Part one of this series on how to apply Kelly Criteria should have given you a background on how the formula works. Applying it to the FX market is a little more complicated as in most cases you don’t lose your entire amount waged as in the example in article one. However, it’s not too difficult to apply the formula to the FX market.

There are two variables you need to apply Kelly Criteria formula to the FX market. These two variables are:

• Win probability (W) - The probability that any given trade you make will return a positive amount.

• Win/loss ratio (R) - The total positive trade amounts divided by the total negative trade amounts.

The first thing you need to do is to work out your win probability. The only way to do this is to keep diligent records of your trades. If you are new to trading, I suggest trading 100 or more paper trades to work out this percentage before moving to real money. Note, that if your win probability is less than 50% you need to improve your trading abilities.

The second variable you need is the win loss ratio. Divide the average percentage gain on each trade by the average percentage loss on each trade. It’s better to use percentage gains to standardise for different amounts invested.

Once you have these two numbers, then you can apply the following formula

These two factors are then put into Kelly's equation:

f = W – [(1 – W) / R]

Where:

W = Winning probability

R = Win/loss ratio

Example of applying Kelly Criteria to the FX Market

Let’s put some numbers together so we can set on concrete how the formula works. Assume that you have made the following winning trades:

Trade 1: 12% gain

Trade 2: 5% gain

Trade 3: 35% gain

Average winning trade percentage gain (12 + 5 + 35)/2

= 17.33%

And the following losing trades

Trade 4: 15%

Trade 5: 19%

Average winning trade percentage gain (15+19)/2

= 17%

Using the above numbers it’s easy to calculate

W = 3 winning trades / 2 losing trades = 0.666

R = 17.33/17 = 1.0196

Applying the formula f = W – [(1 – W) / R] yields the following value for *f*:

*f = *0.666 – ((1-0.666)/ 1.0196)

= 0.3324%

So if your initial bankroll is $1000 you can invest 0.3324% into each trade. The important thing to not that this example is not realistic in that a value of W = 0.666 is extremely high!

Most advocates of the Kelly Criteria system apply 1/15^{th} Kelly to the Kelly fraction calculated to err on the side of caution as under betting is penalised less compared to over betting using the formula. Using the example above, this would translate to betting 0.3324/15 on each outcome which is approximately 2.2% of your bankroll up for risk.

Published on 12th of April 2011

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