Maxmizing Your Returns

I was playing around with mathematical formulas in Excel (which I do from time to time ) and came to this conclusion: my account size should be so much bigger than it is and it's all due to some nice math.

I have attached the Excel file that I have been working on.

If I know the number of won and lost trades (WT and LT) over a period of time (at least 100 trades) and average risk:reward ratio (RR) that my system gives me, then I could calculate my account size based on this formula:
AccountSize = InitialAccount * [(1 - Risk/100)^(LT)] * [(1 + RR*Risk/100)^(WT)]
So let's say that my risk is 1%, and over 100 trades I have won 50 and lost 50, and average RR has been 1:2 (this means that RR = 2) then the formula above would give me that with an initial accountsize of $1000, my current account size would be:
AccountSize = $1000 * [(1 - 1/100)^(50)] * [(1 + 2*1/100)^(50)] = $1628 which is an okay profit. I won't get rich but I'm not losing money either.

Now if I think that these sample trades will be what my average trading would look like, how can I make more money? Some of you will jump out and say: risk more you p**sy!
Of course it's the right answer, but how much should I risk and can I maximize my winnings based on my average trading results? Of course the answer is: Yes!

If I take the derivative of the AccountSize function and put it equal to zero, then that will give me what the risk should be to maximize my profits. And it turns out that the result can be put like this:
Risk = (WT*RR - LT) / [RR * (WT + LT)]
So if RR = 2, WT = 50 and LT = 50, then my risk should be 0,25 or 25%. That means that over the past 100 trades my risk should had been 25% on each trade. My AccountSize would have been $361099!!!

Now hold on you might say: risking 25% is way toooo much! And I agree - it is. But if I know that my system is giving me the results mentioned I should definetly not be risking only 1%, that is also wrong. Here is where we have to ask ourselves: how big of a drawdown can I live with without it affecting my trading? Well looking back at the 100 trades, I never had more than 6 straight losses. So If I never want a drawdown that is bigger than a certain % (call it DD) if I have a maximum number of lost trades in a row (LT) then I should not risk more than:
Risk = 100 * [1 - (1 - DD/100)^(1/LT)]
So if most DD I can take is 25% and most number of lost trades in a row that I ever had was 6, I'm gonna exaggerate and use LT = 10, then the most Risk I should put on is:
Risk = 100 * [1 - (1 - 25/100)^(1/10)] = 100 * [1 - 0,75^0,1] = 2,84% or make it a nice round number of 3% (which would give a drawdown of 26%).

Had I risked 3% from the start my AccountSize today, after 50 winning trades and 50 losing trades with a risk:reward ratio of 1:2, would have been:
AccountSize: $1000 * 0.97^50 * 1.06^50 = $4017 which is big difference from the $1628 that I had when risking only 1%.

In conclusion:
Each trader should have a record over his/her trades. That can help us determine how much we should risk depending on our risk appetite, which in turn can help us maximize our earnings. Don't forget the importance of Money managment.


Note that the above numbers are just an example and not what my trading looks like.

A few notes on the Excel file:
You can change the Init.Account, the Risk (in %) and Reward:Risk to your likings, and set NbrOfLosses and NbrOfWins and it will calculate the Maximizing Risk (risk in % that would have maximized the account size based on the above inputs) and Account Size (which is what the account size would have been if the Maximizing Risk was used on every trade).
Furtheron you can check what you should risk at max if you want a certain drawdown after a string of lost trades using Lost Trades in a row, Max DrawDown and Risk (due to DD).
In the middle is a graph of the accountsize depending on the risked % and it's based on the two columns to the right which holds risk in % (to the right) and the account size based on Init.Account, Risk (in %), Reward:Risk, NbrOfLosses and NbrOfWins. Above the graph are the formulas used in the calculations.

Congratulations, you just reinvented the Kelly criterion

http://en.wikipedia.org/wiki/Kelly_criterion

Lol, I thought my findings was gonna change the world. Turns out I'm 50 years to late .

Ah, but John Kelly didn't do his in excel, yours can be the 'new improved' 21st century version

Don't worry mate, you can be proud of yourself anyway, because you have come up with it on your own... that shows that you have the skills that are needed in this business.

BTW you might want to also take a look at the so-called "Risk of ruin".

Haha... I just read through the wiki-article and it seems that my man Warren Buffet uses this theory as well. Man I pretty damn smart .
I'm always playing around with mathematical formulas, just love math.

Tnx mate. Should I take a look at "Risk of ruin" before coming up with it on my own ? Will have a look at it. Cheers!

Nah, i just think that it is a good complement to the Kelly criterion... kind of looking on the problem from the opposite side, not asking "how much should i bet to get the maximum return" but instead asking "how much should i bet so that my risk of ruin before reaching my goal is as low as ..." <- insert some acceptably low number.

Just read about it. Yes a good complement indeed.

This thread, though seemingly overlooked by many on FF looks like it has the potential to make a huge difference to my account size with no changes to my trading.
Great work NowAndLater.
Thanks again.

It's a little bit different to apply the Kelly criterion to trading rather than gambling.

The formula itself is accurate when it comes to gambling, because the probability of winning as well as losing is well know with precision. However, this is not the case in trading or investment. Probability of winning or losing is estimated usually based on historical results, which will produce errors when applying the formula.

That's why in the wiki article, there is a section arguing to bet less than Kelly.

@NowAndLater

You can try to make some adjustments to your research and include volatility. That is, look for the optimal position size, which not only will maximize returns and minimize losses given the probabilities, but also takes into consideration the volatility of the security.

Best Regards,

Nader

NAL,
I still can't figure this out but I'm kind of done trying. All I need to know is what does the ^ sign mean in the equation
AccountSize = InitialAccount * [(1 - Risk/100)^(LT)] * [(1 + RR*Risk/100)^(WT)]
Once I have this I can go to work.
I'm very impressed but utterly clueless

... to the power of...

3^3 = 3*3*3 = 27
3^4 = 3*3*3*3 = 81

Gotcha,
Thanks very much.

" Here is where we have to ask ourselves: how big of a drawdown can I live with without it affecting my trading"

Tthats the only question you should have asked yourself, since forex is not stationary as roulette or card games. The only stationary thing you assume is your system giving you fixed risk/reward which is a false premise.

Here's an example

I do wholly agree with you and haven't traded at more than 1% risk for years.
But it would be nice to be able to wouldn't it?

The reason for my post was to show that there's no need to risk the absolute minimum when we've found something that works. I wanted for fun to see what the maximum would be for my profits with a certain edge, and I love math, and that's why I created this thread, so others can see what math can do to once trading, and that it's not all about entries and exists.

And I will stress this again: if you for example over 1000 trades (which is a lot) have a decent winrate and RR, don't risk 1%. Risk at least 1.5-2%, because we know what compounding can do to your account and there's a huge difference between 1% and 2% when compounding.