Caution: Math Geek at Work

OK, since we've just had a confirmed switch from an upleg to a downleg I thought now would be a good time to go through all the steps I take at such transition points.

1. First of all, I use a 250 pip reversal threshold as a confirmation that one leg has ended and another has begun. This is just how a standard "zig-zag" indicator works, but Oanda doesn't have one so I have to keep track manually. That's the brown dotted line you always see on my charts. The price has now moved down more than 250 pips below its highest peak in the upleg, so we now have a downleg. Since we're now in a downleg, I have moved the brown reversal line to a point 250 pips above the lowest point in the downleg so I know when the downleg has ended.

4. The next step is to analyze the leg that has just ended and determine the exhaustion level for the current leg. There are only four kinds of price legs, and there is research on my site for each one describing the median move of the NEXT leg in the opposite direction. I refer to this median movement as the exhaustion level, because once price passes that level, there is less than a 50% chance that it will continue in that direction. The four types of legs and the median moves of the next leg are:
NOTE: THESE ARE FOR EUR/JPY ONLY. I DIDN'T LOOK AT ANY OTHERS.

a. Trending legs (HLHH or LHLL): next leg reacts by 80%
b. Pullback legs (HHHL or LLLH): next leg reacts by 110%
c. Contraction legs (LHHL or HLLH): next leg reacts by 140%
d. Expansion legs: (LLHH or HHLL): next leg reacts by 60%

The upleg that just ended went from 151.72 to 161.72, a move of exactly 1000 pips oddly enough. This upleg went from a lower low to a higher high, so it is a LLHH expansion leg. The median reaction is 60% So the exhaustion level of the current downleg is 600 pips below the last peak, or 155.72. That's the dashed yellow line on the chart. When we're in a downleg I make the line yellow like the regular support lines. For uplegs the exhaustion level is a weak form of "resistance" so I make it purple.

3. Now I wait for price to reach the exhaustion level. Let me point out a mistake in my previous (?) post where I said that as soon as this downleg started I would start to place buy orders above the price. Wrong. I changed that several posts back. I will only start placing the buy orders when the price has gone below the exhaustion level. If price reverses into an upleg before reaching the exhaustion level then I won't have any buy orders in at all behind this leg. Maybe the next one.

4. Finally I begin placing the orders in an increasing sequence. There are a few rules I have developed for how to do this.

a. I place them at round numbers 50 pips apart.

b. I start counting at the last peak or trough

c. Based on my current "unit size" my first order is 1 unit, then 2 and so on.

d. If price is on the profitable side of my entry, I "collapse" the orders on the other side into one large order in profitable territory.

e. If some of the orders get filled by a price spike (not large enough to create a reversal) then I will replace the furthest orders with a new order to fill the gap. We saw that happen a couple of times on this last upleg. This means I'm always moving sell orders higher or buy orders lower, which is what the strategy is all about.

So here's the current chart:

The overall account was up 0.9% this week to just under 80% of original equity. The EUR/JPY position management portion of the equity was basically flat. Here's the updated graph.

Hi Scott, IMHO, your method makes good sense. I hope it will make good cents as well. Bon courage, Pippo

Thanks! I'm doing what your sig says; following it robotically!

Happy Monday!

The sell order for 14 units filled so now I'm short 74 units on EUR/JPY. The position is still hovering around 50 pips in the red right now. Also, because of the big recovery after the downward move today, we're getting fairly close to the 250 pip reversal threshold, putting us into a new upleg. If that happens, I would end up heavily short and adding more sell orders as the upleg rises. Interesting to see it play out.

But have you studied fluid dymamics? I see your method as a model of a fluid dynamic. Just a random thought, poorly resolved in this ancient brain. I am sleepy. Pippo

Yes, a long time ago when I was a civil engineer. The only things that come to mind now when I think of fluid dynamics are Mannning's equation and the concepts of laminar flow vs. turbulence.

Failed repeatedly at Math in school. Never took an advanced Math class. I am thinking...estimating the wash by the height/acceleration of the crest.

The downleg has ended and we're currently in a new upleg. The completed downleg was a HHHL making it a trend pullback leg, so the median reaction distance of the next leg is 110%. I forgot to mention in my last long post that when we transition from one leg to another, I also cancel all the unfilled orders associated with the completed leg. That's shown in today's chart:

Well folks, here we are in drawdown territory. Here be monsters.

This upleg has moved past the exhaustion level so I have begun to place the series of sell orders below it.

Notice that I'm not doing the "collapsing of the orders into one" thing here. The reason is that these orders, if filled would be INCREASING my exposure. So I have no incentive to see them filled with higher probability. If they're filled it will only be because the price is moving down toward profitable territory.

I only consolidate (or "collapse") the order series into one when the order is a "profit taking" order, i.e. one that reduces my position at better than my average entry price.

Here's the chart:

The only change to the last update is that the price of EUR/JPY has continued to move north, giving me room to place two more orders for 8 units and 9 units. None have filled, so there are now 45 units worth of open sell orders.

Here's a good illustration of the advantage of this method. During the last long upleg, if all the sell orders I placed had actually filled, my short position would be 120 units, and my average entry would be lower than it is now. Contrast that with the current situation. If all the sell orders get filled, I would have the same short position (actually 74+45=119, close enough) but at a much better average entry price.

So even though I'm in a drawdown period, this period may be setting up a much greater profitable one than I would have had without the drawdown period. Or something. More coffee >>>> C\_/

Same deal as the last update. The carnage continues. I have added three more sell orders, for 10, 11 and 12 units. Nothing more has filled so I'm still short 74 units. Open loss is 455 pips so far.

The account was down 4.6% this week due to the heavy drawdown I'm in with the EUR/JPY position. Here's the updated equity curve for just the EUR/JPY portion.

Oh, you're looking at wave mechanics. There are probably some similarities. All the fluid mechanics I ever did involved fluids moving either under pressure or under gravity through pipes or weirs, etc.

Hi Scott,

This is my first “nosing in” here. I very much appreciate your math background and congratulate for your nice research work.

I beg you pardon if the doubt I describe in the following would be considered off topic. Please disregard if that is the case. No problem if you even ask me to delete the post.

It is about measuring and making a judgement about trading performance. I am trading actually in a completely discretionary way. I follow some guidelines in the most disciplined way I can, but I have no fixed rules. I register in an Excel spreadsheet my weekly and monthly returns on equity, plot charts of the figures and run statistics on them.

I am struggling with the question: “Are my results random?” I am not a random walker. I am pretty sure markets are NOT random. But maybe my performance is. If my results are random, there is no reason for me to go bigger than I am at the moment. If I can find some kind of statistical “edge”, then I may draw a scaling plan.

I googled “randomness test” and found a site that has a java grid that performs a test for randomness in a set of numbers. But I am not sure about the correct interpretation of the results. The result of the test on my personal account numbers confirmed my “feeling” about them. But as a measure of control, I ran a test on a set of numbers that I feel are NOT random and the result puzzled me.

Here they are. I got these monthly figures from a managed fund:

October-2006: 12.18%
November-2006: 10.06%
December-2006: 06.95%
January-2007: 10.45%
February-2007: 07.78%
March-2007: 07.81%
April-2007: 07.06%
May-2007: 07.29%
June-2007: 06.54%
July-2007: 05.77%
August-2007: 08.12%
September-2007: 08.10%
October-2007: 08.17%
November-2007: 05.56%
December-2007: 05.66%
January-2008: 04.52%
Feburary-2008: 04.26%
March-2008: 05.60%


I see consistency here (am I wrong?) May these numbers be random? The test result was this:

In entering your data to move from cell to cell in the data-matrix use the Tab key not arrow or enter keys.

Conclusion: Moderate evidence against randomness

“Moderate evidence against randomness”? It looks to me there is strong evidence against randomness! Maybe I am completely misinterpreting the test result.

If you think the point is valid, I may post my weekly results (the monthly have not hit the minimum required to perform the test yet).

It seems to me that my ROE record keeping is the only (?) valid way to gauge trading performance in a discretionary modus operandi and it may be used for any trading system as well.

Thank you very much for any attention and congratulations for your great thread.

Hi Jairo,

This is a good a place as any for such a question, although it's a little hidden away here on my obscure journal I suppose. You may want to copy and paste some of the discussion onto a general thread to get input from others on the Factory as well. Feel free to copy any parts of my response below.

First, without knowing how the Java application works, there's no way to know why it came up with a "Moderate" reading for non-randomness. But that's ok, because I can show you a couple of basic statistical analyses that I did on your data we could interpret the same way. In any case, this may shed some light on where this "Moderate" result is coming from.

Now there are a couple of different ways we could look at your data. One is in a time series, and the other is just as a set of results, regardless of the order in which they occurred. I'll look at the time series analysis first. Here's a chart of your results, along with a linear regression line, the equation of the line and the "R-squared" value.



You might know all this stuff already, but without going into a lot of detail (which I would have to look up, LOL) the R-squared value is a measure of how much the movement of one variable is "explained" by movement in the other. Now the independent variable here is just time; the number of months that have gone by since you started keeping track of performance. The independent variable is the performance itself.

The R-squared value of 61% is telling us that the decline in performance over the period is about 61% explained by SOMETHING (I have no idea what) that has been changing over these months. Maybe you've been doing something different, maybe it's some factor in the market that's been changing over this time or whatever.

Anyway, an R-squared value of 100% would mean that the change in performance was PERFECTLY explained by change in time (complete non-randomness) while a value of 0% would mean that there is no explanatory value whatsoever between the variables (completely random). So the decline is 60% non-random which I suppose could be called moderate.

Now let's forget about the time series and just look at the results themselves. The mean of the performance results was 7.33% with a standard deviation of about 2%. The mean gives us a measure of "central value" which you can think of as the "right" value. The standard deviation is a measure of how far the actual values are scattered away from this central value, so it's kind of like a measure of "error."

When the values and the mean are all positive like yours are, we can look at a measure called Coefficient of Variance (COV) which we get by just dividing the standard deviation (the "error") by the mean. This tells us how big the "error" is in comparison to the magnitude of the "right answer." This allows us to compare vastly different situations. For example if I'm looking at the diameter of ball bearings made by a factory, my mean and standard deviation might be measured in millimeters. But since the COV is dimensionless, I can use it to compare my ball bearing study to your trading study.

So your COV was (2% / 7.33%) which is 0.28. Now generally anything less than 1.00 is considered to be low variance. So is 0.28 good? Well it depends on what you're talking about.

If I had a ball bearing plant and the diameters were coming out with a COV of 0.28 (meaning the errors in diameter are around 28% of the average diameter) then I would fire everyone, close the plant and bulldoze it to the ground immediately! That's way too high a variance in that situation and I would call the performance very random.

But a COV of 0.28 is pretty good when you're talking about investment results (I think). It's a measure of your risk/return ratio. Investopedia has a little blurb on it here: http://www.investopedia.com/terms/c/...fvariation.asp

So why did the Java application call your results only "moderately non-random?" Well it's simple. The application doesn't know if you're an investor or the owner of a ball bearing factory. In one case, the results are awful, and in the other they're good. So maybe they wrote the program (assuming they're using this method) using different levels of COV such as 0.25, 0.50, etc. for their thresholds between interpretations like "moderate", "very", "extremely" or whatever. You might try making up some numbers with very low variance and another set with high variance and see what result you get. This will give you a better feel for how they designed it.

Hi Scott,

WOW, thank you very much for your very enlightening reply. I am not so strong in statistics as you, so I must digest your comments for a while. The numbers I posted were taken from a fund. I took them as example only. My personal numbers are not so good, but they are good in one sense: the slope of the regression line is positive. It is exactly where my doubt about the randomness of my seeming recent progress resides. I will elaborate better before posting. I have run some analysis on my own.

Thanks again for your reply. Your thread is brilliant. People who don't appreciate this stuff are really losing something valuable.

Thanks! Let me know what you come up with, and keep that regression line pointing UP.

Hi Scott,

Here are my weekly returns on equity:

0,03 1,51 6,03 2,20 1,22 0,63 2,34 1,62 0,33 0,83 44,61 1,15 2,35 0,52 1,05 0,48
0,82 6,40 2,62 1,57 0,70 1,00 1,45

This is the plot:

(44.jpg - I couldn't post the image here )

OMG, this is ugly! The 44,61% is a mad experiment I made one day. In fact, it came from a less than one minute trade. I will never do that again, lol. Replaced by a “reasonable” (?) 4,46%, the plot would turn into this:

(4.46.jpg - The same... )

I made A LOT of “improvements” (?) in my modus operandi along the way. The question is: is there statistical evidence of a real progress? May the regression line crossing the zero level be suspected to express the birth of profitabiliy?

I think it is too early to talk about the big goal: consistency. The COV is too high (5,37). I am risking too much for the results obtained so far.

Well, I don’t want to hijack your thread with this little silly doubt of mine. I just thought running this kind of analysis on weekly ROE figures would be a valid way to judge any trading methodology. Do you think it is? Thank you very much for your very insightful comments. Good trading.

P.S.: the results shown come from a standand account I opened 5 months ago. I demoed a lot and traded some mini accounts before. Never blew up an account but had been a net loser for almost two years. I am putting all my heart and soul in making this new account grow. I think there are many improvements to be made, especially in my price action reading skills.

P.S.: what a bad poster I am... If I don't give up trading I will for sure give up posting...

The comment was too funny.

Anyway, your images showed up at the bottom of the post. I had the same problem a while ago because it's not clear on FF how to put images inline. Here's a thread where a couple of us figured out how to do it:

http://www.forexfactory.com/showthread.php?t=53366

On the analysis, first of all don't use COV on this data because the values aren't all positive. What happens when you have both positive and negative values is that the mean will be somewhere in the middle...meaning near zero. So the mean will have a very low magnitude compared to the standard deviation, and since the mean is in the denominator of the COV formula, you get these really high numbers. So use COV for positive values only. That's why you came out with such a high number.

What we CAN still try is the regression line over time as you did. Here's the chart with the R-squared value:



The part of the positive slope that is "explained" solely by the passage of time (your improvements in technique or any other factors) is only around 7% so that's pretty close to random.

However, that doesn't mean that it will REMAIN random, it just means that the data we have so far don't show us much of a correlation. It's very possible that you're right on the verge of everything "coming together" which leads to consistently positive results. A year from now, this chart might show a very non-random increase in performance.

That's the limitation of statistics. They can keep us from seeing things that aren't really there, but they don't show us everything either.