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TRADING #101 COURSE – PART II TWO: SUCCESSFUL TRADING PIE – WWW.TRADERSCOACH.COM

The Optimal f Formula

Optimal ƒ is the optimal fraction of capital to be risked on a trade. This formula was
originally developed by John L. Kelly Jr. of Bell Labs in the early 1940s, and is
sometimes referred to as the Kelly formula.

Edward O. Thorp in The Mathematics of Gambling modified the fixed-fraction formula to
account for the average payoff ratio, A, in addition to the average probability of success,
p. The figures you will calculate using this formula are more aggressive than using the
risk of ruin tables and will take on more risk.

In his book Money Management Strategies for Futures Traders, Professor Nauzer J.
Balsara defines the formula for determining the optimal fraction, f, of capital to be risked
on a trade as shown in the following.

Optimal f Formula:

ƒ = [ (A + 1) X p ] – 1

A

In the Optimal f formula, the definitions are as follows:

• ƒ is the optimal fraction (percentage to be risked on one trade).
• A is the average payoff ratio (dollars won for every dollar lost).
• p is the average win ratio (probability of success).

Example #1 of the Optimal f formula:

• ƒ is the unknown quantity (or the optimal percentage to be risked).
• A is an average payoff ratio of 2 to 1.
• p is an average win ratio of 35 percent.

Example #1 of Optimal f formula:

ƒ = [ (2 + 1) X 0.35 ] – 1 = 1.05 – 1 = 0.05 = 0.025 = 2.5%

2 2 2

To get a percentage, multiply f result by 100.

In example #1 you get a value of 0.025 for ƒ; to get a percentage, multiply f result by
100. Thus, 2.5 percent is the optimal percentage of your trading account to risk on a
trade based on this historical data and the optimal f formula.

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