Optimized Risk vs Reward Equation

Hi twoblink,

Just trade it yourself for verification. Why make life so complicated? If you can make money from your equation then you know the answers.

Obviously he doesn't need money if he has methods that produce 9,000 pips per week... oh wait... then why is he going to charge someone to read an ebook to help him "verify" his "findings"

Oh lordy lordy! My spidey senses are going wild.

Why don't you all just burn him at the stake? Would that make you happy?

If anyone bothered to read (at least longer than last two pages ), he would realize that the unwritten book would be about reversals and that the discussion here is about money management. And that both have nothing to do with claimed results of a trading system.


on the topic, I'm still practicing solving problems with one and two constraints. There's no universal way of doing this (every function has a way of its own) which makes it more difficult for later implementation in excel. But, If I knew the formula and two initial constraints (I'm inclined to use lenght that is twice the size of stop loss as point where risk goes below zero and the oposite of worst case scenario as a point where the profit margin potential starts to drop) I'm certain I would be able to solve the problem. I nkow how to solve it, now it's time to concentrate efforts on the formula itself.

I'm sorry.. so I should spend a few hundred hours compiling a book; and then give it to you aholes for free?

Was I born yesterday?

I make over half a million a year? do you? no. THEN SHUT UP.

I'd love to see your contributions to the Fx community.. oh wait, you don't!

I put out a LOT of free stuff..a LOT. and like I said before, why burns me would be people like you benefiting from it all.

I do just fine; I would like someone to verify the math, but oh wait, that would be unscientific of me.. to ask my peers to verify things independently.

bigvlada.. apologies... you know why nobody wants to share..? because there are so many productive aholes.. who've contributed so much because they are brilliant and they know it all.

I would just like to know how you all live with the cognitive dissonance of it all; I want to make money in fx but heaven forbid someone actually does, we will burn him.

Hope your fortunes are as big as your mouths are. Because I've posted my trades; let me see yours.. yeah.. not quite there huh?

takef586,

We must not be talking about the same thing here.. because why would my math converge to zero?

Example:

I start off with 15 lots. later on, I put in another 8 lots. my sl would be based off the equationed sum total (don't know if that's an actual sentence) of the 2. So as you add more lots, your total grows, and as your total grows, your SL is a formulated calculation of it.

you are saying (I hope I am understanding this) if I started out with say, 15 lots, then I go something like 15,8,4,1, and eventually 0 additions.. is that what you are saying? Let me give you an example of why what you are saying won't happen.

Let's say the formula is 0.5x, in lot size..

So let's say I go in for 16 lots. 16 x 0.5 = 8 lots next entry.
the next one would be based on a combination; so 16+8=24 * 0.5 =12 lots. would be my next entry.

12 + 24 = 36 * 0.5 = 18 lots would be my next entry..

the graph would look like a ratio back spread graph if you do any options at all.

I also question if any of you actually trade "big" lot sizes.. because if you did, then you would not be saying what most of you say..

If I started out trading say, 15 lots, then by the time I was correct 4~5 times, I would need a few million in the bank just to cover my open positions if i pyramided.. Also, most brokers won't let you break the 100 lot size. So unless you are all institutional traders, who trade like 50% of your account on margin, I can't believe all of what you are saying. I'm sure you all have like $4000 in the bank and actually trade 1 or 2 lots.. that's either stupidity or .. poor math skills. I would assume then that none of you are in it for the long haul, or don't bother pyramiding, or your uncle is Warren Buffet. Because I trade mini or micro lots, othewise, I cannot subdivide the lots and still cover my margin calls.. and I have a lot of money in the bank compared to the average trader.. so I don't know what you are all smoking..

10 lots at 600 raw pips is 60K. So again, you all ever have balls of titanium, have pockets so deep it's sick, or are full of it.. Because if you even did minimum hockey stick pyramiding, you would know that your lot sizes will get up to 30 or 40 really quickly.. and with a 100 pip plus or minus swing per day, that's 30k to 40K a day, which is probably what you all make a year in your jobs.

So like i said, you are either stupid, bad at math, institutional traders, or have never even broken past 1 or 2 lot sizes. because even with $5M in the bank, if I wanted to risk at most, 2% of my piggy bank, that's 100k, which if I got up to 40 lot sizes, would only be 250 pips, which i might get in a day or two.. so of course not.

you all need to check your math.. because you are all smoking something that california is trying to legalize.

And i have no clue about the "teaching newbies" comments, because if the math and concepts i'm presenting is what you all think are for newbies, then i screwed up somewhere.

I'm sorry to say that 600 pips a week would not allow you to own the market in a year. I have hit limits on what my broker will allow me as open cover. So at some point in time, you can't keep pyramiding unless you move to bigger brokers...

Everybody seems so happy and content with 50 pips a week.. and if you are, that's great.. But please, if your dreams are of being a slumdog and not so much being a millionaire; then that's fine; please don't smear on my dreams.

I have put up, and it seems nobody else has but they won't shut up. I am trying to have intelligent discussions but that seems difficult for the non-contributing leech hords.

takef586, not directed at you, your comments seem legit to me.

The math and strategies currently available, cannot possibly yield the results I was looking for; hence new math. But of course, that makes me "out of the norm" and that means i must be lying right? Most who say that, can't add, subtract, or divide... thinks calculus is something you get on your teeth if you don't brush them nightly, and find it ok to lose their fortunes again and again; and while doing so, thank goodness they didn't listen to a damn thing Twoblink said, i mean otherwise, they might have all lost their money.

I ask, what books from my body of knowledge you all would like; and i get ridiculed for writing a book. I said I'll start up a forum, and people said I'm trying to rip them off, and I should write a book instead. I say I'm making money, and they say prove it. I post my trading, and they say it's a lie. It never ends.

I read a survey done in silicon valley in which they asked, "who do you hate the most?" and 90%+ said bill gates. they asked "who would you like to be?" 90%+ said bill gates.

it's seems to be more of the same thing here.. "what do you want to do?" make a boat load of money in fx? "why do you all hate twoblink?" because he says he makes a boat load of money in fx.

I'll never understand the life of those who live with such cognitive dissonance. and yet, these people, what have they contributed in their whole life? NOT A DAMN THING. Those who don't have the skills, just bitch about it online.

Do they put out ebooks about FX? Nope. Do they contribute ANY useful information to the forums? Nope. Do they make people not want to share? yep.

I highly recommend most of you who obviously don't understand the math being discussed here; to shut up.. SHUT UP. put down the mouse, step away from the keyboard, and shut up.. the grownups are talking. And if you've got nothing positive to say, then go say it in the mirror.

Every decent attempt at a good thread is ruined by bottom feeding trolls. I'm sick and tired of it. those of you who wanted to know why I wanted to start a PAID forum.. now you know why.

OK, so I got the wrong impression, in practice you increase the position size, so that you still end up with some profit in case your stop is hit, and the amount of lots is unbound.( But your P&L graph will not be like a ratio backspread, because in that case you go below zero really fast as you move over your second strike - I have run an option desk for years.)

However, since the point of trading is to maximize profit/risk, then you might reflect if this indeed is the best solution, given that trees do not grow to the sky, and the faster you reach your maximum useful position size, the lower the probability that all the pyramid will be shut before you reach your target profit taking zone.

This is a simple law of probability, no matter how strong your trend can be. Therefore, in my opinion, it might actually be more advantageous to pyramid the classic way, i.e. adding equal amounts as soon as your profit equals your initial stop loss. This way, you are always runing the same initial risk, while your maximum profit expectancy will increase much faster.

In order to have a definitive answer to this however, you could either verify it against a monte carlo simulation aka coin toss to generate up or down series, (but the market is not necessarily a coin toss progression), or to actually run an optimization across the markets you trade to find out if your equation or the classic equation yields better results.

Finally, a word about your trading comments. I do not exactly understand what you define as "lots" - 100k units? If you are serious about trading forex, you cannot trade through a "broker".

One of the fundamental elements which impact your probability of making a profit on a strategy is the cost of trading, while the main element which enables you to multiply the money fast, is leverage. This means, that the smaller the risk per trade you can take other things being equal, the more money you can make in the same unit of time. ( This is why I disagree with your ideas expressed in another thread, that trading higher time frames is better).Therefore, the better your market access and the cost of trading, the bigger chance of making it big you stand.

When I said, I could own the market in a year, with a 600 pip profit per week, I meant, that with a simple money management, you could really make it big. I trade the G8 currencies in various combinations - no more than 25 crosses in all.

Let's simplify, the max amount I could trade on each cross would be 50 mio (total max amount 50x25= 1.250.000.000), the max stop loss per trade I would take would be 0.5%, and the beginning stake would be 10k USD. My maximum risk per trade would be 5% of the acount, to yield a 10x leverage. Assuming the 600 pips per week wold be done in 10 trades, and that you trade 50 weeks a year, that gives us 500 trades.

From a fast simulation I can see, that I would hit the max position size-1,25 billion after about 160 trades, and that my final account value would be around 2.6 billion, say USD, simplyfying the fact that we would trade various currencies which have different pip values.

Personally, I have traded on leverage higher than 20 many years of my life, so with such a killing (600 pips a wek) strategy, you might want to risk that, in which case you hit the position limit after 85 trades circa, and your final P&L would be around 3.25 billion.

When you trade with a bucket shop, it is like the Plato's cavern situation: you believe to be seeing the market, and your "broker" is feeding you with crap. From my experience with retail brokers, every time they were realizing I was not going to lose money, the trading environment was worsening very fast to the point where I closed my acount.

Guess what - this is what they wanted. They did not want me to trade multi million positions and generate lots of volume and "spread pips" for them, they wanted me to quit. Why? Simple, because they do not bother with hedging, they only make sure your real trading cost becomes so high, that eventually no matter how good your strategy is, you lose your stake. If they find a real winner, they make sure he quits. The world is full of suckers, and all the ads on CNBC and similar, are there on purpose, so that new ones get the lure every day.

With an account of at least half a million USD and a company set up, you could find a Prime Broker, and access the interbank market - not that it is free of various problems as well, but at least you will no longer be chasing the shadows.

With all due respect, perhaps it is you who does not understand uncertainty. And that, someone not understanding the math is not a mutually exclusive concept to you not understanding uncertainty. Just because a premise cannot be proven false, does not mean that that premise is true.

I never thought I'd see the day when I'd actually attempt to look at calculus again. All over my head at the moment as most of what I painfully leanred 14 years ago has been blocked out. Having said this I can now see it in a new light (thanks to Wikipedia) and how it could potentially be used to solve the problem outlined by this thread.

Twoblink, if your original predication quoted above is now wrong, what is the goal of playing fx?!

??

So which part of what I am saying is incorrect? And which part of my understanding of uncertainty are you certain that I'm wrong about?

Give me an example, because if there's something wrong about my understanding of it, I definitely want to correct that..

TO MAKE RIGHT DECISIONS.

I view it like poker; if you can see the cards the other guy has, would you make the same decisions?

There are times when your hand is dominated, and nothing you could have done would have won; but if you made all the right decisions, then the probability are in your favor and while you might not win this hand, you will eventually win because probability is on your side..

knuckle trading is the way to go

well not sure if this could help anyone solve the puzzle - maybe it might provide something useful. Scroll halfway down to the section on 'Functions With More Than One Variable'.

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

please delte if this link was already posted!.

We discussed multi variable functions a few months back.

Here's an interesting book on the subject:

Solved problems in Langrangian and Hamiltonian Mechanics by Claude Gignoux and Bernard Silvestre-Brac

It will probably take me twenty readings before I figure out what are they trying to tell me.

If there is a mathematical derivation to be done, then at a minimum the community would need to be able to replicate first, the assumptions, and what exactly is being optimized.

If you communicate this part clearly and precisely, then it's quite likely people will be able to attempt the remainder on their own if it requires just some thinking about mathematics.

So far, though I am familiar with say Lagrange multipliers, I do not have a sufficiently picture of what you are trying to do to be able to continue.

Naively, it seems to me that the optimal position size depends on the expected return from a trade. (if expectation is <= 0 then optimal position size is zero, of course). If there is a question of adding to the position, then I imagine that the optimum next position depends on the probabilities of various outcomes, and that may depend significantly on the particular details of the strategy and market behavior. So without further assumptions I can't envision a single general-purpose formula.

I have found that on message boards it is nearly always useless to argue. I personally find it more useful to engage in technically focused conversations with those who appear to be receptive and ignore anything else without emotion.

mbkennel,

I don't know, a few dozen posts ago, I actually posted a photoshopped pic of my original assumptions..


The problem with this sentence is that you then have a "limited profit" mentality, because otherwise, how would you know what the ROI would be on the trade?

Please read in my old journal about:

Limited Loss Limited Profit
Unlimited Loss Limited Profit
Limited Loss Unlimited Profit
Unlimited Loss Unlimited Profit

I deal pretty much with only Limited Loss and Unlimited Profit. So I deal with adding to a position (averaging up) and also moving the SL (limited loss).

If I wanted to deal purely in most optimized profit; then I'd just bet Kelly and either become richer than God, or go bankrupt.

I'm not sure which part of what I have done (not trying to do, I've done it) confuses you.

I would like to maximize profit; minimize loss, and have an equation that does so..

Reread this thread, and if you still have questions, let me know. But given an initial entry position, where would you add the next position assuming the market moves in your favor; how many lots would you buy, and where would you move the SL to? Those are the 3 questions.

I did it initially by brute force, then reverse engineered the equation.. actually, I was a cryptographer for a long time, and so I did it like cracking cryptography; with differential analysis.

@Trumpcard,

We aren't talking about local max, we are talking about a mini-max.
http://en.wikipedia.org/wiki/Minimax

We are looking at a saddle point:

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

Maximized profit while simultaneously minimized risk.

The Lagrangian approach amounts to searching for points where the constraint is satisfied and the constraint and the level curve of the objective function are tangent to one another.

With three variables, the Lagrangian conditions will say that the rate of substitution between any two variables along the objective function must equal the rate of substitution along the constraint and the optimum point must be on the constraint.

The value of the constraint function shouldn't be zero, but instead it should be a small positive value.

The total derivative of the value function with respect to the parameter
is the same as the partial derivative of the objective function evaluated
at the optimal point.

Phew!, I've managed to learn how to code mql a bit, and able to produce this. Its nice to see it mostly ends up positive on different pairs, although the result seem less random when trade time set around market open time for each currency involved. So in my case I found that:
1. Capturing trend momentum is important.
2. Volatility adjustment for different pairs is needed to have optimal result.

But to reproduce this :
I mean, is that really on random entry + random initial lot + random initial sl + the optimized formula for "when and how much to add"? Without your trendfan / volatility adjustment? If it is, then wow ...a really long way ahead of me.

Excel 2007 data analysis for dummies may help you in implementing Lagrange multipliers and constrained optimization into worksheet through excel solver. A good book.

the book:

Lagrange multiplier approach to variational problems and applications, by Kazufumi Ito and Karl Kunisch

excel add-in (shareware):

trilookup 2.2.1
http://trimill.com/TriLookup/TriLookup.htm