Optimized Risk vs Reward Equation

Just some general stuff. Did you take random entries? Did you include transaction costs (I guess not, since it isn't necessarily relevant for finding the fundamental differences between martingale and anti-martingale)? How did you determine after how many pips you entered a subsequent position? And most importantly, what were the money management rules?

Thanks

Twoblink,

At the risk of making a fool of myself, I'd like to share some observations:
I noticed depending on the lot factor applied from one lot position (xA) to the next one (ephemeral C=Breakeven S/L), the proportion of yB-C (b) to yB-xA (a+b) always stays within 0.5 to 0.33.

Without going any further, may I ask if I'm actually on the right path here?

Appreciate your great contributions.

Claus

P.S. On a sidenote regarding the trendfans: how do you determine the ideal lookback period (zoomed-ness) per timeframe and currency pair?

Great thread, thanks Twoblink.



So just a question.....

Are you saying that you have the ability to turn a negative expectancy trade/system into a positive one?

If so, is that purely through MM/trade managment?

Or have i completely misunderstood the statement above.


Cheers

Did not take Random Entries.. Why take Random ones when you can take slightly more mathematically advantageous ones?

No, I didn't take transaction costs into account; but I can tell you that bid/ask is usually what kills most expectancies and makes it < 1. That is why, "landwarring" is very very difficult to profit from.. And no, transaction costs have no bearing on proofing of martingale vs anti-martingale math.

I have a mathematically optimized math system for entry that yields the maximum profit for minimized risk (mini-max i.e. saddlepoint in calculus) That said; I don't use it. Because it proves difficult to apply in real world trading. I am usually mostly "propensity based additional entries"... Let me rephrase that; I am using "propensity entries" as I force every entry to defend itself; so I cannot technically call them additional entries as that has difficult implications.

Without getting into too much Star Trek speak; one of the cornerstones of my MM is that every position has to defend itself. That means while the positions my pyramid; every position itself has to defend its own position.. I know, the English language was not designed to describe calculus...

The newer MM I'm using is based on my new > 1 expectancy barrier proof.. So it's a punctuated space/interval system.. It is really really difficult to use English only to describe what's going on.. Again, I feel it almost Star Trek speak.. But the math is pretty good.

I am not sure as I'd have to double check the math; but just off the top of my head; my guess is going to be that "b" can't "runaway" from a too far; because you are (should be) limited by the fact that a > b or else you've violated ratio's of math and your combination will eventually become divergent.

Regarding Trendfans; because timeframe itself is recursed upon itself in FX; then you have what we consider to be "outlook, period, bars".

So for me for example; I trade on the 1H bars, group mine in 1 week periods (I actually have indicators that stripe the weeks different colors) and I have an outlook against 3 months (1 quarter basically). So that would be my zoomed-ness.

1H bars grouped in 1week colored displays and 3 months as my zoomed-ness.

Hope that helps.. YMMV..

NO.

I am saying that I've now done the math (and really need to revise my book) basically showing that averaging up will almost reach expectancy of 1.00, but it won't... (and that's not including bid/ask). So that means I know that long term, I will not make money. So I have substituted that, with my newer system that is mathematically capable of breaking 1.00. I cannot "turn" a system that's got < 1.00 into one that's > 1.00. I can only throw it out and use something else.

I am not sure why everybody thinks MM is like Victoria's Secret Models and Voodoo all wrapped into one.

MM CANNOT alter your Expectancy! It only exploits it.. If you are playing roulette, all the MM in the world won't change the fact that you have a 0.9474 Expectancy, and that you will lose your shirt the more you play.

The goal isn't trying to get MM to move your system so it's > 1.00, that's IMPOSSIBLE and anybody who tells you otherwise is selling you snakeoil or bad at math.

Expectancy =

((%Winners * Payrate when you win) - (%Losers * Payrate when you lose)) THAT'S IT.

MM is not part of the expectancy equation.

Let me give you the modified equation that you will be working off of:


(nUnits * ((%Winners * Payrate when you win) - (%Losers * Payrate when you lose)))^Frequency.

That's your MM and system and Expectancy combined. MM is the control of the nUnits of betting.. and eventually raised to the frequency. That is why if you are playing roulette; the best strategy, is to take all your money, bet it on black or red, and then walk away regardless of outcome. The more you play with a negative expectancy, the more you will lose. The more you bet with a system that has a negative expectancy, the more you will lose. The more OFTEN you play with bigger bets, you will lose exponentially faster.


With any system, you are looking at 2 parts; the %Win and the Payrate.

100 - %Winners = %Losers

So you have an inverse relationship with the Win% vs Loss%. Payrate when you win vs Payrate when you lose are independent variables.

http://www.seykota.com/tribe/risk/fi...4_image001.gif

This is the generic Risk/Reward bet graph from

http://www.seykota.com/tribe/risk/index.htm

Every single MM graph looks like this.. the difference is:

When you increase your Win%, the entire graph moves to the left. When you increase your Lose%, the entire graph moves to the right.

When you increase your payrate, the entire graph moves up. When you decrease your payrate, the entire graph moves down. Actually, that's not an accurate way to describe it, when you increase your payrate, the graph "squishes" tighter together. When you decrease it, it "flattens out more".

When you average down, you have high Win%, but the payout is low when you win; and the occasional loss will kill your profit.

The reverse is true for average up, you have low win% rates, but when you do win, you get a big payday.

"Trade Management" is a fairly loaded term, so I don't know how to respond to that. Trade management as in what? Entries? Exits? Position Sizing? ReEntries??

Hope I've answered most of the questions.

I knew that MM will not turn a negative expectancy system into a positive one. I was confused in your statement which i copied in my previous response. I see i have taken a very general view from what you have typed and just wanted some clarification.

Appreciate the detailed response.

Thanks

hmm, this also looks interesting but I won't distract myself with it until I've fully solved the MM portion of the problem.

After first reading this reminds me of the sunrise problem or the doomsday argument.

Well, what do you know, there actually exists a paper on this subject:

Nonlinear Optimization with Fuzzy Constraints by Multi-Objective Evolutionary Algorithms by F. Jiménez, G. Sánchez, J. M. Cadenas, A. F. Gómez-Skarmeta and J. L. Verdegay

After a dozen readings or so, I hope I'll understand what are they trying to tell me.

Or you can just hack a rice cooker ;-)

Guys, do you have indicator ''first derivative'' of price (chart) maybe?

Thanks

long gone are the times when I tried to hack something - spectrum+ 48k with interface 2, microdrive and romantic robot gadget, those were the happy times.

I'll think I'll go one step further than that, people who designed the software for rice cookers must have read something like this: Level-cut Approaches of First and Second Kind for Unique Solution Design in Fuzzy Engineering Optimization Problems by C. J. Shih and H. W. Lee. The paper covers FNLP problems and gives examples for nonlinear optimization with fuzzy constraints. I like their implementation better, they discuss space station building.
Death star example (or should I say ds9 (seems that trekkies are in majority here)) beats rice cookers any day of the week.

ps. does anybody know where to find FVK excel add-in? It is mentioned in few papers and should be free.

Twoblink,

Having read your great explanations on risk and money management resp. on avg. up and avg. down, I have been struggeling with the following considerations:

My experience with trading FX indicates, that past performance - be it entry/exit signals or MM - does not guarantee the same in the future. Using Kelly Ratio or expectancy calculations can be as arbitrary as anything else.

Everything boils down to the management of 2 factors:
1) Entry (or avg. price) and
2) Stop-Loss.
(Exits are either given by entry signals in the opposite direction or hitting stop-loss.)

Your avg. position and risk are always defined by those two and can be further "massaged" by managing further entry and stop-loss points.

Assuming you are following a trend following system (limit losers and build on winners) and you cannot predict the future (i.e. how do I know from now to later, if my position turns/stays profitable), it does not matter, if you average up or down, as long as you control your overall risk through Stop-Loss adjustment and correct entry sizing.

In other words, if my system shows me a valid entry below my current avg. price and there is a valid room to adjust my avg. stop-loss to maintain my overall risk, I should do it - because
a) I trade a system (the signals did not become less trustworthy, because of my previous entry prices) and
b) I keep my risk limited.
Critical factor here is to chose the right new lot size based on available space between current stop-loss and new avg. price.

The same applies to entry signals with prices above my current avg. price. However, the difference in the second case would be to make sure, that a winning position does not turn into a losing one, by applying a unit multiplication factor below 1 and strive for a Break-Even Stop-Loss as soon as possible.

In summary, apart from indicating direction and entries, all boils down to your system showing the real S/R levels and accordingly chosing the right Stop-Losses, when managing your overall risk.

Pls let me know, if there is a fundamental flaw in those considerations and if your extensive backtesting/life trading has shown otherwise.

Thanks.

Claus

Let me see If I understood the framework correctly:

The present quality deviation activates two rule sets in a rule base. From each rule set, one control action is selected based on the present constraints.

- Fuzzy quality deviation determines which rule sets to activate
- fuzzy constraints select a control action in each active rule set
- control action is activated to degree to which it is applicable for the current error

Hi Claus, Your conclusions are mathematically flawed.

Let's say Alice, Bob, and Charlie are all long on the EURUSD.

Let's say the positions are:

Alice [email protected]
Bob [email protected]
Charlie [email protected]

so who's making more money?? We don't know... Because:

Alice might exit at 1.2715 and be -2 due to bid/ask
Bob might exit at 1.2800 and make a killing
Charlie might exit at 1.2600 despite having a better entry than the other two.

Entries don't mean anything because by themselves, they are neither profits nor losses.

P/L = Delta(Exit - Entry)

It is the EXIT that defines the profitability ALWAYS.

Fundamentally, that which has no Stop-Losses has the highest potential to make money. (it also has great risk at loss as well.. ) So an SL actually doesn't dictate anything except your risk vs potential continuation ratio.

You seem to be discussing an "always in the market" strategy.

The "obvious" goal is to maximize profit while minimizing risk. You must not have read up on "RoR" yet. That will explain a big chuck of what you are missing. RoR = Risk of Ruin.

I personally do __NOT__ believe in Average position price; I believe that every position should fend for itself. That said, I do use APP to calculate potential damage to my piggy bank as an aggregate accounting method.

Just keep in mind that while you adjust your SL's to compensate so that your risk is still the same; what you are forgetting is that when moving an SL; you also give up your potential of a survival of a whipsaw. That seems to be a factor commonly unaddressed.

''blink..

Hi Albert,

Thanks for the feedback.

Let me explain:

I tried to define the method of "Cut Losers short and let Winners run" via an Exit triggered by a Trailing Stop or a Reversal Signal. While doing so, the TS defined my hard-coded risk until the APP turns into profit. This should not mean that I'm in-the-market all the time - assuming my TS is hit, I will only re-enter once a valid signal is given.

Assuming every position fends for itself, and you add a constant % of piggy bank every time, then you should add your next position only when your previous APP is in (locked-in) profit, because otherwise your new APP allows for only half the previous adverse price move, if you accept the same risk only.

If I understand correctly, the RoR topic is all about over-leverage, but I wouldn't add positions unless I have a "locked-in" move in my favour.

Are you implying, that you close a position, when a new signal is given, thereby increasing/decreasing the piggy bank (lock-in the risk/profit) and then applying an adjusted lot size?

Claus

this page (http://www.foretrade.com/cgi-bin/DownloadOK.asp) has some interesting excel/VB tools, including neural networks and Gann squares of nine.

Particularly interesting is the simple Fuzzy logic controller. It is free to download but without manual

I've also discovered by accident that MSI uses its Fuzzy logic III program to control CPU temperature.

The tutorial for FLC can be found here:
http://www.seattlerobotics.org/encod...z/flindex.html

Now I know I'll shoot myself. This means that I have to implement every possible non linear constrained optimization scenario in Excel. If every sheet is one scenario and first sheet is used to insert initial values, that will be one big xls file.

the tutorial can be found if you click on leters www inside the program.

While browsing through the thread I saw a load of complicated formulas, that reminded me of the maths, physics, mechanics, etc. that I studied in university

About optimizing risk/reward as you have named it, I've learned a very simple principle from fti's thread TAF. When adding to a winner you add in a way that keeps your average price as far away as possible from market price. In case you are averaging down you should add in such way that you bring your average price closer to the market price. The way you do the above mentioned should depend on market state and volatility, and timing is crucial for success, especially in case of averaging down.
Measuring pip distances only wouldn't yield the desired result

Good luck in your research and trading.

I'm reading More money than god, about hedge funds. It would be interesting to find out if twoblink uses some sort of fuzzy optimized hedging of currency pairs or does he look at stacks of transactions of specific currency pair independently of stacks of transactions of another currency pair.

I'm actually currently working on matrix analysis, and bias/equilibrium hacking.

Basing my system off the MIT blackjack guys and their math.. very very interesting.. I however, forgot way too much of my stats and matrix math classes.. Should have paid more attention!!

But that said, what is scary is with the stat analysis, it is the first time my test results matched EXACTLY my theoretical results, down to the T! Amazing.

So I've tested it out in MT4 backtesting and it makes money; so now onto python+sqlite testing..

I might have a workable 15M system; which seems to be the Holy Grail of automated systems.. On certain pairs; I've gotten the system above a 2.00 ratio :-D Sweet!