Fixed vs. percentage based stop loss

Bringing this post back from the archives as Acrary mentions some shocking items that was previously untold of to me in this thread about money management, risk management, and effective position sizing. Hugely insightful.

Up until now I had been using a % equity-risk based positioning method... roughly based on Elder's 2%/6% rule... but now it seems I'm going to have to change it :) While the drag effect seems miniscule, I'd like to have as much edge as I can.. especially in this area. Scalability plays a huge factor when dealing with %'s.

Made a spreadsheet also of this implicit 'drag' effect... seems to increase the more % equity you risk per trade... working on adapting his proposed strategy or modifying it to fit my needs.. will post when I finish (probably later today).
 

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FINALLY SOLVED IT. Derived the inherent drag :P

Lol.. common sense won out in the end... but it took a while to finally realize what was going on.

In Acrary's proposed simulation, there was actually a negative expectancy - the avg. wins and avg. losses in the proposed simulation, as well as the other two I tested, resulted in a net loss of 39.97. Turns out actual expectancy was -19.98, and if you multiply that by the # of trades (in this case, 10) you get the 'drag'.

Now.. why is that?!
Because of the drawdown recovery % rule! Basically what Acrary acknowledged is true... gains are arithmatic while losses are geometric:
As we all know, a 10% drawdown needs an 11.11% gain to break even... now applying that with the simulation... for each 'win' we are only applying a 2% gain... but obviously as we hit 2% losses, we actually need a 2.04% gain to recover... so to actually have a 0 expectancy simulation the Win Rate would have to be 2.04% to match the 2.0% losses.

What does this all mean?
Basically, make sure your system has positive expectancy; namely, that your losses are smaller than your wins. Also be aware that any type of loss you experience will need a larger percent gain to break even... more reason to keep them small as possible.

Common sense, but the inherent drag was bugging the fcuk out of me.

LOL... attached is the excel I used, along with formulas and whatnot... enjoy.
 
Thank you for bringing this back from the dead. Actually what I posted was mostly a bunch of nonsense to see if anyone has done the math. There is no drag using fixed % MMgt. At the mean there is, but it is overcome by the compounding effect of using fixed % MMgt.

And while drawdowns do require compounding to overcome the drawdown, the size of the drawdown is largely a function of how far away from random and independent the trades have been for the account. In reality the drawdown will be overcome as soon as the the account reverts to its normal series of wins/losses with no drag caused by the fixed % MMgt method.

If you do Monte Carlo testing you can set reasonable levels such as 95% probability of a particular max drawdown for any period to protect the account by setting firewalls.

Here's a worked out example showing there is no drag.
 

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Thanks for responding, Acrary.

You are indeed correct. The initial drag simulations did not take into account the possibility of 'win-win' or 'all win' and 'lose-lose' or 'all loss' scenarios... in such instances, 'all wins' are large enough (due to compounding) that they equal the asymmetric leverage or 'drag' produced by the aggregate losers. Losers are minimized by compounding as well. Also note that the +- and -+ scenarios both resulted in a net loss of 90 because of this, which was the small piece of the picture we were looking at.

My brain hurts now.
 
There could even be a theorem here.


It seems like a similar problem as studied in the 18th century.

Various gambling schemes and games were popular in high society. People wondered whether there was some "magic" betting scheme (e.g. martingales) which would give wins---even if the house had an advantage in expectancy per bet.

I believe Laplace proved it was impossible---something that is now of course obvious to anybody with modern mathematical intuition but back then things were far fuzzier in most people's minds.

Let's think about it here:

net return =
S(1)*T(1) * S(2)*T(2)*S(3)*T(3) ...

Now S(i) is the size of the bet taken at any stage---relative to current equity---, and T(i) is the random variable of return per stage (e.g. 1.0 is flat return) Note that S(i) can depend only on T(1)..T(i-1).

take logarithms and collect S's:

Log(R) = LS(1)+LS(2) + .... LS(N) + \sum T(i) =

Log(R) = sum(i) LS(i) + N*expectancy

There is a former normalization in that your 'average' bet size relative to current equity in probability over trades must be some constant that you externally decide---this is a restatement that you start with a known amount of capital that you risk on average a certain amount (otherwise the problem is ill posed).

half assed conjecture: in expectation as N-> infinity 1/N sum(i) LS(i) doesn't depend on the formula you use to compute S(i) as a function of previous S(i)'s and T(i)'s.

Explicit dependencies on N probably have to be removed too (stationary betting algorithm) otherwise of course S(i) could go to zero (walk away from table) or infinity (bet the Federal Reserve on the next spin) arbitrarily.

Thoughts?

Disclamer: I didn't think very much before I typed, it was made up as I went along.
 
Quote from DrChaos:

Thoughts?

Disclamer: I didn't think very much before I typed, it was made up as I went along.
More...

You've done very well, much better than many of us here. :D
 
I'm somewhat confused by this thread. First we hear that there is drag with fixed fractional MM. Then later on, there is no drag? And DrChaos...wow. I can't make much sense of that at all. Has been a long time since I was sitting in the back of math class.

Would someone be so kind as to lay it out for me in plain english? Fixed Fractional MM has drag in it?

I'm hunting for alternative stop loss strategies - is the general consensus that this is the most appropriate? Right now I'm doing the ever so common stop is placed at a constant X ticks on every trade. Feels arbitrary. Gotta be something better then this.

Any recommended reading on the subject of various stop loss strategies?

Best regards,
MK
 
There is no drag. The possibility of an all-win outcome eliminates this, to put it simply. Scroll up and read some of the files and attachments to see that.

This thread was mostly an experiment of thought, probing at convention.

A more sophisticated method of stop usage would involve optimizing distance from price, as well as integrating it into what can be called a "money management matrix" based on market conditions. Read about it in TASC.

Also see this for a start:
http://www.aima.org/uploads/Arcus66.pdf

Stop losses are not everything. Many professionals can not set them outright because of liquidity issues. As such, other ways of reducing risk must be employed...

EDIT:
Just reread your post.

If you are not happy with an arithmetic ( n ticks ) based stop, try backtesting some volatility-based strategies or chandelier strategies.

Quote from MidKnight:

I'm somewhat confused by this thread. First we hear that there is drag with fixed fractional MM. Then later on, there is no drag? And DrChaos...wow. I can't make much sense of that at all. Has been a long time since I was sitting in the back of math class.

Would someone be so kind as to lay it out for me in plain english? Fixed Fractional MM has drag in it?

I'm hunting for alternative stop loss strategies - is the general consensus that this is the most appropriate? Right now I'm doing the ever so common stop is placed at a constant X ticks on every trade. Feels arbitrary. Gotta be something better then this.

Any recommended reading on the subject of various stop loss strategies?

Best regards,
MK
More...
 
<i>"You're right. Positive expectancy was excluded. I was just trying to isolate the money management component. <b>In a method with no postive or negative expectancy,</b> the % of portfolio money management just adds another negative to overcome"</i>

If I read correctly, I think <b>acrary</b> already recanted this statement a few posts ago. It bears pointing out that the constants in this equation are false. Anyone trading a method = system with b/e expectancy cannot improve it with any type of money management. A trading approach that breaks even will never do better than bleed to death, given enough time.

%risk works perfectly fine when a trading approach has some type of (mandatory for success) edge, be that win % greater than 50/50 or (much better) a profit/loss factor of 2/1 or greater.

In other words, scaling trade size up & down as the random streaks of wins & losses unfold works great, providing the trade approach has a performance edge. The bigger that edge, the better %risk works. No edge? No hope for success period, so no need to use that as an example :>)
 
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