Some thoughts about Money Management

Hello,

yesterday I thought about the question, why so many people advise to risk no more than 2% of your account. I thought, is that just a rule of thumb or is there maybe a deeper sense behind it.

So I did the following calculation:

Consider a situation in which you expect to be profitable with a probability of 50% and losing also with an probability of 50%. But if you win, you win twice as many pips as you would loose if your trade is not profitable.

So let's make some calculations:

If you first lose 40% and then win 80%, you end up with 0.6*1.8 = 1.08
If you first lose 20% and then win 40%, you end up with 0.8*1.4 = 1.12

What we see here, is that position sizing is not only about risk controling but also about profit maximizing, a higher leverage doesn't need to mean a higher expected value.

I asked myself, where is the optimal position size, to end up with the highest possible return?

Let's do it universallly and call the ratio of the profit trade to the loss trade c (In the example c is 2), then we have to maximize the following equation:

f(x) = (100-x)*(100+cx)
= -cx² + 100(c-1)x + 10,000

To find the maximum we derive after x:

f'(x) = -2cx + 100(c-1)

and set the derivative to 0:

-2cx + 100(c-1) = 0

<=> x = 50 * (c-1)/c

In our example x would be 50*1/2=25, so we would maximize our profit by risking 25% of our capital.

Of course nobody has an "c" of 2, so lets see what c must be to make x = 2:

If we solve the equation for c (with x=2), we get c=1.04.

We can conclude, that we maximize our profit by risking 2% of our account exactly in the case where we expect to earn 26/25 as much as we lose (in our set up scenario where we win in 50% of all trades).

Of course, to get good results you should take your personal (Total Pips Won) to (Total Pips Lost) Ratio for c. But dont forget, do calculate the Total Won/Lost Pips you have to convert them all to one currency and divide them by the leverage you used.

Maybe that helps somebody who also thought about this topic.

Best,

Antoni

Personally I believe if you are not successful, money management will not help you. I never use money management. Why to put stop loss that can take away half of your account.?

LOL, oh boy I love these forums

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ok, now that is just wrong

Hi Antoni

With your equation.... It would help me alot if you could give explainations to the following factors:

f = ?
c = trade loss or risk?
x = ?





f(x) = (100-x)*(100+cx)
= -cx² + 100(c-1)x + 10,000

To find the maximum we derive after x:

f'(x) = -2cx + 100(c-1)

and set the derivative to 0:

-2cx + 100(c-1) = 0

<=> x = 50 * (c-1)/c

IMO there is a false assumption in your example. Anyway optimal position size can be answered by kelly criterion. Google it.

f(x,c) is a function of x and c,that gives us the new balance after a losing and a winning trade.

x is how much percent we risk, e.g. x=2 means that we risk 2% of our account per trade.

c is the ratio between the pips we can win and the pips we can lose.

Thankyou Antoni

first incorrect assumption there is an optimal position size.. no there isnt.. it depends on how safe you want to be and generally must be adapted to entrance into the market.

2nd incorrect that there should be a set target .. nope setting a target generally will only cap how much you can win and will lower your average win size vrs loss size and will drag normal trading strategies into losses.

3rd % based MM has exponential growth at the expense of higher account risk.. nothing in trading is free.. risk is always tied to reward.. without risk there is no reward and with 0 risk there is always - reward.. in the near term.. fixed position sizing can be set for any number of amounts of trades and managed easily..
example... i think over 100 trades i will make money and have 10k account so 10k/1k =100$ out of 10k every time this does two things...

1. lowers the %win rate vrs loss rate needed to be successful and profit at the same risk:reward ratio by about 15%... and improving efficiency in trading game

2. keeps the effect of wins in proportion to account starting size so as to increase expectancy of positive outcome..

generally exits are not a part of money management.. only the INITIAL RISK is money management thus the effects of how to reduce initial risk without effecting future outcome becomes the bridge to MM and the trades profitability.

newbies start fixed positioning its much safer

Hello domino,

I never said sth. about setting targets! I share your opinion about them and in 90% of the time I don't use targets. c is calculated on historical trades that could be closed manually, or by SLs and not by TPs.

With my calculation I didn't want to give advise to anybody about how they should size their positions. I'm sorry if I didn't state that clearly enough. The main result I wanted to show is, that although you have a EV+ in pips, a higher leverage doesn't need to mean a higher EV+ in $, that is only true up to certain point which is calculated in my post above.

That is true in most cases, but not in any! Consider the following scenario, btw. the formula lacks the fact that nobody is in exactly 50% of the time profitable and vice versa, so the formula shouldn't be used in practice, but the result (bolded above) stays the same:

Your historical trades (>10k) show a c of 1.01. If your compare now the following leverages (position size=account/SL*x):

a) x=0.5% -> EV (Expected value) = 1.00002475
b) x=0.6% -> EV = 1.00002364

What do we see?
a) has a higher EV while having a lower risk than b).

To raise your expected return, you don't have to raise your risk.

Best,
Antoni

Wow all that is confusing but what the hell I will have a go. Money management is important in my view. It allows you to grow with your account by compounding or decrease your risk by following your draw down as well.

Here is how I do it






Trade Size = Risk Amount / Stop Loss



Example 1:
Assume we have a $20000 account balance and our risk is 2% per trade. This means our loss is equal to $20,000 x 0.02 = $400. To determine how many contracts we trade we divide this loss by the stop loss for each trade. Let’s assume we go with a technical stop loss of 40 pips, and assume each pip equals $10 per pip therefore a 40 pip stop loss equals a $400 loss. Therefore we divide 400/400 = 1 standard contract for the trade.



Example 2
Trading the Eur/Usd pair
Account value = $5000
%risk = 2% of trading capital
Stop loss (predetermined) = 30 pips
Risk amount = $5000 x 0.02 = $100
Trade size = risk amount / stop loss
100/0.0030= 33333
This means in this trade you would trade 3 mini lots only

If your account goes down to $4000 then risk 2% of that amount. Just do heaps of backtesting and if you take 7 losses in a row add another 5 to give you a more realistic live trading results.

Sorry about the text i did it in word and could not match it here sorry



Keep it simple

Darren

http://www.fxtradingfactory.com