for /between .01 and 1.00 that results in the largest TWR is the /value to be used in the final calculation. In the final calculation the largest losing trade is divided by / to arrive at the suggested amount of trading capital. This process is then repeated for each market in your portfolio to arrive at suggested trading capital amounts for each based on optimal f.

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