Assume for a moment that you have a magic coin and only you knew of its magical properties. This magical coin comes up heads 60% of the time and tails 40% of the time. Armed with this information, and your magical coin, you could expect to make some decent amounts off your friends.

Let’s say you also have $1000 in your bank account and you know your friends like to gamble so you offer them European odds of $2.0 every time a tail comes up (when the correct price is $2.5). The equivalent U.S odds you are offering are +100 for a +150 chance bet. Your friends are happy because they think the correct odds are $2.00 European or +100 U.S format and they like to gamble.

Each time your friends choose tails, you have about a 25% advantage over them because of your magical coin. You might think this is a license to print money, but there is a constraint in that the maximum amount you have to invest with is $1000. If you accept the first bet off your friend for $1000 your expectancy is 25% profit or $250 because of your magical coin. However, 40% of the time you will go broke when a tail comes up. Clearly, risking your entire bankroll on one bet is not smart.

Kelly Criteria is a formula that allows you to maximise your bankroll growth while simultaneously minimising your risk. That formula sounds almost as magical as your coin! Applying the formula is the most efficient way of trading your FX bankroll and this might be the most important article you have every read.

Using this simple example above (where you either lose the entire bet made or win the entire bet), the Kelly Formula is expressed as follows:

f = (bp – q)/b

where:

*f** is the fraction of your $1000 bankroll to wager with your friends;*b*is the net odds received on the wager (that is, odds are usually quoted as "*b*to 1")*p*is the probability of winning;*q*is the probability of losing, which is 1 −*p*.

Don’t let the math concern you! Let’s work through the formula using the example above:

*b*: For this wager you receive odds of $2 (which is 1/1). If you were receive odds of $3.5 the value for *b *would be (3.5 -1) = 2.5.

*p: *The probability of winning is 0.6

*q: *The probability of losing is 1-0.6 = 0.4

Using the formula the fraction of the amount you should wager is:

F = (1x0.6 – 0.4)/1

= 0.2

So for this particular example, you should take bets of up to 20% of your initial bankroll ($200 bet). If, however, you lose this bet then next amount you should take is $800*0.2 = $160. Similarly, if you were to win your first bet, then you can take up to $240 since you managed to grow your bankroll to $1200 after your first win.

Now that you have the basics, our next article will explain how the Kelly Criteria formula can be applied to the Foreign Exchange Market.

Published on 12th of April 2011

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