Optimal Betting Size - Kelly Criterion, Optimal F...

[CarlRostron]

I am having problems posting the message so it is in 2 parts (maybe it is too long):

PART 1

(I hope this thread is in the correct area of the site, please move it if you think it is better somewhere else)


I am learning to trade FX and I have done a lot of study around 'Money Management' and how much to wager on each trade to be Mathematically optimum. I have a Trading System which gives me the following over a decent population of trades:


Win Rate = 40% (i.e. Out of 100 trades, I win 40 trades and lose 60 trades)
Win / Loss Ratio = 1:2 (i.e. When I lose I lose 1R and if I win I win 2R, where R is my Risk on that trade as a percentage of my account)


Things to consider:
I can be in up to 3 trades concurrently at any one time
My Win / Loss Ratio very rarely changes from 1:2RR so I know Fractional Kelly Criterion is a possibility


I have simulated 1000's of trades to see how the growth of my account would look, and the Simulator picks at Random a selection of trades (between 1-3) i.e. up to 3 trades per selection. On each selection I determine the risk to wager by using the Kelly Formula: Kelly % = W – [(1 – W) / R]


Obviously, I would prefer to know the outcome of every trade before putting on the next trade but in reality this isn't possible as I can be in up to 3 positions simultaneously and I don't know the outcome of any one of them before any of the others close out. So currently I use the same Kelly % based on the same Account Size for all of the concurrent trades in the selection. Once all of the trades close, I calculate the new Kelly % based on the new Account Size. This will be bigger or smaller than before depending on the outcome of the trade selections that have been chosen at random. Of course this isn't ideally how Kelly would want me to play, as it would want me to open and close only 1 trade at a time so it could know in advance my new Account Level before playing the next trade


My question is three fold:

 

[CarlRostron]

Optimal Betting Size - Kelly Criterion, Optimal F

PART 2

1) Because I am in up to 3 trades at the same time, and my current method dictates that I take my Account Balance when I am not in any position as the balance and then use the same risk to all concurrent trades, I am not sure if this is the best way to apply the Kelly method or if indeed there is a better method for me to use? I have also simulated a Fixed Fraction of my account e.g. 2% and re-basing every time I am not in a position. It performs well, but it vastly outperformed by Kelly when the traded population sets have many 'streaks' of winners.


2) Is there a Mathematically Optimum 'Fraction' to play Kelly? E.g. At the moment I have Fractional Kelly set to 15% in the simulator. So in essence, the maximum Kelly can trade up to is 15% of my account. In other words, if K% in the above formula said risk 100%, then fractional Kelly would risk 15% of my real account because I multiply the K% by a Percentage outside of the formula which it can risk up to of my account as a risk multiplier. Is there a way to Mathematically find out what optimum Fractional Kelly I should be looking towards?


3) I have done some reading around Ralph Vince's Optimal F. Much of the Maths in his book is too advanced for me to understand as I have only studied to A'Level myself. Nonetheless, I have given it a go and worked hard to try and understand it. He mentions that I can 'iterate' through the Optimal F function he provides. That being: N=(F*Equity/Risk)/Price (N: No. of Shares or Contracts to Trade, F: the Optimal F you choose to use, Equity: Your account level, Price: Price of the asset being traded). I think he wants me to iterate F from 0.1 to 1 in steps of 0.1 to find the optimum result. However, in my case, I am Spread-betting, so I cannot see how I apply the Optimal F formulae as N isn't something that I buy and Sell as a quantity in Spreadbetting. I was hoping someone could help advise how I can work out my Optimal F from a Spreadbetting Approach?


I appreciate any help the Mathematicians out there can help with this.


Can post anything else you would need to help get me going and I can model things you say to improve further my Money Management. I am happy to put work in myself, just need some help with the Maths side to get me going in the right direction.


Regards and thanks


Carl