Optimized Risk vs Reward Equation

I guess that is how most people (traders) will look at it. What reason should anyone have to pay more?
Of course i can only speak for myself but i don't think i am that much different from the average person (trader) and if i was going to pay more than most other books i would need some prove that this is something very different from other books. The question is how to prove that? It is probably possible to prove it but will it be done?
And even if prove is given how do i know this is useful for me and my trading? That is also something that have to be proven in some way if i would pay far more than most other books. Is that even possible to prove? Maybe it is, i don't know...

So in the end the question as i see it is this: Would traders be willing to pay far more than other interesting books just because the author say this is something new and revolutionary that have not been published before and it will guaranteed be of great use in your trading?
This are claims most of us see regularly from marketers and snakeoil sellers so again how can people know this is different? Only way to know is to be given prove right?
Of course those that have been following Twoblink for years and feel that they know him and trust him do not need prove but how many is that? Is it enough to people to make it worth selling the book only to them? I don't know.

My conclusion is if i was in Twoblink's shoes i would probably keep it to myself or make some sort of prove that it is worth to pay big money for it.

Arctic4x

As I have replied to a few people who have asked the question;

When I first started FX, I just got married; I now have 2 beautiful daughters; I'm not getting any younger, and my time is now at a premium.

I am not Andrew Wiles, and would actually like and WANT help, especially from people who are better at math than I am. It would certainly progress everything I do quite a bit; but at the same time, I am unsure that sharing would help others as much they think it would.

Optimization of a position does not guarantee optimization of expectancy; but it does optimize your profit vs risk.

One of two conclusions I can currently draw:

1) Nobody else has discovered what I discovered (arrogance aside)

OR

2) They have discovered it, and are going to take it with them to their grave.


I think #2 is the more likely one. In between the starting of this thread and this current post; I have also added to the stable, math proofs on averaging down vs averaging up.

So if there are those out there "in the know" and aren't sharing, perhaps I am missing the reason they aren't sharing... Based on the Euler/Newton Calculus Emergence paradox; someone out there knows all this stuff already; and is probably running the Chicago chapter of the Illuminati's or something...

Having been away; and reading a bunch of threads; it makes me kind of sad; there seems to be no real breakthrough progress (or at least none that's shared); the ideas seem stale, and nobody seems to bother with the math side of things afaict.

As far as paying for it like paying for an interesting book; that is an interesting comment; as, if the tables were turned around, I would pay for it like a optimized method of maximizing my return on investment... which it would be.

I guess it's decided then; I will now crawl back under my rock, and be the Asian Andrew Wiles once again.

You are the only one knowing if it is "a optimized method of maximizing my return on investment"
The rest of us just have to take your words for it. Like i wrote in my last post, that may be good enough for people that know you well enough to trust you but for most of us it is just like trusting a marketer selling any other product.
I can only speak for myself but i don't trust marketers and experience have shown me that the absolute worst (not to be trusted) marketers are those selling trading products in general, and the worst of the worst are those selling forex products.
Personally i learn some every time i get burned. Some people never learn, but i do..

Arctic4x

Actually, it's not a trading method; it's just math that proves optimization; doesn't help your trade any if your expectancy < 1.

And I agree with you about marketers and snakeoil salesman.

When I started working with FX; I had (and you can even look it up in my old posts) always conjectured that there was an equation that did just that; optimize profit and minimized risk; I guess nobody else did or thought it as important to find a proof for it as I did. As far as brainy people; I've known dozens of people who are scary smart. That said, I'm not sure any of them have the passion or focus or desire to find the answer to this; as I did. So just because many brainier people came before doesn't guarantee that they too have discovered it. Having said all that; my bet is still that someone has; and they ain't telling....

Hi Twoblink,

We are not discussing the maximization of returns because there need to be returns before you can maximize them. The other way around: it's nice to minimize mistakes, but you have to make a mistake first before you can realize how to mend it.

Therefore, why pay for an idea at a leveraged amount, if we need to come up with the crucial basis ourselves ? It's like the brokers letting us play with margins while providing us with their delayed price info and "fantastic" technical platform besides charging us spreads, slippages, commissions and swaps - in the end we still have to come up with real money first and make all the relevant decisions ourselves complicated by all the above.

Again, I'd be highly interested in your optimization techniques, because I'm a firm believer in non-predictive trading of supply and demand driven data series - i.e. being right in average or managing to find a way, that allows us to be continuously and profitably on the right side of the trade (not the price), have a directional bias while remaining largely impervious to non-directional price movement (consolidation as well as S/R), manage reward vs. drawdown, protect against as well as profit from wild excursions and grow with account size. It is obviously an always-in method, I'm talking about, and it has been so far very interesting given the extremely erratic price movement since the beginning of this year, but I just guess it could be even more interesting, if I'd understand and apply your discoveries.

Let me know, if you would like to discuss further privately, because I won't on this platform.

Cheers, Claus

Hello twoblink,

Well done Sounds like brilliant work.

It seems like you have found a solution to a minimax stochastic program.

For a general minmax stochastic program one would need to specify the underlying process as well as the objective function that one wants to optimise the expected value of.

Using some form of risk:reward as objective function, using some proportionality assumptions in the definition of the program, and using a process defined by historical data, one would arrive at a solution in terms of the exponential function.

Without such assumptions a mathematical proof in the general case would be impossible.

To take your work further, the way to go, it seems to me, would be to open up the more general study of applying minimax stochastic programs to trading. Could be quite interesting.

EDIT: After finishing my post, I did a search and found this: http://www.stanford.edu/group/SOL/di...lombthesis.pdf. And it seems like there hasn't been much research done along these lines. Consider yourself one of the pioneers!

For those interested, this paper contains a solution method and some good references on other methods: http://www2.isye.gatech.edu/people/f.../MinimaxSP.pdf

i think he is is referring to the two tiered position sizing...saw something like that in van tharps book and it increased profitability exponentially with the same risk.....jeff yass the mathematician of the market wizard fame also said something to this effect....that you should be willing to risk your profits for more profit than lock in...that said it should be done logically.

Exactly, and optimised such. Which in twoblink's formulation amounts to a minimax stochastic program.

Truth be told, the entire thing yielded I think the greatest non-spoken-about item as far as I'm concerned; and that is the "Ephemeral Position". I think of all my work; this is probably the most progressive; the concept that A position + B position yields Ephemeral C; and if you substitute Ephemeral C back into the equation; then you can now do EC + B' = Ephemeral D. etc...

I got this from phi actually; and also from e. It "folds" into itself; and so it's possible to verify itself with itself. There is a generalized equation for calculating nth digit of the Fibonacci; and while I haven't rolled my equation backwards to formulate a calculation for the nth degree of Ephemeral-ism, I now believe that there is as well.

Like 'e', my Ephemeral work means that given any position, I can take the equivalent of a derivative or an integral, and still be "on the line". A formula that folds into itself and then unfolds onto itself is really just plain badass. More so than the equation; it might be the more proud portion of this work.

Jeff talks about two tiered; but with the Ephemeral work; I can now do nth-tier without problem; and that is rolling it forwards AND backwards. And that makes me smile.. because I'm a nerd.

After reading through the thread last night a few times, this is what i came up with. I have nowhere near the level of math skills required to tackle this problem, but this is what I conjured up based on what I understood.

I drew up an example chart to demonstrate. In this example, I'm trading USDJPY, and I enter at a potential corrective swing fizzling out and momentum now drawing price down to a new expected structure low. So, I enter a SELL position A at 131.071. I risk 1.0 lots, and my stop loss needs to be above structure at 141 points (14.1 pips). Those are my "known" variables. So, using what I understand to be your method, I would proceed to calculate B, and eC (ephemeral C), and subsequent D, like so...


Entry A = 113.071, SL(A) = 141, Lot size = 1.0

AB Phi distance = SL(A)*phi = 87.14

Entry B = Entry A +- AB Phi distance = 112.984
long Phi distance (A) = 87.14*phi = 53.855
short Phi distance (B) = 33.285
Entry B SL = 33.285 = 113.017
Entry B lot size = Lot size of A * phi = .618

ephemeral C = Entry A + short Phi Distance (B) = 33.285 = 113.038
eC SL = SL(A) + SL(B) = 141 + 33.285 = 174.285
eC lot size = Lot(A) + Lot(B) = 1.618

eCD Phi distance = SL(eC)*phi = 107.713

Entry D = Entry eC +- eCD Phi distance = 112.931
long Phi distance (eC) = 107.713*phi= 66.569
short Phi distance (D) = 44.144
Entry D SL = 44.144
Entry D lot size = Lot size of eC * phi = .9999

As you can see, Entry B is smaller than entry A, and Entry D is larger than B, because Entry D is a phi of Entry C, which is calculated as A+B. Subsequent Entries would grow and grow and grow.

Example chart shows Entry A and SL for Entry A at the Aqua colored lines. Entry B and SL for entry B at the BLUE lines, ephemeral C at the Chartreuse(green) line. I didn't place the SL for Entry C as it is ephemeral and doesn't really exist, although you can see the calculation for it above which is used to calculate the SL for Entry D later. Entry D and SL for Entry D is at the DeepPink lines.

Assumption: Each point move in price for a 1.0 lot is $1.00 exactly. We aren't accounting for Spread or Slippage here.


Scenario 1: We hit stop loss at Entry A without making any further entries. We would lose $141 because 141 points SL (14.1 pips) = $1.00 per point move. This is our RISK. We assume this risk whenever we enter the market. This is what we want to minimize, and will quickly go to 0.

Scenario 2: We place Entry A and Entry B, and then Entry B's SL gets hit. Well, iff at Entry point B, we move our SL for Entry point A to Entry Point B's SL, thus locking in profit for Entry A of 54 points. At 1.0 lots ($1.00 per point == $54 profit). The loss on Entry B would be 33 points at 0.618 lots, which is $0.62 per point, which is $20.46 loss. Total PROFIT would be $54-$20.46 = $33.54 profit.

Scenario 3: We place Entry A, Entry B AND Entry D, but then Entry D's SL gets hit. Well, iff at Entry point B, we move our SL for Entry point A to Entry point B's SL, AND IFF at Entry D, we move BOTH Entry point A and Entry point B's SL to Entry point D's SL, we have still locked in profit. Entry Point A profit is 97 points (1.0 lot is $1.00 per point, so $97), Entry Point B profit is 11 points (.682 lot is $0.62 per point so $6.82). We then have a loss at entry D of 42 points (.9999 lot is $.99 per point, so $42). Total PROFIT would be $97+$6.82-$42 = $61.82

While this method seems scalable infinitely, it seems like it would only be good for riding longer trends. If you're looking for anything less than a 3:1, I wouldn't suggest this, because you'll be leaving too much "on the table", or in other words, you would be giving back too much of your profits.

This all presupposes that I got the calculations correct, which I may or may not have. But I do like the fact that each entry after Entry A would have no risk added with this method. There's absolutely no risk after you break even on Entry A. The only thing you're doing is giving back some of your profits if your expectations fail to reach another level.

Thinking more through this. It appears that the nth entries are growing too large too quickly with purely using Phi. Such that, on Entry E, if the price moves to hit stop loss, there is such a large loss due to that, that we don't even see a 1:1 ratio on the original Entry A point. It's close, but it fails to reach it since profits are swallowed up by the Entry E. So, to circumvent that, but still allow for growth over the nth Entries, I decided to use Phi^2 (phi^2 == Fibonacci .382) to calculate every entry after B.

This looks nearly identical, except On breakdown (SL) of E (A+B+D+E, 4th entry) you would achieve slightly more than a 1:1 risk:reward from original Entry A. Remember, Entry A had 141 point SL, which is $141. With the use of Phi^2, Entry A would have $158 in profit, AND get to keep it all, instead of using it up to pay off the negative Entry E SL. This helps us 1) Preserve capital at all costs, and 2) Leave less on the table when price decides to swing against you.

Here are the updated calculations:

USD JPY

Entry A = 113.071, SL(A) = 141, Lot size = 1.0

AB Phi distance = SL(A)*phi = 87.14

Entry B = Entry A +- AB Phi distance = 112.984
long Phi distance (A) = 87.14*phi = 53.855
short Phi distance (B) = 33.285
Entry B SL = 33.285 = 113.017
Entry B lot size = Lot size of A * phi = .618

ephemeral C = Entry A + short Phi Distance (B) = 33.285 = 113.038
eC SL = SL(A) + SL(B) = 141 + 33.285 = 174.285
eC lot size = Lot(A) + Lot(B) = 1.618

eCD Phi distance = SL(eC)*0.61803 = 107.713

Entry D = Entry eC +- eCD Phi distance = 112.931
long Phi distance (eC) = 107.713*.61803 = 66.569
short Phi distance (D) = 44.144
Entry D SL = 44.144
Entry D lot size = Lot size of eC * (phi^2) = ..618


ephemeral C1 = Entry eC + short Phi Distance (D) = 44.144 = 112.994
eC1 SL = SL(C) + SL(D) = 174.285 + 44.144 = 218.429
eC1 lot size = Lot(C) + Lot(D) = 2.236

eC1E Phi distance = SL(eC1)*phi = 134.99

Entry E = Entry eC1 +- eC1E Phi distance = 112.859
long Phi distance (eC1) = 134.99*phi = 83.427
short Phi distance (E) = 51.563
Entry E SL = 51.563
Entry E lot size = Lot size of eC1 * phi^2 = 0.854

And here are the actual dollar numbers, given the same assumptions:

Using Phi for every Entry. ( 1 Lot == $1.00 per point, .618 lot == $0.62 per point, etc.)
$33.54 (A profit, B stop losses)
$61.82 (A+B profit, D stop losses)
$137.70 (A+B+D profit, E stop losses)

Using Phi^2 for every Entry AFTER Entry B
$33.54 (A profit, B stop losses)
$77.78 (A+B profit, D stop losses)
$170.84 (A+B+D profit, E stop losses)

Attached is a chart with the updated Entry E included. That Entry and SL for that entry are the Khaki/light brown colored lines. Note also the additional eC1 line, again, a Chartreuse(green) line.

I placed a trade today using this formula. I was disappointed to see my stop loss get hit early on and leave me with a small profit. I have found that this is indeed the best method for adding to price. But, IFF price moves in a straight line for a long time. Which it doesn't. If you're looking to trade a long trend (weekly / monthly charts), and you have a large initial stop loss, then this will work amazing for you. IF you're an intraday trader, and you have small and tight initial stop losses, then this isn't the formula you would want to use. Because you have to give price room to breathe. So, I have devised another formula, initially based off of this one, that will keep your trailing stop loss large enough, for the most part, to be safe from a small corrective swing on the intraday.

I no longer use ephemeral C at all, but I do agree with twoblink, it's the most badass progressive thing I've seen really. #mindBlown.

An entry is only as good as your system. And I have found that the best entry is the entry I make initially. Meaning, I'm getting in at the ideal spot for my first trade. Adding on to trades after is risky, because once price is moving in my direction, shortly after it begins to make some corrective adjustments because 'indicator traders' are catching up and their laggy indicators (no offense, use what you want) are telling them to get in (or out) of the trade. And growing the trade each time, even when using a small growth such as fib 38.6% of the last C+X entry, ends up leaving a larger portion on the table than I want to leave when price ultimately comes back to tap your stop loss. Again, I really think it works better on weekly/monthly charts.

With that said. I have reduced by 1/2 my initial Entry A, and Entry B is now Phi lot size of Entry A. Every nth trade afterword is identical to Entry B in stop loss distance and in distance from the previous entry placed, but in lot size they are all Phi of B. Which makes them Phi*Phi of A, or Fibonacci 38.6% of A. :-) It's a beautiful thing to look at. And an even more beautiful thing to trade with. I made an indicator today which plots the levels for me automagically. :-) All I have to do is enter Entry A price and Stop loss, along with a maxSpread (which keeps me at breakeven for moving my stop loss on subsequent trades), and the number of nth trades to plot. If you don't use a maxSpread to adjust the SL for breakeven, the SL is actually the entry point of the previous trade, which is always 38.6%! Hah!

Anyways, the indicator prints horizontal lines indicating where to place Entries and Stop Losses. Each Entry+SL combination is a different color. Entry A is Cyan. Entry B is blue. Every entry afterword is alternating deep pink and orange. Once price hits a new Entry point, you move your stop loss for all trades to that Entry points SL mark. Easy Peasy. IF you miss an Entry, just continue on and place an Entry at the next level if/when it reaches the next new Entry point. You can/should continue to move your Stop loss to the entry that you missed if you want. In a test trade today, my old money management strategy would have netted a 2.41 : 1 Risk to reward. This new strategy yielded an 8.11 : 1... Without increasing risk. Here's a picture. I can go into details, but I don't want to hijack twoblink's thread, even though it's been dead for 4 years now. ;-)

Still tweaking my indicator. But it worked nicely today. Price moved so fast in a trade I was in that I missed a 3rd entry, but I still moved my SL to the new level to lock in profit. It's nice to see those zones, and if they don't line up well with structure, you always follow structure. So if it looks like an area where you shouldn't make a trade, don't. ;-)

Talk about old threads!

Tim; I had conjectured that it's possible to treat the FX market like an options; having a dY/Dx against time (theta), against volatility (vega), and against price differential (delta) and the differential of the differential (sigma). My partner has been able to largely prove me right! So that's what we've been working on; all these years.

The problem we are now tackling is multi-variant balancing. Question; is it possible to create an ephemeral position out of a sum total of 18 pairs?

New breakthroughs today!

1) Ephemeral Expectancy! !!! With this; and in decimal format; we eliminate underlining currency homogeneity problems as well as lookback problems.

2) Triple Integral Super Ephemeral multi-pair multi-variant positions.

I figure I have to write this just in case a few years later; someone claims they came up with all this first!

Exactly my thought but I am willing to tell and share but I got attacked and being despicably dismissed that killed my enthusiasm which tired me out. Still trying and maybe my energy level will be fully depleted by then and it will be my final lights out. The irony here is it's easier to fool traders with heavy financial semantics and nuances than to get them to know something simple and very easy to assess and disprove.
Can't get my head around this illogical rationale.

Hehe
GS