Caution: Math Geek at Work

Knocks on the microphone... IS THIS THING ON?? I'm confused about what you're saying because you seem to be agreeing with me and disagreeing at the same time.

I said basically: Expectancy is negative!

You said: You're wrong dude! Expectancy is negative!!

Ummmm, we're both saying it's negative.



Again, we agree. I don't use TPs either. I've mentioned that several times.

My reason is that they violate what Taleb would probably call the "black swan advantage" or what a statistician might call the "fat tail" advantage. Essentially, the market tends to discount unlikely events by a greater degree than the numbers would indicate, so the smart play is to bet on the unlikely event. In other words, don't discount the possibility that your position WILL reach extreme profitability.

Check the conjecture again in the last long post. The formal statement is down under #9. I would love to see a counterexample that disproves it. But we're both saying the same thing. There is no counterexample.

I'm finally finished with this monster research project.

The third part of the project involved looking at the internal dynamics of a single price bar and how that correlates with the internal dynamics of the next bar. By internal dynamics I mean things like once the bar opened, which did it hit first, the high or low? Which did it hit last? How many times did it hit each extreme? I'll be putting the entire set of notes into my site's archives in a while, but here is the conclusion page for the third part:

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LOOKING INSIDE THE CANDLES - SUMMARY OF FINDINGS
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1/17/08 – 2300GMT:

1. We can model the internal action of any price bar in terms of which extreme (high or low) the price reached first, and which the price touched last prior to the close. There are four possibilities:

a. Open è High è Low è Close
b. Open è Low è High è Close
c. Open è High è Low è High è Close (this is an “M” or a series of “M” shapes)
d. Open è Low è High è Low è Close (this is a “W” or a series of “W” shapes)


2. The second two possibilities are extremely rare in higher time frames but common in low time frames. Also, the number of individual times that price reaches an extreme is much higher in lower time frames than in higher ones.

3. For both time frames, if the price hits the high of a bar more times than it hits the low, there is a slightly greater tendency for the next bar to be bullish and vice-versa.

4. For the daily bars, if the last extreme to be hit was the low, there is a greater tendency for the next bar to be bullish and vice versa. In other words, the performance of the next bar is positively correlated with the direction of the last leg (high è close or low è close) of the previous bar.

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Time for food and sleep!

No trades again this week. I finished up the research I was doing and am now working on integrating what I've found into a simple method. I'm also in job-hunt mode unfortunately. Anyway, the account was down 2.8% this week due to fluctuations in the NZD/USD position.

I have a trading method mostly outlined now. In order to firm up the details and do "reality checks," I've been trading in the NZD/USD. I placed several buy orders on the pair last night in such a way as to increase my position if the pair advanced.

That worked, but because of the unexpected Fed announcement the last two of my orders were slipped by 58 pips each!!
They're still all in profit and I've moved the stop up now. I checked the one minute chart and saw that the spike was virtually instantaneous, so I'm not going to battle with Oanda about the orders.

I'll post more about the method I'm developing a little later, but for now here's the NZD/USD action.

Scott, your works are astonishing, I like them. I'm an hungry reader of this kind of researches and I also do a lot of them on my own. I'm reading everything on your site too. Very good works!

About your post 78, even if without the rigorous formalization of your approach, I came to the same results as yours years ago when I studied exactly that kind of things. Whatever fixed SL and fixed TP you use you have no way to profit from the markets, unless you have some edge on the entries. So I have no counterexamples to your conjecture, instead I totally agree with it even if, of course, I'm either not able to demonstrate it.

Anyway, on post 79 I think you run to a conclusion that is not correct when you say:

In fact, of course, this would be true only and only if for "risk/money management" we intend only what you allow in your conjecture, which is fixed SL and fixed TP and (you did not say that, but I assume you intended it) fixed position size for every trade.
Well, in that case you are right.

But we know that this kind of "risk/money management" is just a very small subset of all the techniques that are available on the front of "risk/money management".

When we include the whole set of techniques of course your conjecture, even if proved true, cannot demonstrate that also dynamic positions sizing, trailing stop losses and other "risk/money management" techniques are not enough alone to have a system with positive expectancy even if we have no edges on entries.

Indeed, maybe, I don't know for sure (but I believe yes), a good risk/money and position management could be enough to build a profitable system even if entries are established by coin flipping, provided that all of the money management techniques are allowed at every time.

In fact, if you think about it, allowing those techniques even at entry time (variable position sizing) is indeed a way to have an edge on entries even if the direction of the trade (long or short) and its start time are established randomly.

So it's at least not sure, even if your conjecture would be proved true, that whatever risk/money management techniques you use, those alone will always yield negative expectancy in the market. Or not?

Hello Scott

Great read you have here. I wish you a whole bundle of good luck .. you are certainly well read on FX and well prepared to make a roring success of trading.

Hi ubeee,

You're right, I was using the word "expectancy" in a very limited sense there. I was thinking of just a fixed SL and TP because it's the easiest thing to test.

As far as not having an edge on price direction, I'm still thinking about that but you may be right there too. An argument in favor of what you're saying could be found in simple dollar cost averaging. Assuming that price fluctuates at all, adding to a position at a fixed risk level at different prices means buying more/selling less when it's low and buying less/selling more when it's high. So the average entry cost of the position is always at a favorable point relative to the average price during the same period. Even if the market is moving against us, our loss is less than it would be if we had simply entered at one spot. So this is an example of a risk/money management technique giving us an advantage without having an edge on price direction.

I'm worried that it may not be enough though to overcome the (possibly very non-random) price behavior that causes the "negative expectancy" that I was seeing. Did you read the last few posts of my thread called "Expectancy is always zero?" I gave more detail on what I was seeing.

Anyway, thank you for your comments on my research! One caution I would have about the notes that are archived on my site. Some of them are probably pretty worthless either because:

a. I was just rambling and the notes are confusing (the early ones)
b. I went down a bunch of dead ends and didn't find anything
c. I was too lazy to do proper followup, like out of sample testing, etc.

But even though I'm not a professional researcher, the notes might give some good insight into how a market research project might be organized, etc. I'm glad somebody's reading them.

I'm out for the night. Time for java (not the program) >>> C\_/

Thanks FxPip! I hope so. Been working at it for years but still just treading water.

With my last research project complete, I used some of the research results to build my new trading method. This isn't the only method I'll use because it's long term and only requires a few minutes of daily maintenance. So I will continue working on a short term "session based" scalping method with EUR/JPY too. But for this post I'll concentrate on this one.

There are a bunch of details to the new method, but I'll only sketch a broad outline here.

The goal is to build long term, low risk positions in pairs with positive carry. Instead of just watching a daily chart, waiting for good entry points and using a "buy and hold" approach, I make short term trades in both directions around the core position. I use any profits from those trades to add to the long term position, risking only a portion of the profits.

Right now, the pairs I use are NZD/USD, GBP/CHF and AUD/JPY. However, I've only used the method with NZD/USD so far. I'll start the process with the other two pairs later today.

More details to follow in the next few days, and I'll start posting more frequent trades now.

Trying to keep my posts short enough so that they don't all look like novels.

I'm back again. That was quick. :

I figured that since I'm doing the initial work to set up AUD/JPY for trading, I'd post it here.

The first thing I do is to identify points of S/R. I consider any level-1 fractal which hasn't been violated since it was formed to be such a point. I don't bother with pivots or fibs or any of that stuff because if the pivot/fib was really an effective S/R point it would show up as a price bounce, and I'd have a line there already anyway. If the price doesn't bouce there, what's the point of having a line there?

I use the S/R lines for two things. I avoid buying too close to a support line or selling too close to a resistance line. "Too close" has a specific meaning which I'll explain in a minute. The other purpose of the support lines in this case is to identify places for stop placement when I add to my long term long carry position.

I know, I know stop hunters or weird price action or the great pumpkin will take out stops at those key levels sometimes. But there are always points on any chart that form long term lows or highs that aren't violated for a long time. My view is that each support fractal that forms might be another of those points.

My S/R lines are shown in the zoomed out view below.



The next thing I do is to analyze the price action to see what kind of price leg has just completed. In my last research project I identified four possible types of price leg (trend extension, trend pullback, range expansion and range contraction) and found the median amount by which price pulls back after each type of leg.

Working from RIGHT TO LEFT I work backwards to draw zig-zag between tops and bottoms as defined by level-1 fractals. I only need three legs to define what the last one is. In the case shown below we have a LHLL leg; a leg that goes from a lower high to a lower low. This is a trend extension leg.

From my research I know that the median pullback on such a leg is about 80%, so I figure out where that is and draw a dotted "exhaustion line" there. That's the purple dotted line. It's kind of like a resistance line, except that it's not firm. It just shows that once price moves higher than that line, the probabilities get lower that price can continue the advance.

This is what I mean by "too close" as I mentioned above. If price is between that exhaustion line and an actual resistance line, I consider that a "no buy" area. Buying is off limits there even if I get a buy signal (more on those in a future post).



I think that's about it. That's how I prep my daily charts, and I check them each day to see if anything needs to be changed. If a S/R level gets violated I remove it, I add new S/R levels as they are formed, and adjust the zig-zag and exhaustion lines as the bars are formed each day.

Be back later!

:surprised What th...

I knew the Pound has been weak but I didn't realize the GBP/CHF was in such a steady downtrend like that. All resistance levels and no support levels.
Kind of hard to build a carry position with that going on.

Since I'll only be risking trading profits to add each new piece though I'll stick with the plan. Who knows; each support fractal that forms could be THE ONE.

I caught the surprise Fed annoucement with buys in place on NZD/USD from the night before, so that helped out this week. The account was up 1.7%

I've expanded my new method to AUD/JPY and GBP/CHF as well. I'll post more about the method a bit later.

This is a cute little trade I did a little while ago, just after the London session closed. It's the EUR/JPY, my favorite scalping pair. I just used the same concepts that I use in my "long term carry position builder" method; the statistical length of different price legs, price exhaustion, & price bar "internal dynamics" (did it last bounce off the high or low of the last bar?)

The three white lines are price legs drawn on the M15 chart from fractal tops and bottoms. That's why they don't line up on this M1 chart. Anyway, at the time I was watching the chart, I had that third confirmed leg which went from a higher low to a lower high (HLLH). This is a range contraction leg, and my stats say that these kinds of legs have a median retrace of 140%. So I estimated where such a retrace would end and came up with 157.50 which is where that dotted yellow line is. The solid yellow line is an actual support level where price bounced before.

The area between the two yellow lines is where I wanted to buy because at this point the downleg would be getting exhausted (greater than its median value) and we would be near support. I got kind of impatient and actually bought at 157.56. My stop was well below the support at 157.15, and my position size was small enough so that I could actually add double the amount down at 157.40 and still be inside my max risk limit. So I grabbed a little piece at 157.56 with the hopes of getting some more down closer to the support.

It never got that far though. Price started to move back up and so now I had a newly confirmed downward price leg (unmarked) that went from a lower high to a lower low (LHLL). This is a trend extension leg, which has a median retrace of about 80%. Although it did eventually retrace that far (up to 157.90) I got out early when I saw what looked like a pin bar on the M1 chart. So I only made 22 pips on this one, but that's ok.

On the chart below is some detail on two individual trades I did with GBP/CHF. The first one was a small loss and the second was a small gain. I took the profits from the small gain and used them to add to a long term position with a stop below the last support point at 2.1200.

The way I set up the trades should be pretty self explanatory from the chart.

The signal I use is really simple. I consider a daily bar to run from 1600 to 1600 my time, because this corresponds to the close of New York and the open of Sydney. When I block this out on an M15 chart, I look at whether the price hit the high last or the low last. If it hit the high last, I sell and vice-versa. This signal tested out the best in my research, and it conforms to the common sense "what is price doing NOW" test (usually). If price has just moved from the high to the close then it's going down. Right?

The reason for the stop loss placement on the first order isn't clear on the chart anymore because I deleted the horizontal line, but there used to be a resistance level there.

I scale in with order sizes of 4, 3, 2 and 1 units. By making the distance between these orders equal, if all four orders fill the average entry price is always exactly where the 3-unit order was. That appeals to my laziness. The actual size of the orders is based on how far away the stop is and my preferred risk level of 1-2% per trade.

I check the market at 1600 my time each day Sunday through Thursday and readjust orders then. This is what the situation in GBP/CHF looked like on Sunday night ( I think). I have since closed the 2nd trade for a small profit.

Whoops, this is late again but here's the weekly update. I've been trading my main long-term position system each day and it's looking good. For the nine trades I've completed so far, there have been 4 winners and 5 losers. The average gain on the winners has been more than twice as great as the average loss though, so the historical expectancy is positive at this point. Here's a chart of the actual vs. required win rate for the system:



I've had four successful scalping sessions in a row with EUR/JPY although the last one was a struggle to get it two pips in the green. The totals were 22, 10, 19 and 2 pips. I'm using the "earn the right to increase position size" principle and am looking for 10 straight winning sessions before raising my position size with this.

Overall, the account was up 2.9% this week for the second winning week in a row.

I've been offline for about 48 hours because on Tuesday a tornado went by across the road from where I live. It damaged a mall and took out a power substation, cutting off power here until about three hours ago. So I've been shivering in the dark for the past couple of nights.

I thought I had it set up so that I could draw power from my car's cig lighter to run my laptop if I had to, but I found out I'm not. I also found out that my clock radio that's supposed to work with a 9v battery doesn't. I also found out that I didn't know the best place to go and buy firewood.

Basically, I found out that I really need to get my emergency response plans in better shape. I know there's a thread about that here on FF somewhere, so maybe I'll make a comment there and revive it.

Anyway, I haven't checked my account yet, so I don't know if I've got any damage. Gotta email my sister too. More later!

Glad to hear you're ok then!
Stay well,
Mick.

Thanks Mick!


I've got my account all updated now with current trades. There wasn't any damage except for a lost opportunity of about 100 pips or so I think. Looks like I'm still a bit up for the week.

Time for a late dinner.

Well, last week included a near miss with an F2 tornado and two days with no power but I still managed to eke out a small gain of 0.2% on the account. That was the third straight profitable week. I'm up to six profitable scalping sessions in a row, and the historical expectancy of my long term system is still positive. Not too shabby.

Ok, first of all, Fade to Grey by Visage is playing in my headphones right now. So as Bridget Arendt whispers "devenir gris" in the background, here's the latest...

Just as I try to shed calories from my diet, I try to shed unnecessary complications from my trading. No longer am I dealing with three pairs and trying to run a carry position and a short term strategy with each one. Say goodbye to GBP/CHF and AUD/JPY. The only carry position I'm holding now is NZD/USD with no stops and low to no leverage. That position is in a sub-account to which I add funds whenever I have sufficient profits in my day to day trading account.

For day to day trading I'm now using only EUR/JPY for both multi-day trades and scalping. It was this pair I used in my last research project, so it only makes sense.

Finally, the experiment is shown in the chart below. I'm messing with my method a bit to see if I can take better advantage of the stats. Below is the trade I've currently got set up in the account. It consists of a series of 12 sell orders for varying amounts, set 50 pips apart across an area which I think will encompass the current upleg. Based on my research, I'm expecting this upleg to fail at some point prior to the high of the last one, and then continue downward past the last low.

The orders are set up so that the ones at higher prices are for larger units. This facilitates scaling into the short in both directions; averaging down as price moves against me, and adding smaller units as it moves in my direction. The stop for all the orders is at 160.50. Worst case is that price moves down to catch the lower orders, then moves up to fill all the others, and finally hits my stop. This is a low probability event, but if it happens my loss will be about 2% of the account value.

I'll update this trade as it progresses.