The Semi-definitive guide to Pascal's Triangles in Forex

Hey omg, I just realised that this might actually be a way to trade any pair... just find three levels, fix the first SL, and aim for a retrace (61.8% of the distance between level 1 and the SL) entry and distribute lot sizes based on the distances between the levels. (biasing towards taking the trades where the distance between the 1st level and 2nd level is the largest)

It's not as easy as you think... because you are effectively trying to "outplay the bookie". Turn on the tv, find your favorite vegas website; look at the over/under; and try to get a 10 out of 10. That's what you are essentially trying to do.

And I screwed up; I gave you numbers assuming the perfect world with no bid/ask, no taxes, and no fill slippage. When you add it all up, you are in the hole in both directions to begin with.

haha ok I know what you mean. It was just a random idea that I came up with, don't think I will actually do that for my trading without testing it thoroughly first lol!

What is there here beyond the hypnotical spirals and the mystical magic numbers?
Not the shadow of a proof that this binomial progression is any good. Why should this be better than any other progression? Why not a uniform (1, 1, 1, 1) or linear (4, 3, 2, 1) or exponential (8, 4, 2, 1) progression instead? Especially why is it better that a single position (1, 0, 0 , 0...)?

You pretend it is optimal but you don't specify in which regard. What is it supposed to optimize? Certainly not the profit nor the risk.
Let's analys this:
The first entry has a SL of 45 pips with a lot size of 8.4. You say you exit at X3, which is 36+28+7=71 pips from the entry. The RRR is 1.578
Let's normalize the pips. risk=45*8.4=378 and potential profit=71*8.4=596.4
At X1 a new position is added. The SL of this new position is 45 pips (SL=P+36-45=X1-45). The TP is now 71-36=35. The RRR for this addon dropped to 0.778
The risk is now 378+45*5.6=630 and the potential profit is 596.4+35*5.6=792.4. The global RRR is 1.258.
At X2 another position is added. The SL of this new position is 45 pips (SL=P+28+36-45=X2-45). The TP is now 71-36-28=7 pips. The RRR is 0.099
The risk is now 630+45*2.1=724.5 and the potential profit is 792.4+7*2.1=807.1. The global RRR is 1.114. 30% worse that the initial position alone.
As far as the RRR is concerned, "set and forget" wins over this mystical scaling.
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What if the price retraces to the third entry SL before reaching the goal?
The first position makes +378, the second makes +196 and the last one -94.5. This sums up to 479.4 for a risk of 724.5.
Should one size his first entry to 724.5 units of risk using the same 45 pips SL the lot size would be 16.1. The profit would be 16.1*71=1143.1. 57% better.
As far as the profit is concerned, "set and forget" wins over this mystical scaling.
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I leave to the reader the demonstration that the expectancy ( E=winrate*(RRR+1)-1 ) is also worse in the general case.
(see the pdf I made in Expectancy Management for an idea of the proof)

So I'm sitting at the roulette table, and I look at the ball spinning. What should I do? Well, I could bet $20 and try my luck, or I can empty my entire bank account and bet it on a single number since that is the highest potential rate of return.

Nobody is arguing that dumping it all has the highest Rate of Return, and if that's all you want to do; then I suggest you not even deal with FX; and do as I said; go down to the local casino, and bet it all on black or red, and then walk away. Or in your case; if you really want serious Rate of Return then bet it on a single number.

Nobody pyramids because it's yields the greatest return on investment; and if they did, then they don't understand pyramiding. You do so, to mitigate risk against the cost of rate of return. If I can afford to buy 15 lots; should I just enter all 15 lots, or should I break it up into 10 lots, and if it shows profit, buy 5 more lots? If I bought 15 lots and it went up 20 pips; I've made 300 pips return, hip hip hooray! If it went down 20 pips, I'm -300 pips in the hole. If I only entered 10 lots; and it went down 20 pips; I'm down 200 pips, but I still have 100 pips to fight another day.

Risk of Ruin is also not factored into what you posted above. If you've read any of my old journals; I always advised people to never go over your Kelly/2 number, and more than likely one should never go over your Kelly/3 number as your Risk of Ruin is great.

These "mythical numbers" really do what they are intended to do; which is; allows you to add to your position when you are correct; and the market moves against your last additional position(s) your damage is mitigated because it's always decreasing in lot size.

You seem to have missed the point of scaling in general... and that's probably my fault; I assumed that everybody knows that "set and forget" as you call it will always yield the most potential profit; with total disregard for Risk of Ruin.

May you please define "risk against the cost of rate of return"? I don't know this term and couldn't find anything relevant on google.

That's not true. "Set and forget" has a linear potential profit w.r.t the pips move. A grid has a potential quadratic profit w.r.t the pips move. Who is interested in the potential maximum profit anyway? Your example shows it clearly betting your bank roll on the double zero because it has the greatest potential profit is a clear and obvious nonsense.

Again I don't know what "risk against the cost of rate of return" is; so I don't know what you're really trying to optimize. But "all-in 15 lots" is better in term of RRR and it is better in term of expectancy (what I want to optimize).
You overlook the cases where the price retraces to the add-ons SL before reaching the target. Perhaps you disregard this because overall you're in profit. But the increase of risk and the accumulation of thoses little losers don't seem to be counter-balanced in the long run.

The DD is reduced if you can both maintain the expectancy and increase the winrate. But this is not the case here: the expectancy is always decreased. Therefore the increase in probability of winning must also cover for this reduction of expectancy. I mean that you have to achieve a reduction of the DD which allows for a increase of the lots size to compensate the reduced expected numbers of pips per trade (trade = execution of your plan, irregardless of the number of positions involved).

I'm not rejecting the idea of pyramiding. I acknowledge the fact that the probability of reaching the TP before the SL given the price went in your direction is greater than the initial probability. But it doesn't guaranty that it will do so without a deep pullback before. Entering the market because the price went higher then retraced is acceptable in term of probability; I'm not sure in term of expectancy. Entering blindly (with a stop order) because the price reaches +X pips for the first time is not.

You didn't explain why the binomial progression scheme is better than any other.

I'm not sure what more I can explain as far as risk vs rate of return.

Please look up "Risk of Ruin"; very little to be google'd but there is a lot in terms of books on the subject.

Let's say I flip a coin, and I tell you, if it's heads, I will pay you 2x what you bet, and if it's tails, then you lose your bet.

In reality, you have a positive expectancy; but let's say you have $100. What should your strategy be?

If you bet $1 at a time, you aren't optimizing your RATE OF RETURN as expectancy is positive.

If you bet $100 at a time, the first time tails comes up, you are RUINED <== The technical term, not the Webster's Dictionary Term.

If you are insane, you can risk up to $25 per bet; surmising that this might be your Kelly number and betting that amount. But understand that your Risk of Ruin is probably close to 50%. Insane in my book.

While I haven't crunched the numbers, I'm betting that your Risk of Ruin for a bet of $8~$10 is < 2%. And I'm betting that will go up only slightly to 20% on a bet of $16. I would personally half the Kelly or 1/3rd the Kelly (Written as K/2 or K/3).

Assuming you are in a situation of positive expectancy, and that you are able to calculate your Kelly, almost any K/3 will yield less than 12% Risk of Ruin, and almost any K/2 will yield < 22% Risk of Ruin. Those to me are acceptable numbers, but YMMV.

A pyramid progression is based on the theory of: "The Trend is your friend, until the end when it bends." It is the mathematical fact that the more a price goes in one direction, the more likely it will turn around AND so the amount of energy it takes to push price to new territories is inversely proportional to the price it moves.

Easiest example is actually using a car:

Let's say a 50 horsepower car can go top speed of 70mph.
Let's say a 100 horsepower car can go a top speed of 100mph.
We get a +30mph for our additional 50 horses.

BUT..

Let's say a 650 horsepower car can go a top speed of 190mph.
To go an additional +30mph You would need almost an additional 150 horses.

a movement of 190=> 210mph takes 150 additional horses
a movement of 70 => 100mph take only an additional 50 horses.

The reason for this is friction and wind resistance. Not to get into coefficient of drag and friction; but the same with FX.

If the traditional USDJPY is around 100.00, a movement of 100 => 101 is fairly easy. BUT, a movement of 105 => 106 is quite difficult. The amount of bears pulling on the price is quite large at that point in time.

So why a progression of a pyramid style. It takes advantage of 2 things:

1) Averaging Up
2) Situation of more "work" required for the price move, the fewer lots you have in because the higher the propensity for failure.


Average Up. I have written some 400+ posts on this, so I will not bother. Needless to say, you are averaging up instead of averaging down, which is the right thing to do.

As confidence decreases and difficulty increases; you are entering with smaller lotsize. If you were to progress with same lotsize; then you will have created great negative potential expectancy; because your risk in terms of lot size is the same even though confidence and probability has decreased. Same with increasing lotsize when you progress.

So that leaves you with 3 options:

1) Decreasing lot size
2) Increasing gap size between entries
3) Tightening SL's as price moves in your favor

Given these to be the options; how do you correctly optimize?

I actually solved that in 2008, and don't care to share. But when you do the math; you come very very close to the golden ratio; and so when you try and muck with the numbers, you find that using Pascal's set is almost optimized. If you would like to do multi-variant optimization (and let's be frank, who doesn't?) then you can do so with a 7 column programmed excel spreadsheet like I do... OR you can just use the pascal chart.

I asked you two things:

1- To define "risk against the cost of rate of return".
You ask me to search the definition of "risk of ruin"....

2- To prove that your pyramid schema is better than any other since you dare pretending so
You just confused the issue with a story of horsepower which BTW shows that the more the price progresses the less interesting it is to increase your exposure (Situation of more "work"). That is that the best option is to NOT pyramid.

100 to 101 is a 1% move. 105 to 106 is a 0.95% move. As prices increase the relative percentage of a move decreases for equal pip movements. It is easier to make a 0.95% move than a 1% move. This is simple market volatility mechanics. This is also why ATR measurements are tied to (change with) the absolute price level. For example, when the S&P price was 400, a 10 point move was a huge range day. Nowadays at 1800 on the S&P, 10 points is a small range day. The same phenomenon can be seen on stocks that double. When USDJPY was in the 70s, 100 day ATR ranged from 30-60pips, now with price at 100+ it ranges from 67-120 pips.

And I too would like to hear a definition of "risk vs rate of return". Are you defining it as "risk of ruin"? If so why have you chosen to use a different term than the commonly understood one? When I do the search: ["risk vs rate of return" definition] it leads to this post as hit #2 on Google and only 27 results, which indicates that nobody else is using this term. In other words, you made it up. It is fine to make up terms, however unless you explicitly define this new term, such made up definitions do nothing to facilitate understanding, which is the transfer of words and ideas. Instead, made up terms tend to obfuscate meaning and inhibit validating the information being presented. It seems clear that this is your intention.

If you are defining risk vs rate of return in some other way than risk of ruin could you please post the mathematical formula for your definition or point to where you have done so? Without doing so it is impossible to validate the claim that Pascal's triangle is "optimal", because as PipMeUp stated, it begs the question, "optimal with regards to what?"

"I asked you about friction and why it matters and to define it, yet you tell me to Google thermodynamics..." I will assume neither of you know what risk of ruin is...

Risk, how much from your piggy bank you are putting the betting table.

If you bet all of it, and are correct, then you would make more, but if you are wrong then you are broke. This is difficult to understand?

And if you think yen moving from 105 to 106 is easier, then you don't know what a central bank is.

So let's assume USDJPY is at 100 and we have 3 traders and each has 400 pips to risk, trading micro lots of 1 pip movement = 1 pip profit/loss.

Let's look at the scenario where the price moves from 100 => 99, and the second scenario of 100=> 101.

Trader #1 PipMeUp
Trader #2 FXEZ
Trader #3 Twoblink

Trader #1 enters with 400 lots and an SL of 1, because he is all about the maximization of profit with rampant disregard for actual risk. That's how he rolls.
Trader #2 enters with 20 lots, with an SL of 20, because he too didn't bother to read up on risk of ruin.
Trader #3 enters with 8 lots and an SL of 21.

Assuming all three went long and looking for the price to go up; and assuming TP at 101.

Trader #1 has a maximum downside of -400 pips, and an upside of 40,000 pips. This is by far the best risk to return ratio, which is all he cares about.
Trader #2 has a maximum downside of -400 pips, and an upside of 2,000 pips. This again is because he hasn't read up on Risk of Ruin.
Trader #3 has a maximum downside of -168 pips, and an upside of only 800 pips.

Best case scenario, the price does hit 101 and Trader #1 is smug, Trader #2 is smug, and Trader #3 doesn't care if they are both smug.

Now let's take a look at the downside.

So the price goes to 99.98 and Trader #1 has lost his shirt. Why? Because he doesn't give a crap about Risk.
So the price goes to 99.78 and both Trader #2 and Trader #3 are both SL'ed out.
Trader #3 decides then, that he was wrong, the market has flipped, and he SHORTS 8 lots with SL at 100.01.

The price drops to 99.00, Trader #3 TP's out, and makes a +624 pips on the exit, with his trading account still intact.

When you are a punk and don't know anything, I'd be less aggressive on someone else's thread. When you are a punk and someone tells you to Google something and you don't, I'd not post until I did.

I'll give you the Ed Seykota definition of Risk of Ruin; the rest you will have to google yourself. And please PLEASE for the love of Forex don't tell me "Who's Ed Seykota". That colorful thing on your browser called Google, it's your friend, use it.

Risk of Ruin, the inability for your account to recover after a loss.

If my account tanked by 90%, I would need to make *NINE TIMES* the amount with my remaining 10% JUST TO BREAK EVEN. If I lost 50% of my account, I'd have to make 2x just to break even again. Most of us aren't doubling our accounts, and certainly not people who don't even know what Risk of Ruin is.



As to why the pascal's triangle is optimized; aside from the fact that you have not studied it nor the Fib sequence and have personally I assume never contemplated adding to a winning position, (I can assume because you've never had a winning position) I have said before; if you progressively enter in fixed intervals, and add to winning positions, Pascal is optimized so that YOU SHOULD NEVER EXIT ALL POSITIONS FOR A LOSS WHEN YOU ADD TO YOUR POSITIONS. PipMeUp actually provided the math himself; so I find it very stupid how he can do the math and still ask why it's optimized.

If I entered with 20 micro lots, and I'm showing a profit; at what point is a good point to add more lots? And how far away should it be? As I posted in the initial introduction, Pascal's triangle answers that. It will tell you how far you should be to add to a position to not compromise the open profits; either in lot size, or in intervals. <=== That's why it's optimized. But I cover this above...

Do you guys actually read or even try any of the math before you type? You should try it, it saves you from looking like an arse.

TwoBlink

When it comes to adding to a winning position , based on your extensive research , is it "smarter" to enter at fixed intervals, or is it better to enter based on a pascal pyramide intervals. there is a mathematical way to calculate which one is better (fixed or pascal )

Thank's in advance for your time

Landsat

Interesting thread. I guess you could use the same ratio to increase your trade volume each month by applying it to your equity curve. But you would have to proceed as though the trend in your equity curve (assuming it was positive) did not end the same way as the Turkey's life expectancy!

First, understand that you add to winning positions only because you either didn't have money to put into the initial position; or you didn't want to risk that much initially because you don't know if you are correct. In the book "The Way to Trade" he talks about this and I tend to agree.

If you are going to add to a position; you can either add with a fixed interval and a pascal lot size... OR, a pascal interval and a fixed lot size. I wouldn't recommend entering at a pascal interval and a pascal lot size without help from software or knowing (REALLY KNOWING) what you are doing. Of those two, I would definitely if I were to add to my winning positions, pick fixed interval and pascal lot size. This is the easiest to understand and that is something noteworthy; the easier it is to understand the less likelihood of making a mistake.

Hope that helps.

I would advise against it actually. For equity exposure calculation; I would __HIGHLY__ recommend a fixed percentage; that way, if your equity increased; the amount (in terms of $$$) is increased automagically. If your equity decreased, exposure would be decreased automagically as well.

Okay, I just like applying numbers as beautiful as these to everything! Maybe even length of time with mistress', or their age.. no wait that wouldn't work...

I wonder if this would be a better way to delta hedge options. Whilst an option's delta is a given, in practise I find that less delta hedging volume is better than more. (if I'm writing options that is) Adding to a delta hedge via these numbers might make very interesting results....

I personally probably take a delta neutral, gamma neutral on REAL options; but if trying to fake option behavior in the FX world; I'd prefer to have close to delta neutral; but slight gamma bias; I would want to pick a side. 48 hour rollovers on FX is a killer if you are on the wrong side; so staying near gamma neutral isn't really an option IMHO.

Rereading this reply from myself. Glad more than a year later; I have been able to make a Pseudo Delta Neutral AND Gamma Neutral System.. Guess I was wrong; you can be Gamma Neutral. Shabang! Love proving myself wrong.

I have a wife for that