A Neat Money Management System

[Henry]

The Kelly criterion is a way to optimize your “winnings” in forex. He developed a formula to calculate the percentage of your trading balance that you should risk on each trade.

There are two basic components to the Kelly Criterion:
• Win probability - The probability that any given trade you make will return a positive amount.
• Win/loss ratio - The total positive trade amounts divided by the total negative trade amounts.

These two factors are then put into Kelly's equation:
Kelly % = W – [(1 – W) / R]

Where:
W = Winning probability
R = Win/loss ratio

The output is the Kelly percentage, which we examine below.

Putting It to Use
Kelly's system can be put to use by following these simple steps:
Access your last 50-60 trades. You can do this by simply asking your broker, or by checking your recent tax returns (if you claimed all your trades). If you are a more advanced trader with a developed trading system, then you can simply back test the system and take those results. The Kelly Criterion assumes, however, that you trade the same way you traded in the past.
Calculate "W", the winning probability. To do this, divide the number of trades that returned a positive amount by your total number of trades (positive and negative). This number is better as it gets closer to one. Any number above 0.50 is good.
Calculate "R," the win/loss ratio. Do this by dividing the average gain of the positive trades by the average loss of the negative trades. You should have a number greater than 1 if your average gains are greater than your average losses. A result less than one is managable as long as the number of losing trades remains small.
Input these numbers into Kelly's equation: K% = W – [(1 – W) / R].
Record the Kelly % that the equation returns.

Now if we can get the stats for Ash's trade calls, we can use them to calculate our position size on each trade.

Let's take the attached picture to try and figure this out.

Let's assume the following: (for illustration purposes)
a 50:50 ratio of winning to losing trades, thus W = 0.5.
the average win divided by the average loss is 1.2. (This has to be greater than 1. If it is less than 1, your balance will get less and you'll soon join the 95% who loses their initial deposit.)

Now we have a Kelly ratio of 0.5 – [(1-0.5)/1.2)] = 0.08.

If your available balance is $2000, you can risk 8% that is $160 per trade. Let us take the attached chart and apply this.

The system calls for a trade to be entered into at 1.66841 with a stop at the previous swing high, which is 1.70423. This is 3582 piplets or 358 pips.
Now 160/358 = $0.45. This is the value that a pip can have with this trade. Therefore the lot size can be a maximum of 0.045.

Now if the win loss ratio is 1.3, it changes the trade dramatically. The calculation then changes to 0.5-[(1-0.5)/1.3] = 0.12. The Kelly ratio is now 0.12 or 12%. That is $240 that can be placed at risk. The pip value now changes to 240/358 = 0.67 and the lot size to 0.067.

So from this we can deduce that each trade has it's unique stop loss which calls for a unique lot size.

The profit targets are another issue.

PS. If you find any calculation errors, blame Excel. :D

[ForexGuy]

Henry this is very good research. You may not know it, but what you are talking about is called “figuring positive expectancy”.

We use this method at the end of our back testing in order to calculate the probability of a particular system or model. The expectancy calculations begin to have real value when weighted against other trading systems.

Back testing can provide many other valuable pieces of information such as:

1. Maximum Draw Down
2. Maximum Draw Down Duration
3. Maximum Number of losing trades in a row
4. The effect of various money management systems on the model.

Using these factors we can optimize our system to affect the greatest return with the least amount of risk. What you must be careful of is what is called “form fitting”. This is where we manipulate the data by using optimal parameters for the testing sample. You will find this in virtually all EA systems where the seller shows you unrealistic returns based on a specific period of data.

Here is the bottom line; if you are not doing this type of expectancy calculation prior to trading ANY system you are WRONG. You are a 95%’er. EVERY SUCCESSFUL TRADER I KNOW OR HAVE WORKED WITH USES SOME FORM OF EXPECTANCY CALCULATION BEFORE THE TRADE ANYTHING.

Excellent work Henry. Keep it up.

[Henry]

Forexguy, I have been thinking about this method a lot and like all methods, it has it's flaws. If we take a sample of 1000 trades from a specific strategy and calculate the Kelly % we get a figure of say 10%. If we take the first 250 trades, will we still get 10%? Or the last 100?

I think not, but then again some rationale is better than nothing. :D This is where many signal services are flawed. The customer normally incorrectly assumes that signal services should have a hit rate in the 90's or so (If they sell their service they must be good. :p)and then they wager a disproportionately large percentage of their capital.

I think that if a signal service will not give you the Kelly % of their calls, you should be carefull before trading them live.

[fatonahfx]

thanks for this information sir..
We always lack of trading strategy...

[DirkNannes]

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[fxarms]

good research.

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