Optimized Risk vs Reward Equation

hmm, risk function is the integral of the loss function.

bigv....
your making this WAY more complicated than it has to be......
And I don't understand a word you are saying.

All this reminds me of one of my favorite cartoons

Hi bigvlada,

I hardly ever participate in any discussion on forums; I'm here for the awesome calendar service. But all this math caught my eye and I understand your trying to find the optimum risk/reward if and only if the first take-profit is reached.

Honestly, I don't see what the problem is... the 'optimum' by far is to exit right then and there. Your risk is virtually zero and you reward is infinite times the size of your risk. No matter how much math you do you will never beat that type of risk/reward ratio.

Don't waste too much of your time looking for something that may or may not exist. You are not twoblink and thus you do not know what assumptions he is making and what definitions he is using. I mean no disrespect when I say that twoblink could have a completely different view of what optimized means.

I just hope your not going on some sort of wild-goose chase because of a miss-communication.

In any case it seems to me that you are simply looking for the perfect trailing stop. The biggest difference between a regular trailing stop and the pyramiding type is simply that added variable of lotsizes on reentry.

It certainly does have it's benefits over a traditional trailing stop; but pretty much only when price moves in one direction for an extended time without too much resistance. I suppose most traders look for the same condition.

I would humbly suggest that you not look for some magic number that may or may not exist and instead optimize for the market(s) you actually want to trade.

Also I'd like to remind you to have a healthy skepticism towards everything anyone tells you. When anyone gives you a tidbit of 'information' it is on you to make sure that they are not full of sh**.

I don't know twoblink and I really couldn't care less if he was Jesus Christ himself; I still would not believe him solely on his word. If you want to use the information someone is 'offering' you then your job is to do everything in you power to disprove it.

Only after a violent period of trying to disprove something and not being able to then and only then you should ask yourself a simple question: If I assumed it was true, what merits would it offer?

Most theories do not get to phase 2 because some genius 'cracks' them Who knows maybe you bigvlada are that genius. I do not care whether twoblink's proposed theory is true or not but I just wanted to warn you to proceed with caution.


Wow! I just read everything I wrote and it sounds really cynical. If this offends anyone, in particular bigvlada or twoblink, then obviously I apologize. I assure you that my intentions were good I guess it's true what they say about the 'best laid plans'.

Short Summary:
EVERYONE = ;
NEW.INFORMATION != UNLESS NEW.INFORMATION() returns(FALSE) && NEW.INFORMATION() returns(TRUE);

Cheers, Monek

OK.... here is some very good stuff for you if your serious......
It's the Definitive Guide to Position Sizing by Dr. Van K. Tharp.
So instead of trying to reinvent the wheel why don't you get the info from a reputable and proven source.
And no I am not affiliated with Dr. Tharp in any way.

Here ia also an intro to his trading game you might like to read.

A bit more re MM.

Monek87, not a bad one, perhaps this one is more appropriate

http://img517.imageshack.us/img517/5619/cartoon.gif

Read post #37, I was taught how to determine the validity of the source based on available data. Besides, twoblink gave the best explanation (and definition) of the trend than anybody else (and I've read a lot - every post in rookie section of the forum for the starters plus a few hundred books on the subject of trading). Based on his previous posts, I have no reason to assume he is pulling my leg on this one.

The goal here is to determine the best mathematically possible MM, a pure strategy (http://en.wikipedia.org/wiki/Pure_strategy) using only mathematics. I have found no reason to believe that this is impossible to achieve.

If you exit after the first position is positive and second potential position is reached, you throw away the potential profit. You earn more on that first position, but compounding will surpass any single position transactions in the medium to long run (If you have read this carefully, you know that growth we are talking about here is exponential).

ps. I've added funny old man as my avatar, just because of your cartoon. I even have a picture of two of us together (no, I'm not that old, it was taken at London's wax museum ). Why him? Well, when I'm in a good mood, I like to think that he coined the name for the General Theory of Relativity while he was visiting his first wife's (mathematician Mileva Maric)family in Novi Sad. He even tried to find employment in Belgrade, without much success. (our ability to spot extraordinary people is legendary ). The story goes that he had a lot of quarrels with his father-in-law who often used the term it is all relative when dismissing the view's of his son-in-law. The story may or may not be true, but it is amusing. If any of you visits Novi Sad during the EXIT music festival, ask the locals about it, they may know the full version.

@tradestar1

Thank you for your effort, but I have read Van Tharp's books almost two years ago. My first insight at the importance of the MM. It is great reading, but not applicable in this discussion. He shows that pyramiding is possible, potentially lucrative, but he either talks about lowering risk or increasing
profit, not optimizing them and certainly not at the same time.

OK, back on the subject.

While rereading the article about minimax theory, I may have solved the other 2D graph, the profit one.

We have a zero sum game, with a large but finite number of players. The notion that you determine the worst possible scenario by entering initial values for your stop loss and lot size got me thinking. If that is the worst case scenario, according to theory, the best one is just opposite of that, meaning it is position when the price moved in our favor for the length of the stop loss size. True, it can go further, but will the potential profit be the same? If this is the point when the profit potential is biggest (and after that begins to descend), then we have second point for our saddle point.

The risk is lowest when the price moves for twice the size of the sl and potential profit is biggest when the price moves just for one sl size. The saddle point is somewhere between these two points. Hmm, this is woth investigating further.

Nice illustration there bigvlada... really enjoyed the laugh

Yes, of course I understand the compounding possibility of pyramiding. It's not rocket science

However this does bring to mind the limits that you will have to work around when looking for your optimization.

First we have lotsizes... after buying 5 lots, brokers, or at least those that I have dealt with, require their employees to confirm your transaction manually. This will increase slippage and possibly spread.

Also when compounding lotsizes you will notice that the more you increase your lotsize the more margin your broker will ask for; this depends on your leverage as well.

However if pyramided correctly then yes it can be done if and only if your broker takes it's margin from your equity and not your account balance; which I believe they do.

I only mention it because if the market gaps over your stops at any point with a heavily compounded position you will lose your account and depending on your broker you may be asked to pay them more than your total account balance.

Also I would like to know what assumptions you are working under. In other words what are the rules to your 'game'? No game can be optimized without a specific rule set

I have found that a trailing stop of some sort is superior to a pyramid for the first couple of pyramid re-entries. A pyramid only begins to shine after a given amount of re-entries which is dependent on the lotsize growth.

I'm attaching an openoffice calc file to let you play around with it so you can observe what I'm talking about. All cells in yellow can be adjusted; so play around with them if you dare I also added a profit to margin comparison graph to illustrate the danger of gaps.

The file is set up to calculate growth of re-entries of a certain type of pyramid. Basically it assumes you'll re-enter the market every certain amount of pips and if it moves against you a certain amount of pips it will close all 'trades'.

By default it illustrates 23 entries where 21 are profits-spread, one is break-even-spread and another one is a loss-spread. The 23 in the yellow cell is a variable that one can change to anything lower than 23... I didn't see the point of having it calculate to more wins than that however; so do not put in a number greater than 23.

Oh yes and it is in CHF but that is irrelevant as all the calculations work the same; so pretend it's the currency of your choice The variable 'sum lotsizes/x' is where all the compounding is done so change it to whatever you wish.

It basicaly takes the sum of all previous lotsize entries and divides it by this 'magic' number Optimum for growth in 23 entries is around 1.1; it would be less if it was not for spread or the stoploss' static distance.

EDIT: I had to convert my openoffice calc file to the microsoft type; let me know if it's working cause I really have no idea

Enjoy, Monek

Monek,

First, I'm not Jesus Christ.. I don't have the facial hair.

Second, I've put in somewhere between 4~8 hours a day for over 2 years, this July, it will be 3 years into this.

Third, I had a theory, and it took over 2 years to actually prove it mathematically, and I was WAY more cynical than you.

That said, I actually don't care too much if anybody believes me. When I started the journey, there wasn't even a SINGLE SCIENTIFIC REPEATABLE DEFINITION OF A TREND. Not a single one, and so it took me a year to formulate the very backbone of "trendtrading". I have 800 Gigs of trading books, mp3s, and videos about trading on my HD. I taught FX trading for 3 years in Taiwan, the first and ONLY FX class in the entire country. I generated over 120+ hours of FX video for my students. I've read 700+ books on trading. So I would LOVE for you to disprove me.. because as you said, if you do a good enough job, you should find out what I found out.

and that is:

Given X lots @A point, there exists an optimal Y@B such that potential risk is at a minimum while potential gain is at a maximum when combined with a SL@C.

I have drawn diagrams, I have run multi-day simulators, I have written programs to crunch numbers, (I recall a 61 day program that I ran, calculating from lot size 1 to lot size 10,000 with all running combinations in-between.. shoving that data into a database, and then graphing against it both from a SL risk assessment as well as a "what if" movement of price against re-entry).

It seems to me that people who are either bad at math, or just don't have the will-power to see something through, poo-poo on everybody else.

If that is you, this is not the thread for you. I advise you to spend your time more wisely and read another thread.

BTW.. I also caught your mistake. FX is not Las Vegas. It's not a roulette table where the expectancy is fixed and (in the case of roulette, it's -5.26%). So taking profit will NOT make you more money in the long run. Far from it.

Cut your losses and let your profits run is the ONLY way to make more money. Cutting your profits and letting your losses run seems to be what everybody else does and while it seems intelligent at first blush, it will get you KILLED in the market.

What I am waiting for is when bigvlada independently verifies what I have done.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

To bigvlada:

I know you know what "Average Up" is.
I know you know what "Average Down" is.

I am now working on a new math theory I think technically should be called "Averaged second chance". It's a new theory I picked up while re-reading one of the books that inspired me to learn about trading, "How to Make $1M in the stock market automatically" by Robert Lichello. His Average Down automated method (AIM) has lead me to a few new theories.

I've had a the person I work with from MIT independently program and verify it.. and so this will allow me to mitigate some losses when you pick the wrong side.

So hope all this is working great for your trades! I want to encourage you because there is SOOO much more to the FX world that what most are doing.

Well thank God for that, then.

I know this is off topic but you mentioned Donchian channels on a different thread and wondered if you could give us some pointers as to your thoughts, maybe a new thread, maybe a link? Thanks in anticipation. I would have pm'd you but I'm scared to.

hi all,
I've been really such a big fan off you guys, and since we are here, why not focused our attention to the market analysis..? DSP, fitting, .. anyone?

twoblink can be bitter sometimes, but I am hardly surprised. If anyone invests some time in reading all of his posts (and I mean all) he/she will see how many times people ask the same question that was answered a few posts above.

I have much more tolerance (repairing computers while you are a teenager can teach you patience - in those cases when you have tried everything but the damn thing won't work - and I am talking about zx81 and spectrum) towards repeating questions but it can be boring.Nobody should be scared or ashamed to ask about something he does not know. But some reading before you ask questions can be more energy efficient for both parties. And sometimes people just don't get it(While I was working at a press clipping agency, I had a new employee and tried to explain to her how to scan a newspaper article, send it to computer and add it to database; I've tried for 4 straight hours, she didn't get it so I let her go).

OK, lets traverse to some explanations:



hmm, If you start with 5 lots (with 1-3% risk) you must have a lot of money to start with, so the broker will probably dedicate one employee to satisfy your needs. Version two is that you gradually reach 5 lots, but by that time your SL will be several hundred pips so few pips of slippage can be considered as statistical error.



This sentence tells me that "you didn't get it". This statement is false. Your entire risk is situated in your first position (0,5;1;2;3 or more %). After you reach the first add on position, you know you will earn money (and that amount is the best compromise between risk and potential profit). After that moment you can't lose money.The risk after the second position is reached is 0, zero, nada, zilch, nothing, nula (нула). That's why this thread is called optimized risk and reward and other threads deal with risk and reward. Read the thread again (I read it regularly, because there is always something I've missed in previous readings).



When you enter a transaction, you set the initial rules (SL, lot size and next add on position). What I am trying to do is replicate twoblink's set of rules, what to do when your transaction is positive, meaning when and how much to add.I used the term pure strategy because the player has no room for speculations and doubts of any kind (when this happens you must do this and this and nothing else) The spreadsheet is nice but it cannot be used for our problem.This problem cannot be solved using only two dimensions. The solution is in 3D, the saddle point can be seen only in 3D and you use the result in 2D.

No magic, no god, no divine items; just numbers, definitions, theorems, formulas and a lot of calculations. :nerd:

Averaged second chance

hmm, interesting, it reminds me of reserve parachute strategy; when the primary folds, you will not get killed, you will only break both legs and lose a few teeth. You will not be pretty but you will be able to do more jumps.

hmm, it's like you assume that your opponent (all the other guys in the market) will play flawlessly and you use mixed strategy (determine the best losing outcome for you if you know the other one will execute his best strategy). You used Nash equilibrium for that?

Something like example 2.2 from attachment?

It's a form of games theory, yes.

I think the confusion comes from a "pure math answer" vs "common sense".

Math answer is to bet Kelly every time.. That of course, is the mathematical optimization; and if that's all you are looking for, look no further. Common sense though says that I RARELY go beyond K/3 (Kelly Value / 3) and once in a while I will brave it and go K/2, but I've never gone Kelly.

The proposition though is that the limiting reagent be minimized risk.

I have been discussing with a friend that even with heavy optimizations, there might not be anything you can do in actuality about it.

For example, let's say the optimized math say 5 lots in and 2.3 lots added. Do you have enough capitalization to cover 7.3 lots total risk? Even if you are adding when you are guaranteed profit, do you even have enough $$$ to cover 5 lots? 5 lots is A LOT (pun intended) for the average trader.. I wouldn't trade 5 lots unless you had 6 figures in the trading account. So the optimization is for math, and also tells me what number I eventually have to work up to as far as my account capitalization so I can fully realize the system.

And also, some seem to confuse what this thread is talking about, vs > 1 expectancy discussions. This does NOT discuss the expectancy of your system. This simply asks about the optimization of profit vs minimization of risk in positions, pyramids, and ephemeral positions.

It is strange, in most everything I have scoured on the internet, there is little talk, if any, about ephemeral positions and what to do about it. I think this is why most "pyramid in" systems suck because they don't deal with when you HAVE pyramided in, what then?

As far as Averaged Second Change, it's more like this.. Let's say you find a lottery scratcher ticket, and you scratch it and it gives you the option of winning $1, or getting 2 more scratchers. You are giving up the potential of $1 for 2 more potential chances. You risk the $1 reward, sure, but had you simply taken a dollar and bought a scratcher, you'd only get 1, in this case, you'd get 2 new ones. So assuming there is a big price, the mathematical smart play long term might be to trade for 2 tickets..

As far as DC's.. What did you want to discuss? This btw, is not the thread for DC discussions..

I thought of some kind of Nash's equilibrium in a forex environment, although I still cannot picture it clear enough. From what has been said here, we know that there are more variables than just TP, SL and lotsize. Let me try to point them out:

Account balance (AB) - tells you what is your biggest allowed lotsize or a sum of numerous smaller lotsizes
Leverage - defines boundaries of max. lotsize within AB
Spread - plays an important role in the final equasion for the proper TP & SL variables
OpenPrice - when do we open our first position
ClosePrice - when do we close all our positions on one currency pair, if that happens?

Your Time for Trading - if trading is not automated
Complete understanding - in order to know if and where are the boundaries, in all the ways

I would appreciate if anything is forgotten, that you add it in your posts. If anything is wrong, please correct me.

And afterall, I would like to ask you twoblink, have you came up with your theory of OR vs. RE on a different logic in opening new positions, than you had described in your post on trading with a pascal's triangle figures? There you described, that additional trades are added when price action (PA) goes in your favour. But from what we discuss here, I get a feeling that in our case some kind of "hedging" is involved. Am I mistaken?

I'm gonna be blunt as I just want to get this out of the way:
I was hoping that this thread would be a purely academic one.
I do not care about anecdotal evidence.
I do not care what your beliefs are.
I do not care about feelings.
I do not care about opinions.
I do not care about quoted famous or powerful people.
If it isn't empirical it is meaningless.


HOWEVER I DO RESPECT EVERYONE AND ANYONE THAT POSTS ANYTHING ON THIS THREAD EQUALLY. I DO NOT PERSONALY KNOW ANY OF YOU AND AS SUCH YOU ARE ALL EQUAL IN MY MIND.

If anyone at any point feels insulted by my words then be advised:
a. there is nothing I can do about it.
b. your own emotions are under your own control.
c. I do not care nor should you.
d. let us simply continue our discussions.


I will speak of such things no further and would like everyone to be aware of them as it may save you some time (if your intent is to post hate of any kind).


Ok, so lets get down to the theory first. Now that I have your attention twoblink. You may want to rephrase it to imply that more than one trade is mandatory.


Otherwise like I said before your best bet is to enter the second trade with nothing and exit. Although I know what was implied; the semantics are important so that no miss-communications occur.


“Given X lots @A point, there exists an optimal Y@B such that potential risk is at a minimum while potential gain is at a maximum when combined with a SL@C.“


You enter with 1 lot at point A
0 lots at point B
Making SL@C 0 pips away from market.


In other words you close your position at B. Now you must agree; as would any sane person that if you were never to trade again this would be the optimum thing to do in an 'iff' situation.


This is optimum for a number of reasons:

 

1. YOU RISK NOTHING
2. YOUR GAIN IS INFINITE TIMES BIGGER THAN YOUR RISK
3. YOU ARE PLAYING THE HAND OF PROBABILITY CORRECTLY

Now granted this is only true if we walk away after the first trade and we are dealing with your 'iff' situation. This is why you need to change your theory to imply the continuity of entries into the market.


Otherwise your theory is:

 

1. TRUE AND EASILY SOLVED
2. USELESS FOR FUTURE TRADES

For the record I do not think either of those two things about your theory; I simply have my doubts.

I very clearly understand that this is not the purpose of your theory and is pretty much word play so I will not mention it a third time; it would simply be a waste of both our time and ever-precious gray-matter.


As for bigvlada... yes you are correct in stating that if the market gaps over your stop and you close it you will not lose money. But 'iff' it lands in-between point c and your gapped stop. However if it moves past it you can still get margin called.


Perhaps there is something I'm missing. But the discussion would be perhaps trivial as there is very little a trader can do against an unexpected gap in the market. So let us speak of it no further. After all it was only meant to caution you and anyone else of what is possible; but not what is probable.


After reading your answer of what you're actually looking for I can safely say it is what I expected you were looking for. It is good that we are on the same wavelength.


My spreadsheet was not meant to prove or disprove anything to do with said theory. It was merely to illustrate how margin plays into an over-leveraged pyramid. In other words it was also meant as a friendly warning to anyone willing to read it.


ASSUMPTIONS I AM MAKING AT THIS POINT:

 

1. spread doesn't exist (will factor in later)
2. gaps over stoploss will not occur
3. I have successfully reached point b after entering at point a.
4. price will move in an equally probable way... ie the chance of it moving 10 pips up is the same as the chance of it moving 10 pips down.

I say assumptions because they are completely and utterly changeable and only illustrate my thought process.


I suppose the first thing I would begin to look for and try to understand is the relationship between risk and gain. To simplify this further I will assume that spread is at a fixed 0; I will factor it in later.


The following picture sums up my assumptions thus far on the relationship between risk and gain and what it has to do with this theory. It is purely conceptual and has no specific numbers... I just put it on a chart to add to the understanding.


Please correct me if I am at fault.


Thank you twoblink and bigvlada for your timely responses and for this provocative discussion,
Monek

@monek


No. You can add up to 0.9999 lots (9.99 cents per pip) as your second position. The problem is, what is the ideal number between 0.0001 and 0.9999?


This is true for any system and the responsibility for it not to happen is at broker's side. Bigger broker - lower possibility that it will happen.

You have to babysit your positions more at the beginning (when your risk is very low (measured in amount of currency you risk)). At later stages, when your lot size and stop loss size are much bigger, the probability that market gap will be bigger than stop loss (your risk is still low but more money is at stake) is infinitesimal (if the gap is more than let's say 500-600 pips that means that either the broker is an absolute idiot or somebody have just blew up NYSE or LSE).

When you increase lot size, the stop loss size and the length the price needs to move in order to form the next saddle point also must increase. That's why I do not worry about slippage, spread or market gap. You could add another factor - human physiology - The biggest downside is that you must sleep and eat sometimes. There is a real possibility that price will reach the next add-on point while you sleep. You can still add if it stays above when you wake up (you'll lose some of upside potential profit but c'est la vie). Or you can invest in hardware and software that will do that thing for you automatically (when you enter your first position).

A is a point on some surface. B is a saddle point on that surface.
C is a point on hmm, inflated surface (same shape as first surface). B2 is a saddle point on that surface...etc...

I never used the probability in my calculations. That's why I like IFF, you do not have to worry about probabilities. If the price reaches the next level, great; else it will kick me out, I'll take what's on the table and look for next setup. With each new level, the market will have to try harder to kick you out.

@twoblink


No, I do not like to use Kelly, because it depends on the system I use (some will give me bigger win rate, some will be less successful) and it also must implement common sense of some kind (don't bet 19% even if the system tells you that you can ).

This approach with fair trade off between risk and reward looks like the thing i want to base my MM on. On one of the first pages, you posted a graph with random entries, was that for ill-fated first theorem or for the real thing?



That's why I started with nano lots, 1c/pip and am working my way up from there. By the time I earn the right to trade 5-6 lots, I will have 6 figures in my account.

I perfectly understand that over leveraging on first position is still over leveraging. 0,5-2% range on first position is just fine for me. Eventually, one set of transactions will go to level 10 and I will be able to trade larger sums.
Patience and discipline, patience and discipline.


I'm reading a few books about how to find saddle point of convex-concave function when you do not know the surface equation. Sounds familiar

I see. So you are assuming that a trading system will take care of the probability part of risk and gain... You only worry about the actual value of risk and gain.

I suppose that is fair seeing as how this discussion has nothing to do with a trading system. Very well I'll think about it under the premise that probability doesn't matter.

This is a money management discussion, it was stated that it is mm discussion several times by different participants. You can use any system you like for your first entry. After you do that, we are discussing what is the most profitable way to proceed with regards to risk.

Twoblink posted a graph with random entries that was profitable.

I'll repeat again, in my opinion, the statement that success is made of 50% trader's mentality, 40% mm and 10% actual system you use to trade is true.

It is perfectly logical that you will be stopped more often when your sl is 50 pips then when your sl reaches 400-500 pips. But if you can afford larger sl, your success rate will go up. It is up to you to choose initial terms. You may want to check the excel file I've posted, labeled position size, that lets you experiment with starting conditions based on your risk appetite. If you start with 600 pips sl, and go up from there, you'll probably have close to 100% success rate. You choose how often you are right. You choose what is more important to you: to be right or to extract more pips from same distance the price makes? I don't care if I'm right on only 5% of all transactions if I can make 300 times the total amount of my losses with them.

Probabilities?

Where we go, we don't need.... probabilities