Optimized Risk vs Reward Equation

Trading system deals with: What situation to enter, and what situations to exit.

MM deals with, when you are going to enter, how many lots should you enter at?

Random entries with carefully planned exits and very good MM are known to make money.

Probability: With expectancy; you deal with win% and payrate. You increase your win%, usually at the cost of your payrate. Or you can increase your payrate, at the cost of win%. If you establish a system where your expectancy is > 1, then your system will be profitable long term, assuming you have the correct MM.

Whenever I have a new group of students, we start off by playing the "flip a quarter" game. Flip a quarter, and you guess heads or tails. If you guess right, you win 2x what you bet, if you guess wrong, you lose your bet. Having a positive expectancy, almost all my students STILL lose money, or make so little that if there was a commission or bid/ask on it, the rake would have taken all their profit.

So in simple postulate format:

1) The Best MM in the world doesn't help if your expectancy is < 1.

2) Even if your expectancy is > 1, if you have no MM that is profitable, you can still lose money.

This thread is focusing on the MM portion... specifically the Optimized Risk vs Reward Equation. (Says so in the thread title!! Imagine that!!)

@Monek,

I'm looking at your chart image. I didn't see a Ephemeral (Combo Entry point of Initial+2nd+3rd entry) or I'm just blind, which might be the case.

I am starting to see your thinking; and I'm gonna see if I can help change a few things so it might make more sense.

Like calculus, even though the price might be in continuous movement; at any point in time, you can name the price, and so at any point in time, a potential max loss (yes assuming your SL get's hit and not jumped, but nothing we can do about that.. so it's a horrible assumption but until you are your own FX dealer, not gonna bother talking about a jumped SL point.).. a potential max loss can be calculated at any point in time. So you can ALWAYS calculate your max risk, regardless. You are dealing with probability, and I am deal with what is known as "the two 100%'s". It works like this:

assuming I ALWAYS hit my SL, what's my max loss?

assuming I ALWAYS hit my 2nd entry point, what's my potential on the upside now?

Dealing with probabilities makes it near impossible, because now you are mixing "Trading system" with "MM".


Errr.. no.

If you entered with lot size 0.1, and assuming that is the smallest lot size you can trade with that broker, you are DONE. The math confirms it. Because in a pyramid, the 2nd entry HAS to mathematically be smaller in lot size than the first. Otherwise, you'd have an upside down pyramid.

Ironically, it's a pairing for optimization; given A, what's optimized B? But because we can simulate a ephemeral C, we can then start with a new A, and derive a new B. And on and on and on..

What is kind of cool is that the answer is self-affirming. It's like a fractal..

A month ago, I would have given you a different answer.. But I have stumbled upon the new "Averaged Second Chance" theory that is strange... When price action is in my favor, the optimal play is always to add, adage "Big when right, Small when wrong". BUT, with the newer math I'm working on, I'm kind of doing something that is like a hedge but not really.

In options, we call it a "Save", and so I'll be drawing more from that in a little bit. But I'm basically doing "Big when right, big when wrong, but with no additional risk involved." Monopoly analogy works the best, like a "Get out of Jail free" card, where you didn't pay money to get it, but in a jam, you can use it to get out of jail.

Stock example:

Let's say you bought 1000 shares of XYZ Corp @ $50/share for $50K. The stock tanks to $35/share and you are sweating 'cause your wife's probably gonna divorce you now. The "Save" in options goes like this:
Sell DEEP (as deep as you can go) in the money Calls. Because you are on the write side, you pick up premiums; If the price stays the same, you pick up Theta, if the price goes up, you still pick up theta, but your profits from the stock offsets your options loss. If the price keeps going down, you pick up theta and delta.

With the Second change averaging I'm doing, it's like I'm simulating a deep in the money call write; I don't technically gain additional risk; I do lose some upside potential, but curbing losses and increase probability of recovery is the goal here.

Hope that answers the question.

PA in my favor; aggressive average up.
PA against me, second chance averaging.

It isn't "kind of" a hedge; it actually *is* one. My own reading has pretty well convinced me that hedging gives the illusion of safety but doesn't really solve anything (with regard to FX type hedging).

The option hedge you illustrated is better than an FX hedge but isn't as good as it seems. When you sell a deep in the money option you use up margin very quickly and the premium you collect is relatively small. In your example the stock tanked from 50 to 35; by selling ITM calls you're locking in your loss and getting paid a paltry premium. If you kept selling the same ITM calls every time the previous option expired to collect premium, it'd take decades to make up the loss.

Good catch

It was irrelevant to the point of the picture. Yes. I understand that ever entry changes the ephemeral point. The picture tried to demonstrate how to measure risk/gain from the start point.

That formula could have just as easily took place at entry 3 although instead of an initial entry we'd use the ephemeral point.

Thanks

Agreed. I came to the same conclusion in my previous post. Thank you for your explanation; it does help.

Therefore I'm only going to use the 'value of risk' and 'value of gain' from my picture; and substitute probability of gain and risk to 1...

“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.“

In that case this theory has many hidden/'common sense' rules to it.

X and Y >= 0.01

Y < X

SL@C and any of it's fractal children are our obligatory (MM) exits.

SL@C is in such a place that net profit of pyramid > 0

ABS(SL@C-ENTRY@B)>0

ABS(ENTRY@A-ENTRY@B)>0

ABS(ENTRY@A-SL@C)>0

Term 'risk' = X*ABS(SL@C-ENTRY@B)+Y*ABS(SL@C-ENTRY@B)

Term 'gain' = X*(ABS(ENTRY@A-ENTRY@B)*2-ABS(SL@C-ENTRY@B))+Y*ABS(ENTRY@A-ENTRY@B)-ABS(SL@C-ENTRY@B)-ABS(SL@C-ENTRY@B)*Z
(the above formula is a work in progress and for the moment is completely and utterly wrong)

Where Z (the lotsize of the newest entry) is mathematically derived from X and Y in the same way that Y is derived from X.

In other words:
X/Y=(X+Y)/Z

Therefore the theory is looking for:

MIN(risk/gain)
or
MAX(gain/risk)

In either case the answer should be the same.

Now the biggest problem I had was trying to mathematically determine how to calculate 'gain'. As you can well see it is quite long and most importantly INCOMPLETE. 'risk' on the other hand was a bit easier.

The problem I ran into when accounting for 'gain' is two-fold:

1.) Am I to assume that the distances from every stoploss and its entry (excluding initial entry) is constant?
2.) Am I to assume the distance from A to B is equal to the distance from ephemeral(A+B) and the next new entry. And so on and so forth.

If any of those is not right then I'll need to change gain's calculation completely.

Needing help with 'gain'; thanks a bunch,
Monek

ah, you are using the gradient, don't you?

The arrows literally pointing at the saddle point.

Permutations of all possible value combinations were how I did it initially; (with graphs)

Again, why I know so well the sqlite,python,ramdisk combo.

You will find that when you do all that, it's all divergent.. It's SUCKS. I mean it. It sucks badly.

There is one key element that brought it all together though..

Take a look a lot of posts back, where I posted the initial theory in a drawing. If you put in increasing values for B and calculate the phi, you'll find it's divergent and divergent and divergent.. So this horrible things like this that made me work 2 years..

The other sneaky bit I wanted to help you all out on is the fact that some of your answers might not make sense because you are assuming some rules of the game, but those assumptions might be incorrect.

Example:

Let's say we start out with 5 lots as our A.

We know in pyramiding, that B will be < 5 lots.

Let's say B turns out to be 3.5 lots.

Now we are looking for a 3rd entry.. MOST think it's gonna be < 3.5 lots.. NOT TRUE. It could very well be that the 3rd entry is 5 lots! The reason is, most are basing the pyramid off of 5 -> 3.5 -> something smaller. But in reality, on your 3rd entry, you are basing it an ephemeral 8.5 lots (5+3.5) but with different entry prices. So please be careful with your math; when you propagate to the next entry, make sure you are using ephemeral numbers, not singular positional numbers.

This is why you can compound and grow bigger in size as you get right, WHILE pyramiding smaller. It seems like a paradox, but it's not.

Twoblink thank you very much for your last answers. They were a reason for a breakthrough in my head that generated an approximate to the process you describe here.

I must admit I (still) do not have the formula through which I would get the optimized risk vs. reward but I generated a mathematical concept that bases on "pascal triangle's figures" and brings very encouraging results, no matter what scenario I run through it. If I combine several scenarios together, as how usually trading goes, the outcome is always bright supposing to use a strategy that brought even results so far without this concept of managing trades.

Despite being very enlightened with a concept, I will still go on trying to optimize it and come very close to what you've come in last years of your work. Very much appreciated once again!

OK, given any two 3D points in 3D space I can now procure formulas for all three 2D exponential functions.

I'm struggling to implement this in excel.

A few new questions have emerged:

1. If one of 2d functions is risk and second is profit, what is the name of the third one, what does it represent?
2. Which one is risk and which one is profit?
3. Do I have to find an intersection of all three 2d functions in order to obtain saddle point or two will suffice (profit and risk)?

After I resolve this, only the implementation of rinse and repeat process remains.

Or should I invest some more time in order to figure out how to get formula for 3D exponential function?

I have figured how to calculate the formula for the function of the area G(Г). And the hint was in one of my old math books.

http://img211.imageshack.us/img211/3269/surface.jpg

The funny thing is, I've never predicted that there isn't a single formula. All 2D functions and surface formulas will vary, they are all dependent of the initial terms.

Next task is to figure how to extract saddle point from that surface.

TwoBlink, (or anybody)

Can you explain in simple language, to a man who's never attended university, exactly what you mean by an "optimized risk vs reward equation"?

If we were to generate an imaginary price chart by repeatedly tossing a fair coin (heads=uptick, tails=downtick), would it possible to optimize risk/reward in terms of trading this randomly generated chart, and if so, how? If not, then (moving to a 'real' chart) wouldn't any MM-related optimization have to somehow be a function of (the non-random aspects in) price behavior?

I can see why it's preferable to be bigger when right, smaller when wrong. But, to justify risking a bigger amount on one event ("A") over another ("B"), doesn't one need to know in advance (at the time of entering the trade) that the probability (actually, overall expectancy) of a favorable outcome with trade "A" is greater than with that for trade "B"? Otherwise, what is the mathematical justification for varying one's bet (position) size?

The way I see it, and if I may speak in generalized terms, averaging up is taking a 'let profits run' strategy one step further. Both tend to work better the more strongly prices 'trend'. Doesn't this depend on the assumption that there's a bias in price behavior that causes it to trend far enough, often enough, to make such a strategy viable?

Thanks in anticipation for your answers,
David

hanover,

I will explain in terms of real estate; because it will make more sense that way.

Say there's a house for sale worth $100K; and let's say you have 2 choices:

1) Get a Call Option on it. You plop down $200, and get the right to buy the house at $100K. You've got 90 days before the option expires.

2) You plop down $100K and buy the house outright.

Now let's take scenario #1 really quick. You get an option on it, you don't own the house, but you control it for $200. In 90 days, if you haven't found a buyer, you've lost $200. Let's say someone comes along and says, I'll buy the option off of you (called an assignment of option)... He offers you $3000 for the option. You assign the option to him, happy as a clam.

Scenerio #2, you buy the house, and you think you can sell it for $120K minus closing costs.

Which is the better choice? Well, #2 makes more money.. but wait.. You put $100K of your money at risk to make a potential $20K.. so a 5:1 risk to reward profile.

But in scenario #1, you put $200 to make a potential $3000, 1:15 risk to reward profile.

Now I gave 2 scenarios, but of course there is an infinite amount of possibilities between those to. What is the maximized point in which profit is as good as it gets with respect to the risk being as low as it gets?


As far as averaging up.. look up my old journal.. I cover averaging up extensively. It's not just a ++ version of letting profits run; it's a necessity to leverage previously correct decisions.



Let's say I have something popular, we'll call it an xpod.. and let's say the xpod is selling like hotcakes.. Do I raise the price, or lower it??? If you say lower it.. I would fire you. Because why on God's green earth would you kill the cow that's bring home the bacon? If anything, I'd RAISE the price, because you'll find that even if demand tapered off, the price increase more than likely will compensate for the decrease in demand. But had you lowered the price, I doubt the increase in demand due to the decrease in price, will offset the price.

It's the very basics of marketing, and one that most haven't learned, especially the marketers. Price, and psychology both work this way. If you cut the price in HALF, you'd have to DOUBLE your sales just to breakeven! But if you increased the price by 10%, you can take a 9% hit on the volume and still make more. Fewer customers yet the same or more profit.

Remember what I always say, the logic might seem ok at first blush, but if the math doesn't jive, then the logic is faulty at best.

Many thanks for the detailed explanation.

I was just looking at my old notes at the point of discovery; as some of you know (or not) my wife and I are expecting a baby girl the end of this month; and so I am not sure how much time I'm going to have to devote to FX.

But more importantly, my thinking has somewhat changed; as I think that there is so much material I would like to write down and leave for my daughter; and so will begin my journaling of everything I have investigated; and thought about and discovered.

I am however, uneasy to do so at FF; people seem to expect everything for free.. and so I'm thinking of a creating a paid forum, to take the discussions a bit more "private".

Would there be any interest at all for this?

I am in... as long it is within my means. Cheers!

First, congratulations for your daughter. If you manage to be as thorough as you are in your trading research, I’m sure you’ll be a great dad.

As for the forum, do you really think you’ll have time to visit it and converse with the forum members regularly?

My brother became a father last year; we celebrated his daughter’s first birthday a few days ago. In those 365 days, he never had the time to read a magazine or visit the movies. Raising the kid is a full time job on it’s own, and one with low margins of error.

The discussions on this thread helped me tremendously, and the biggest concept I’ve gained is that I have to increase/decrease all three variables simultaneously, something that I haven’t done previously (changed only one per time). Although I still haven’t found the optimized way to change them, I’m using the same principle in my trading (a bit more on the safe side).

This reminds me of an earlier situation; I’ve tasted squids a la setoaz; loved them , searched for recipe for years; found it and then it took me more than a several attempts to correctly replicate the sauce; but I knew what the right taste was, I knew what I was looking for.

Same with this, I”ll know when I find the correct hmm, balance and in mean time I’ll have to eat a dish which is a bit more spicey or salty than it has to be.

I personally do not want to participate in new forum; for me it would be like someone told me that the butler did it and I’m still in the middle of the book.

You should consider one more thing: What math skills do you future forum members possess? Most people struggle with anything more complex than four basic operations. If you ask twenty people on the street what is the formula for the area of the circle, the safe bet is that not a single one will know the answer.
I was shocked some fifteen years ago when I’ve watched candid camera with Dom de Luise. The sketch was about a 4-5 year old girl who asked the people at the mall to help her do her homework. The problem I believe was 21/3 (yes, a simple fraction) and out of 22-23 people no one knew the answer. In the end, the host said that the people from the backstage told him the answer was 7.

Can you explain the money management without math? If not will you give math courses as well? Will you have to repeat the math course for new participants or just post a f.a.q.? How much time would that take?

May I suggest an alternative?
You thought about writing a book. Why don’t you? It’s something that you can write at your free time (and you won’t have a lot of it) without a deadline.
Write it as a diary. Reading about what is wrong and why is equally important as the right answer (if you still remember what you did wrong). State in the impresum that the book is meant for people who understand the integration and differentiation (although hawking was able to write brief history of time with almost no formulas – a brilliant task in it’s own right). In this way, the reader has the choice: read the inner workings that led to the answer or just skip to the end and use result (it is not necessary to know how combustion engine works in order to drive a car). The reader can have as much or as little information as it likes.(and the universal answer to all questions is – read the book again) The best thing is that you don’t have to publish it at all. Call it your legacy.
If you decide to publish it, I suggest the hardcopy (it’s more time consuming to scan a book then to torrent a pdf) plus the CD with software you used to test the theory. It would be a normal way to test the theory over and over again until it’s validated and accepted. The funny thing is that if all the traders use it and use it efficiently in the future it would still be useful .

I currently own 2 companies, will be opening up a 3rd, 4th, and 5th. I work from home, and my 2 companies take me a little less than 4 hours a month to operate; and they have highly profitable, with no debt, and their piggy banks are quite full. I currently have 12 active projects; of which all of them are outsourced, and so all I do is send an email regarding them, and it gets done. I pay very little to buy other people's time, so I can concentrate on the important things in life that I cannot substitute... such as FX research. I would be more than happy to outsource this; but there's nobody (at least that I've found) that is even remotely close to doing the research that I'm doing..

I generally believe that I am more than capable of handling whatever life throws at me, most babies do 3 things: eat, sleep, and poop. Eating will be handled by her mother at least the first 6 months, sleeping will be handled by the crib, and pooping.. well.. I guess I will be handling that. But aside from that, I work from home, so time is not a problem.

I actually don't mind explaining the math behind it all; because as I've said many times before; the dirty little secret is that teaching is helps me more than it helps you. It clarifies my mind, and forces me to present things in a logical manner.

The forum will be fairly exclusive... It will be filled with people who are either up to speed, or willing to put in the time to catch up to speed. I don't mind either group.

There are a lot of things that I would like to share; and more and more so; I see that content control is a big problem, and so the only way to not have it be a problem is to go ahead and restrict the content's presentation to a forum you control.

If a question comes up, I think I've proven as far as my track record that I answer all the questions; if they are intelligent and the questioner genuinely wants to know the answer.

The forum will not be a "The Butler did It" thing; it will be a place to discuss at length, methods to the madness.. and to have things independently verified.

The problem with writing a book is that I don't get feedback while writing it; if I get feedback afterwards, it's too late to change the book..

I have done this research two years ago, I have an optimal positive expectancy pyramiding system. I am quite sure somebody has been spying on my codes again.

Of course, I ain't accusing anybody though.
Smart people can think alike and do things alike.

Is the membership fee to be used for building a wall, or, perhaps, for some type of security system?