Caution: Math Geek at Work

The only thing I did last week was to get rid of the short silver position. Between that and the fluctuations of my NZD/USD long position the account was down 1.3% for the week.



I'm still in the second phase of my big 3 part research project, looking at reversal patterns now. After 12 more pages of research notes, the best thing I've come up with so far is that when there are two or more consecutive bars with equal or higher highs and the last bar's close is at least 40% of that bar's range away from its high, there's about a 20% chance that we're seeing a significant top. The reverse is true for bottoms. This is for daily bars on EUR/JPY only.

I'm using the statistical concepts of type-I and type-II error (false positives and false negatives) in this search for indicators of bottoms and tops. Even if I don't find any mind blowing predictive patterns, at least I've developed a good new research tool and have a better understanding of what these kind of searches are all about.

To give some flavor for the kind of information I'm able to generate, the topping signal that I described above occurs about 150 times in my dataset of 1400 bars. There are about 70 significant tops in the data, so they happen about 5% of the time (I'm rounding all these numbers off for clarity). Of the 150 signals, 20% are correct, so the signal found about 30 of the tops and missed 40 of them.

So we have this breakdown:

Top present? Yes No

Signal 30 120

No signal 40 1210

False positives = 30/150 = 80% Hit rate = 20%
False negatives = 40/70 = 57% Capture rate = 43%

All of this points out a common tradeoff in trying to find any kind of signal (not just in trading but in medical tests and all other kinds of testing). If you make the test too broad (i.e. a signal exists any time a price bar happens), the capture rate will be very high (low type-II error) but hit rate will be very low (high type-I error). If on the other hand you make the signal too specific (only if conditions A, B, C, D, and E are met), then the hit rate might be high (low type-I error) but the capture rate will be low (high type-II error) meaning that a lot of opportunities will be lost due to the strict signal rules.

Anyway, the research continues. I may try some simple "which way is the market going now" type trades this week, but I don't really have a bread and butter method yet.

I had a random thought about the "right way" to draw support and resistance lines, which led me to a train of thought about how different traders will often have their own personal style and methods when it comes to doing even the most basic things on a chart. Over many years of trading I have seen all kinds of different methods, and each time a trader explains one it always sounds like the most logical, objective self-evident way of doing it and why haven't I always done it this way etc. etc. So I have to be careful about constant method-hopping and just settle on a consistent way that makes sense to me.

Consider trendlines. Back in the 90's I read one of Victor Sperandeo's books and he described the "right way" to draw a trendline. It involved the highest high or lowest low on the chart for the TF you're interested in, and rules about how not to cross through price bars. Then along came someone else who likes to draw trendlines based on the candle bodies but not the wicks. Then along comes Hector (WTB on ForexFactory) who makes the great point that since trendline placement is so arbitrary, why not use a couple of moving averages instead to keep track of the dynamics of the trend? Then we have the Tom DeMark trendlines which are drawn from right to left. And so on....

Same thing with support and resistance. Fib lines? Pivot points? Double or triple tops? How far apart? Pin bars? Confluence of all, some, most or none of these? I saw a good rationale for S/R lines from someone on Skunny's thread (who later decided that thread wasn't for him ) which described support as a point where buyers came in to reverse a decline and vice versa for resistance.

This last idea is what makes the most sense to me because it also involves the idea of larger market participants with orders in at those levels. I just add to it the caveat that the S/R point hasn't yet been violated. So if a buy at a support point were still in profit today, that point is still valid.

To illustrate, I used NZD/USD over the past few months since I have a long term position in that (will Peter Jackson film "The Hobbit" there? ). Anyway, I found eight valid support points and 3 resistance points. I like this method because it's objective and you can see areas of "confluence" without having to search all kinds of different methods for them. They are just areas where several support or resistance points have occurred at price levels close to each other like #6 and #7 on the chart.

To some traders this will seem like the most obvious thing in the world, and to others it will seem like a crazy way of doing it. We each have our own style.

Would it be rude if I asked... where is the discussion of use of 2nd order derivatives??

Not at all!

Welcome twoblink! Gotta love that Dogbert.

You won't find much in the way of analysis (in the mathematical sense of the word meaning smooth, continuous curves, calculus, differential equations, etc.) here. I'm a much bigger fan of discreet mathematics. You're probably familiar with the distinction, but for those who aren't:

http://en.wikipedia.org/wiki/Discreet_math

I've just finished the third week of my "research sabbatical" so I didn't do any trades last week. I'm also going into job hunting mode now since I only have about 5 more months of savings left, so that's becoming more of a priority.

The account is up 2.4% because of the NZD/USD position.



The research is going swimmingly. :

I built a backtesting tool in Excel and am now using it to test entry signals. The tool lets me specify parameters like spread, trailing stop loss amount in pips, and something I call "threshold value" which has to do with defining whether or not a specific bar would have been a good buy/sell opportunity. It assumes a stop and reverse trading method and additions to existing positions on new signals.

The tool doesn't give me "win rates" on individual trades because it's an "always in" method with varying position sizes. However, because I identify all of the good trading opportunity bars in the data, the tool can give me a "hit rate" which shows what percentage of a given signal actually occur at good opportunities. The tool also shows me the equity curve of each signal, including stats like max profit, max loss, average drawdown and max drawdown. The equity curve includes the value of open positions.

I'm pretty confident in the tool because it's a "hard grader." I started testing on the ultra low 10-second bar timeframe, and of course most signals I try turn out to be disasters because of the spread and the tendency for price to revert to the mean at those TFs. After trying a bunch of signals I finally found a fairly simple one that shows a pretty smooth profitable equity curve, which is quite a feat for the 10-second TF!

The signal consists simply of buying when the close of the bar is at least 4 pips below the close of the previous bar and selling when the close is at least 4 pips above the previous close. The trailing stop has to be very wide (essentially non-existent), so positions are closed and reversed only when the opposite signal occurs. By the way, I have found that trailing stops are generally unprofitable at low time frames. I haven't used the tool with my higher TF data yet.

Anyway, the test on my 10-second EUR/JPY data showed a 900+ pip profit over the course of about 2 days. Don't get exited because that represents almost 17,000 continuous 10-second bars of trading back and forth (note to self: add #of trades to backtesting tool stats). So I'm looking at an average of about 9 pips per 170 bars, or about 18 pips/hour with this signal. Also, the signal is based on a test of only this data, so who knows if it will hold up.

The key thing is that I have a nice shiny new tool to test this stuff out quickly. So if a pattern doesn't work for long I can always go in search of a new one. Also, this is only a way of trying to improve my entries, which is maybe 1/4 of what constitutes successful trading. Yep, 25% of trading success is due to entries. Did you know that 76.467% of all statistics are made up right on the spot?

Anyway, once I find some acceptable entry signals for the 10-min and daily time frames I'll (FINALLY) finish up this second phase of my project. The third and last phase is one to which I'm really looking forward. It involves looking at the "price chart inside each candle" and seeing if there are correlations between the price action "inside" one candle and the next.

My trading finger is getting itchy, but after some destabilizing trading activity (the silver trade, trying to get proficient at "rainbow scalping" etc.) I think this break is the best thing. Hopefully over the next week or so I will finish up my research, find a menial, low stress bill-paying job, and get back into the market refreshed and with new tools at my disposal.

Bye for now!

Whew!!! After 24 more pages of research notes and 12 days I've managed to wrap up the second in my three part mega-project on price action and structure. After all that struggle and frustration I managed to create a new backtesting tool and come to a few conclusions. Here is the page from my notes showing the conclusions from this section of the project.

-------------------------------------------------------------------------------------
MICRO PRICE ACTION - SUMMARY OF FINDINGS
-------------------------------------------------------------------------------------

1/13/08 – 0230GMT:


1. Combining a random entry with “good money management” CANNOT result in profitability over any finite trade time. This is actually still a conjecture at this point but it’s based on the “target optimization” test I did on pages 39 and 40.

A more formalized statement of this conjecture is that for any price bar and for any period of N bars following that bar, the probability that price will move to a given target before it moves to a given stop is always less than the risk/reward ratio of that target/stop combination.

For example, if we set a target of +30 pips and a stop of -20 pips, the probability that price will move up 30 pips before it declines by 20 pips is always less than 20/(20+30)=40%. The same happens if we reverse the target and stop. If we set a target at -30 and a stop at +20, the probability that price will decline by 30 pips before it rises by 20 will also be less than 40%. The two probabilities might be 35% for instance, with the remaining 30% probability being that the price will hit neither point during the period.


2. Because of different behavior in different timeframes, no single set of entry rules will work well in different time frames, even for the same pair.


3. The more specific an entry signal is, the more opportunities it will miss. The less specific it is, the more losing signals it will give. This is the classic statistical tradeoff between type-I and type-II errors (statistical specificity vs. statistical power).


4. The usefulness of entry signals will change over time as market behavior changes. Frequent backtesting of signals with fresh recent data and the flexibility to replace outdated signals with better ones are keys to profitable trading.

Because I love the effort on your part, let me help you with your conjectures, as I have been through all of them already.

Your focus on entries, is only partially correct, and I use "partial" very liberally.

The part you are missing is:

The Position Theorem:

A position, good or bad, can ONLY be measured after __BOTH__ and open and a close.

This is what you seem to be lacking in your effort. The EXIT DETERMINES the position. If you have an open position showing +100 pips... so what? It can drop to -200 pips and hit a SL.

Corollary: The EXIT determines the quality of the entry, not the entry.

If the Yen is at 112.00 and you go long, is that a good entry? Who knows? There is no proof it is a good entry. It goes to 113.00, so the 112.00 is a good entry right? WRONG. It's a good entry, only if your exit was 113.00. It might go from 112.00 to 121.00 to 100.00 and if you sold it at 100.00, you are SOL, and everything that happened between the time you entered and the time you exited, means squat.

The math:

Given entry point = X

Given exit point = Y

Profit = Delta(Y,X)

But given only datapoint X, the profit is indeterminant, and thus, the focus on only entry is a fallacy. So the quality of the entry point is determined by 2 things:

1) The distance of the exit point from it
2) The direction of the exit point from it

Given Y = f(X) is what we expect, but the reality is:

quality of X = f(Y)

To make an attempt at your conjectures:

1) "Random Entry + MM" is not a determinable item, since it's missing exits. Random Exit or deterministic exits? Without talking about the quality of the exits, no entry can be deemed good or bad.

2) Timeframes are fractal in nature; and the shorter the timeframe, the higher the signal-to-noise ratio. I cannot say that no system works for all of them, but good systems should be relatively timeframe agnostic, and should work for almost all timeframes.

3) The more specific an entry signal, the more items it filters out, and so probability of its occurrence goes down. Again, you seem to be focusing on the determinant variable, the exit.

4) Backtesting proves nothing, so heavy dependency on it is fairly fatal. Beware something called "backtest shaping" in which you work your system so its profitable in the past, which means nothing about the profitability of it in the future.

Good luck on your research. I encourage you to focus on the relationship between the entry and the exit, this is paramount to the math of it all. The obsessive focus on the entry will not get you to where you want to go. It is the obsessive focus on the exit..

And I'll shut up now...

Nice post twoblink! I have been trading like that without even realising it, i.e. the entry, while I looked for a better one was only a small part as I had my targets set before entry. Sometimes you win, sometimes you need to re-enter with another unit or two and adjust your exit or stick with it depending on PA, MM is then my highest priority.

Hi Cap', how's it going?

I think what twoblink is trying to say is that you would probably be better off putting your excellent math ability to use with profitable MM strategies rather than market prediction/analysis. Even the weather forecasters can't get close and they use some wicked algorithms together with past data and conditions, you'd think they could get closer with the forecast than we could with the market!

Play with the numbers so that you can be profitable in both directions, it is possible. Fti hasn't commented on this post yet but have a look, Zoran has done some ground work here that's very enlightening -

If there's one thing we do know is that price oscillates to and from a mean/median value, that is, it continually swings, this is key!
If we can organise our position size to capitalise on these swings 'when' they occur - not if - then you have a safe trading strategy IMO.

This is what I'm working on at the moment, I'm trying to get my MM figures in line to suit my account size so I can ride the swings - good and bad - and make small amounts often rather than kill the market on one trade and be killed the next.

Cheers,
Mick.

P.S. let me know if you are keen to work on this, I'll lend a hand where I can

Hi twoblink,

First, let me say that I appreciate your kind words and encouragement. I have read through some of your (many!) journals in the past and found them fascinating.

I'm going to write a longer post to address the rest of your comments (later on tonight) but I wanted to address this one by itself for two reasons. First, because it's easy to address, and secondly because this post may break a rule about links so I want to keep it short in case admin has to delete it.

I agree to some extent with your view of backtesting and its pitfalls. What you call "backtest shaping" is probably what I refer to as either "overfitting" or the "multiple hypothesis problem." I've been aware of this issue since it bit "The Motley Fool" in the butt with their "Foolish Four" back in the late 90's. You may be interested in a more comprehensive article on this here:

http://market-geeks.com/articles/002...Datamining.php

I'm the author.

(NOTE TO ADMIN: The above link goes to a site that I own. There's nothing for sale there, but it's ad supported. If the link violates the FF rules, please delete this post. That's why I made it short. I just didn't want to spend a lot of time writing about an issue that I've already addressed a bunch of times in the past, when I could just as easily link to an article about it.)


twoblink,

I will address the meat of your post a little later tonight. You make many points that I agree with, but it may not have been clear in my earlier post what I'm saying. I'm not disregarding exits at all. I love exits!! So stay tuned; I'm off for a brisk walk...

Hi Mick!

I somehow missed this second post of yours when I wrote my last one. Anyway, I think I get what you and twoblink are saying, but I may not be clear on what I'm saying. I'm going to put up two more posts to try to clarify. These are absolutely key issues to traders, and I want to make sure we're on the same sheet of music. I think we may all actually agree, but maybe not.

One thing I'll mention right away is that I don't think there is any such thing as a "profitable money management strategy" in a vacuum. In other words, the only way to make a MM strategy successful is to have some actual statistical edge in determining market direction. Heads and I go long, tails I go short will not work no matter what MM strategy we use. If it did, we would be able to make money playing roullette with a good MM strategy.

Some may say that a martingale will always come out ahead, but that's not true for any finite bank. The bank would have to be infinite to achieve a break-even expectancy there too. There must be proofs of this all around the net so I'm not going to reproduce one here.

I want to be very clear about my view on this subject.

Signals matter.

This isn't just a guess. I'm basing it on empirical evidence from testing. I'll post more about that in the next two posts. Stand by!

I agree, but I think it's more important what you do 'when' you get the signal, if the signal turns out to be false, what are your options? I can think of only 2, either sell at a loss or wait for the next signal and fight for your position.

The trick is to have the MM strategy worked out before the trade so as to limit your exposure on the downswings (even extreme swings) but be profitable with the upswings. Would you agree that on average the daily price movement is around 100+/- pips? There is only one way to capture the swings within this range - be 'in' the market when they happen. If you play the stop loss game you will find yourself out of the market more than in it, then you have compounding working against you.
At least if you're 'in' the market you can then use your signals or profit targets for profitable exits

Hi again twoblink!

I'm going to divide this into two posts to try to clarify what I'm saying. In this post I'll discuss the importance of entries vs. exits. In the next I'll give a full explanation of the conjecture I made in conclusion #1.

I don't have a focus on only entries, but the confusion is my fault because I kept saying "entry signal" in my original post. This is why I'm glad you posted your thoughts because it motivates me to express myself more clearly even in my own mind.

Let me clear this up, because I think we agree on this point. This is a point that I have seen Merlin try to make on at least one occasion, and a lot of people just don't get it.

Entries and exits are equally important.

All trading markets (and the universe as a whole I think) is a study in symmetry. There are always pairs of opposites which always balance each other at some level. Long and short. Calls and puts. Entry and Exit. Advantage and disadvantage. Trend and range. Risk and reward.

I know some traders think that entries are the key while others swear by good exit strategies, but this has never made sense to me. Here is how I see it, at the risk of sounding like Yoda.

There are no entry signals.
There are no exit signals.

There are only long signals and short signals.

Unfortunately, I keep saying "entry signals" and it makes it sound like I'm concentrating on just entries for some odd reason. I should be saying "long signals" and "short signals."

A few arguments on why I believe entries and exits are symmetrical.

1. There are only six possible kinds of transformations a trader can make to a position:

Flat to long (entry)
Flat to short (entry)
Long to flat (exit)
Long to short (exit & entry)
Short to flat (exit)
Short to long (exit & entry)

Three of these involve buying and three involve selling. Three involve entries and three involve exits. Symmetry.


2. The arguments for the "importance" of each are symmetrical.

Consider the following arguments:

"Entries are more important because if you have a great entry (such as buying at a bottom) even a terrible exit would be profitable. Also, if you have a terrible entry (buying at a top), the best exit in the world won't help you avoid a loss."

"Exits are more important because if you have a great exit (closing a short at a bottom) even a terrible entry would be profitable. Also, if you have a terrible exit (closing a short at a top), the best entry in the world won't help you avoid a loss."

Note that these arguments are exactly the same except that I've switched the words "entry" and "exit" around. Symmetry.


3. Risk is neither created nor destroyed; it's just transferred.

A common argument I hear about the importance of exits or entries is that with an entry you are taking on the risk of a position while an exit involves the removal of risk. So they must be different.

There are a couple of counter arguments to this.

First of all, there is as much risk to profitability in closing positions as there is in opening them. If this sounds strange to you, consider the common advice to "let profits run." Failure to let profits run can hurt an account just as much as failing to cut losses short. In fact, failing to let profits run can cost you a lot more, since you can only lose a set amount, but the amount of lost profit opportunity is potentially unlimited. And how do you fail to let profits run? By exiting positions. So the risk of exits is not less than the risk of entries. They both involve acting on an expected market direction, which may be right or wrong. Symmetry.

The second counter argument to this notion of risk is a bit abstract, but it's fun. Suppose we allow the idea that closing a position reduces risk in your account (which it does by a certain definition). Did that risk just disappear? No. One of several things happened. First of all, there was someone on the other side of your transaction. If you close your long yen position by selling, someone else buys those yen from you. They may be opening a long yen position, so now the risk has just moved from you to the other trader.

"Aha!" I hear you say. "But what if the other trader is closing a short position? Then we're both closing positions!" Correct. This is similar to the concept of "open interest" in the options market. If you sell to close and the other person buys to close, then the open interest in yen in the FOREX markets has just declined. So did the risk disappear? No. It just moved outside the FOREX market.

Consider why there IS a FOREX market. It's to allow companies in the real economy to move risk to someone else. If Honda is shipping a bunch of cars to the U.S. for payment in dollars to be received next month, they don't want to deal with the risk of currency fluctuations so they enter a hedge against their exposure. Someone in the FOREX market takes the other side of this, and thus the risk. This increases the "open interest" in yen on the FOREX markets. When two traders close offsetting positions, this reduces the open interest, which means that somewhere some car company or whatever has reduced its hedge position. So the risk didn't disappear, it moved from the FOREX markets to some commercial enterprise in the general economy.

"But wait!" you say. "Sure, if open interest disappears from the FOREX market then it's possible that some commercial player is taking on more risk because their hedge is reduced. But what if they've reduced their exposure as well? Surely the risk has now disappeared." Sounds good, but not so fast. Sure, let's say that a lot of traders close their yen positions, reducing risk in the FOREX markets, and that risk does not manifest itself in the commercial market because they have less currency exposure due to operations. The only way this can happen is if their operations are reduced. In other words, if Honda is selling less cars, then they don't have as much currency exposure so they don't hedge as much so there are less yen positions in the market. But don't we now have a new risk? The risk of economic slowdown? Recession? Unemployment? Higher divorce rates? More crime? Social unrest? Revolution? LOL.

You see, the risk never disappears. It just moves from one trader to another, or from one market to another, or from one form (financial) to another (economic or social).

The great symmetrical balance of the universe is always maintained.

I just finished my (longer than expected) post about why I think exits and entries are of exactly equal importance. Before I go on to the next post about my "price behavior conjecture" I'll answer this one. You guys are making me work tonight!

Ok, first of all the part that I bolded jumped right out at me. I think this is important. How do you know if the signal has turned out to be false? If you answer, "well, I would know because of XYZ." Then think about this. Isn't XYZ a signal?



I think the "stop loss" game is something we have discussed before, and we agree on this. A stop loss is not an exit strategy. Stops should be used for emergencies (my system is down, the power went out, my shoe is on fire . You still believe this I assume. So do I. I use signals to go long or short, to enter or exit.

As a matter of fact, when I test a signal with the backtesting tool I made, the signals almost always perform best when I set the stop to like 8000 pips or something (in essence removing it). This is because the tool assumes an "always in" method which swithches from long or short only when a new signal occurs.



But I get the impression that you guys are assuming I'm doing something I'm not.

I do NOT consider entries to be more important than entries or vice-versa
I do NOT use stops or TPs as exit strategies. I don't use TPs at all actually.

Maybe what's confusing is the difference between my research techniques and my trading methods (which are still in development). These can be TOTALLY different. For example, I may take a dataset and test it using various combinations of stop loss and TP values. That doesn't mean I trade that way. It just means that I'm using that as a tool to study market behavior.

I think when it comes to trading methods, we are in the same ballpark. Here are some of the ideas I want to incorporate into my overall method:

1. More frequent trades at lower TFs to allow me to generate continuous performance data. This is a huge confidence builder.

2. Scaling into positions when they are moving in my favor.

3. The use of signals and only signals for entries and exits.

4. A method of managing a position from a lower TF to a higher one in order to capture the potential for long term moves without being shaken out by noise.

So I envision a method where I generally trade in low TFs, but do not necessarily close out profitable positions at the end of a session. These positions may develope into long term, larger profitable positions. Meanwhile, as I manage those longer term positions, I continue to scalp for new opportunities inside the candles of other traders.

Ok, I'm actually going to have dinner first.

I'll do the post about the "negative expectancy market behavior conjecture" a little later.

No prob's, love your work

Looking forward to the next installment.

wow, this thread is lovely.
just reading with much dedication your posts.

please keep it up, a great source of probability info.

Welcome acidguy

Thanks! This post will involve stats as well, but I don't know how many people are going to be happy about it. The news is not good.


Ok, twoblink and Mick and anyone else who noted my first conclusion in post #66, here is a more detailed explanation.

Introduction

I started a thread a while ago called "Expectancy is always zero" where I claimed that in the absence of an edge, expectancy should always be about zero. My conclusion in that thread was based on an entirely analytical model. In other words, I didn't go and try to find actual evidence in the market to back it up, I just used a fairly simple logical argument with a few assumptions.

During the research project that I'm currently working on, I encountered some very compelling empirical evidence of the same thing. In fact, I found that (rather dishearteningly) without an edge, the expectancy of any given risk management (stop and target) combination is not only zero but quite a bit below zero! In one of Jack Schwager's Market Wizards books, one of the traders has a theory that "the market will do whatever hurts the greatest amount of traders" or something to that effect. Well I'm finding measurable evidence of exactly that kind of behavior.

I bet that there are market researchers who are well aware of this, so I'm not claiming that it's any great ground-breaking discovery. However, there are probably traders here that are going to freak out and want to argue about the conclusion. To any of you who are inclined to do so, I will give you an iron-clad way to prove that this conjecture is wrong. Ready?

Find a single counterexample.


It's kind of like Fermat's last theorem. Everyone was pretty sure it was right, but no one could actually prove it for centuries (a guy named Wiley cracked it in the 90's I think). But if anyone had found just a single counterexample, that would have settled the question. Of course no one ever could because the theorem was right.

So now I'll explain what the conjecture is in more detail, give an example from my research, and describe what a counterexample would look like.


The "Negative Expectancy Conjecture"

The very informal statement of the conjecture is basically that the market will screw you no matter what you do, unless you have some reliable edge. But let's get more formal than THAT shall we?



1. Start with a dataset of at least 1000 price bars or so. Any pair will do, and any time frame will do.

2. Pick a "test period" consisting of N bars where "N" is no more than 1 or 2% of the length of the dataset. I used 30 bars, but if I'm right it doesn't matter. This is a "look-ahead period" a "test window", a "trade window" or whatever you want to call it. The period just has to be small enough so that it doesn't "use up" too many of the bars in the data.

3. Pick a risk management method consisting of two values: The number of pips you want to use for a stop, and the number you want to use as a target (NOTE TO ANYONE WHO'S FREAKING OUT: No I don't trade by picking a set stop and TP based on an absolute pip number like this. This is a research technique only). You can choose from any combination on the risk/reward spectrum; tight stop, wide target, tight target wide stop, equal, whatever. Use a stop of 10000 pips and a target of 2 pips or a stop of 10 pips and a target of 800 pips. Or use something common like 50 pips and 100 pips (or whatver is appropriate for the time frame and pair). It isn't going to matter what you choose. That's the point.

4. Now let's list our variables.

N = the length of the trading window (the maximum length of any trade) in bars.

G = the take-profit distance from entry in pips (the potential gain)

R = the stop-loss distance from entry in pips (the risk)

LWR = long win rate; you will find this by testing the data. It is the percentage of long trades that hit the target before they hit the stop.

SWR = short win rate; you will find this by testing the data. It is the percentage of short trades that hit the target before they hit the stop.


5. So we have our 5 variables; N, G, R, LWR and SWR. The first three we chose ourselves and the other two we will discover from the data.

6. Hopefully everyone knows the relationship between win rate and risk/reward. Basically, to be profitable, win rate must be greater than risk/(risk + reward). For example if our stop is 40 pips and our target is 60 pips, our win rate would have to be at least 40/(40+60) = 40%. This is like trader math 101, so if this is confusing, take two aspirin, back slowly away from the thread and do a search for "what does risk reward mean" or something like that.

7. OK, let's do some testing! (I'm not really suggesting you do this unless you really want to try to find a counterexample. I'm just phrasing it this way for dramatic purposes). We take our several thousand price bars and dump them into an Excel spreadsheet aong with our choices for N, G and R. Then we set up a column for buys and another for sells. We're going to try buying at the close of every price bar and see how that goes, then we'll do the same with selling. For each price bar in the data, you set up Excel with a formula that looks forward by N bars (the "trade period") and checks to see whether the stop was hit first or if the target was hit first (or neither). If the target gets hit before the stop, then we have a WEINER!! Err.. I mean a winner. Mark that price bar by putting a "1" in the column at that point. Otherwise leave it blank. (By the way, if anyone wants to actually do this, I can help you set it up in Excel; you have to use the MATCH function and some other mildly tricky tricks unless you know how to use VBA which I don't yet).

8. Whew! Anyway, now what you end up with is a count of how many times your risk management strategy was a winner. You have this for both long and short entries at every bar. Divide these by your total number of bars and you have your LWR and SWR numbers. Voila!

9. Here is the formal statement of my conjecture: For ANY given set of price bars, for ANY values of N, G and R, the following will always be true:
LWR + SWR < 2R/(G+R)

10. Here's an example. Suppose you are looking at EUR/JPY hourly bars. You set your stop at 50 pips and your TP at 50 pips. Your breakeven win rate is 50%. When you test both longs and shorts for every bar, you might find that the win rate for longs is 42% and the win rate for shorts is 37%. So if you went long at every bar, you would lose money, and if you went short at every bar you would still lose money.

11. Why am I adding the win rates and using a factor of 2? This is because in a dataset from a strongly trending period it is possible that one of the directions will have been profitable. But this will cause the other direction's win rate to be abysmal. For example, using daily bars from EUR/USD over the past four years or so, with a stop of 100 pips and a TP of 200 pips, your breakeven rate would have to be 1/3. When you run the test, you would probably find something like LWR=40% and SWR= 20%. So long positions would have made money but short positions would have more than wiped out the gains.


This sucks! Do I have evidence of this???

Yes I do. Not much because I was only working with one pair, EUR/JPY. But sometimes you find something and it just LOOKS like it's got to be true generally. This is one of those cases. I hope I'm wrong but I don't think so. If someone could actually find a counterexample I'd love it.

Anyway, here are three charts from 10-second data, 10-minute data and daily data. They show the win rates for different numbers of pips (always in a 1:1 risk/reward ratio but I checked others too), and you can see how they max out at less than 50%. Even the daily, which comes close to a breakeven win rate on buys, has an awful win rate for sells.







This post is really long, so I'll put my final conclusions in the next one.

That's my conclusion from all this. Since risk/money management alone will always yield negative expectancy in the market, it is imperative that a trader find long and short signals that actually work. I'm not using the term "entry signal" anymore because I know twoblink's Dogbert avatar would probably leap off my screen and bite my nose off! :

Anyway, this stuff about being able to flip a coin and still be profitable with good money management is nonsense (by the way, I don't think Van Tharpe claimed that; he was talking about one way trades in a trending market). Anyone who believes otherwise is NOT invited to come and argue about it here, but they ARE invited to show me a counterexample of the conjecture at the end of the last post. Don't give me arguments. Show me evidence.

Note also that I am NOT saying that the markets are random. Let me say that again. I am not a random walker. In fact, I think what I'm talking about here is actually very NON-RANDOM behavior. If the market were truly random, the expectancy of any risk management strategy would be just about zero on average. But it's not. It's a lot lower.

Why? Do I think the market is a big bad evil concious entity that's out to screw me and all my fellow traders. Ummmm....no. I think it's an emergent property of price movement that has something to do with the irrational behavior that many participants bring to the market.

Can I stop typing now??

Because of the bid/ask spread, you will always enter a position with a negative expectancy.. unless your bid/ask is 0. So while your conjecture is true in theory, it's not true in reality.

Also, you might want to revisit your theories on pyramiding and also on entries vs exits. I agree that if you look at it from a purely order form format, entries and exits are the same thing; but just know that in order for a debt to be considered "settled" then you require an entry/exit pair. it is the "pairness" that is of importance.

I trade a system in which there are no TP's. The reason being, TP's violate what I believe to be fundamentals of trading.

If the trade is good, then you add to it (average up!) If the trade is bad, you close it out (quick to take your losses), if it's 50/50, maybe you let it play out. At no point do I see a TP as a functional strategy. And in fact, the very notion of TP almost guarantees that your expectancy is negative.

Example:

TP = +25 pips
SL = -25 pips
B/A spread = 3

When we enter a position, assuming we flip a coin and decide the direction; we have the same odds in either direction, and if we set the TP and SL to be the same, we assumes a push.

BUT, because our BAS is 3 pips, 3/25 = -12% inherited expectancy.

That's a RIDICULOUS handicap to overcome. Even roulette with 0,00 is only -5.26%.

That is why almost everybody will lose in the game. So I totally disagree with the theory that the market does whatever hurts the most people; simply that with the current structure, unless your system posts a ridiculous advantage to break out of the BAS inherited negative expectancy, you never will win.

That said, we can now discuss timelines.

Given the average bar to be 7 pips on the 15M timeframe, and given bid/ask to be 3 pips, we then see that BAS is 42% of a bar in 15M timeframe. Given trading that happens in 15M, then you have a ridiculous amount of movement you need.. If the average coverage and overlap of a bar compared to the previous bar is 60%, then to move 3 pips away permanently, requires at least 3 bars; which means that if you are trading 15M, the first one hour of trade is required JUST to cover your BAS. If your average exit distance is 8 bars away, then you need an expectancy close to 2.0 to BREAK EVEN on a 15M chart. That's why people who trade lower timeframes get screwed.

My students who work at the big banks, trading $300M blocks.. their spreads are 0.5 or 0.25 pips... So they can cover those easily. If you are using a regular broker with chump change, you can't overcome 3 pips a hit every time you enter..

Your theories are right, but the system is not set up to support your theories... Because in theory, because FX can't really go to ZERO, then using a Martingale (in theory) should make you richer than Bill Gates.. but the rules are set up to prevent theory from becoming reality..