ETMA_The Evolution

Position Sizing Strategies

Position Sizing

What is it?

Money management is a very confusing term. When we looked it up on the Internet, the only people who used it the way Van uses it were professional gamblers. Money management as defined by other people seems to mean controlling your personal spending, or giving your money to others for them to manage, or risk control, or making the maximum gain—the list goes on and on.

To avoid confusion, Van elected to call money management "position sizing." Position sizing strategies answer the question, "how big should I make my position for any one trade?"

Position sizing is the part of your trading system that tells you “how much.”

Once a trader has established the discipline to keep their stop loss on every trade, without question the most important area of trading is position sizing. Most people in mainstream Wall Street totally ignore this concept, but Van believes that position sizing and psychology count for more than 90% of total performance (or 100% if every aspect of trading is deemed to be psychological).

Position sizing is the part of your trading system that tells you how many shares or contracts to take per trade. Poor position sizing is the reason behind almost every instance of account blowouts. Preservation of capital is the most important concept for those who want to stay in the trading game for the long haul.

Why is Position Sizing so Important?

Imagine that you had $100,000 to trade. Many traders (or investors, or gamblers) would just jump right in and decide to invest a substantial amount of this equity ($25,000 maybe?) on one particular stock because they were told about it by a friend, or because it sounded like a great buy. Perhaps they decide to buy 10,000 shares of a single stock because the price is only $4.00 a share (or $40,000).

They have no pre-planned exit or idea about when they are going to get out of the trade if it happens to go against them and they are subsequently risking a LOT of their initial $100,000 unnecessarily.

To prove this point, we’ve done many simulated games in which everyone gets the same trades. At the end of the simulation, 100 different people will have 100 different final equities, with the exception of those who go bankrupt. And after 50 trades, we’ve seen final equities that range from bankrupt to $13 million—yet everyone started with $100,000, and they all got the same trades.

Position sizing and individual psychology were the only two factors involved—which shows just how important position sizing really is.

How Does it Work?

Suppose you have a portfolio of $100,000 and you decide to only risk 1% on a trading idea that you have. You are risking $1,000.

This is the amount RISKED on the trading idea (trade) and should not be confused with the amount that you actually INVESTED in the trading idea (trade).

So that’s your limit. You decide to RISK only $1,000 on any given idea (trade). You can risk more as your portfolio gets bigger, but you only risk 1% of your total portfolio on any one idea.

Now suppose you decide to buy a stock that was priced at $23.00 per share and you place a protective stop at 25% away, which means that if the price drops to $17.25, you are out of the trade. Your risk per share in dollar terms is $5.75. Since your risk is $5.75, you divide this value into your 1% allocation ($1,000) and find that you are able to purchase 173 shares, rounded down to the nearest share.

Work it out for yourself so you understand that if you get stopped out of this stock (i.e., the stock drops 25%), you will only lose $1,000, or 1% of your portfolio. No one likes to lose, but if you didn't have the stop and the stock dropped to $10.00 per share, your capital would begin to vanish quickly.

Another thing to notice is that you will be purchasing about $4,000 worth of stock. Again, work it out for yourself. Multiply 173 shares by the purchase price of $23.00 per share and you’ll get $3,979. Add commissions and that number ends up being about $4,000.

Thus, you are purchasing $4,000 worth of stock, but you are only risking $1,000, or 1% of your portfolio.

And since you are using 4% of your portfolio to buy the stock ($4,000), you can buy a total of 25 stocks without using any borrowing power or margin, as the stockbrokers call it.

This may not sound as “sexy” as putting a substantial amount of money in one stock that “takes off,” but that strategy is a recipe for disaster and rarely happens. You should leave it on the gambling tables in Las Vegas where it belongs.

Protecting your initial capital by employing effective position sizing strategies is vital if you want to trade and stay in the markets over the long term.

Van believes that people who understand position sizing and have a reasonably good system can usually meet their objectives through developing the right position sizing strategy.

Position Sizing—How Much is Enough?

Start small. So many traders who trade a new strategy start by immediately risking the full amount. The most frequent reason given is that they don’t want to “miss out” on that big trade or long winning streak that could be just around the corner. The problem is that most traders have a much greater chance of losing than they do of winning while they learn the intricacies of trading the new strategy. It's best to start small (very small) and minimize the “tuition paid” to learn the new strategy. Don’t worry about transactions costs (such as commissions), just worry about learning to trade the strategy and follow the process. Once you’ve proven that you can consistently and profitably trade the strategy over a meaningful period of time (months, not days), you can begin to ramp up your position sizing strategies.

Manage losing streaks. Make sure that your position sizing algorithm helps you reduce the position size when your account equity is dropping. You need to have objective and systematic ways of avoiding the “gambler’s fallacy.” The gambler’s fallacy can be paraphrased like this: after a losing streak, the next bet has a better chance of being a winner. If that's your belief, you'll be tempted to increase your position size when you shouldn’t.

Don’t meet time-based profit goals by increasing your position size. All too often, traders approach the end of the month or the end of the quarter and say, “I promised myself that I would make “X” dollars by the end of this period. The only way I can make my goal is to double (or triple, or worse) my position size. This thought process has led to many huge losses. Stick to your position sizing plan!

How to measure a system's edge

Many traders and authors out there constantly say things like "You need a system with positive edge", "You need to trade with odds on your side". But very few people make a more serious effort at going deeper. What does it mean to have a positive edge? and more importantly how do we measure and mathematically demonstrate that a given strategy has a positive edge?

Well, in today's post I want to address this subject by specifically talking about how to measure the edge of a given entry logic. I will use the Forex markets as I find it easy to program routines and test them on the Metatrader 4 platform. A very popular tool that's also freely available to everyone.

But first, let's define a couple of concepts that will be important:

Maximum Favorable Excursion (MFE): This statistic measures the largest temporary profit that a trade had during the whole time it was open. That is, if you entered a trade based on some logic, and you closed the trade x number of bars later, MFE measures the most favorable balance that the trade had during those x bars.

Maximum Adverse Excursion (MAE): MAE measures the largest temporary loss of trade during all the time it was open. That is, if you entered a trade based on some logic, and you closed the trade x number of bars later, MAE measures the most negative balance that the trade showed during all that time it was open.

Let's say for example that you enter a Long (BUY) order on EURUSD at 1.3000.
Your trade goes down to 1.2980, that is 20 pips against you, but then it reverses and goes up to 1.3050.
Now it is 50 pips in your favor. You decide to stay in the position.
A few minutes later EURUSD drops to 1.3040 and you decide to exit for a profit.

As a result, you had a profitable trade that yielded +40 pips, but your Maximum Favorable Excursion (MFE) was 50 pips. That is the most the trade went in your favor while it was open. On the other hand, the trade presented a Maximum Adverse Excursion (MAE) of 20 pips, that is the worst this position was, got to be 20 pips against you.

In order to analyze and quantify the edge of your entry logic, you need to calculate the MFE and MAE for as many past trades as possible. All the entries of course based on the same entry logic you are trying to evaluate.

Finally you calculate the average of all the MFE values and the average of all the MAE values. If the average MFE is greater than the average MAE, then the entry has a positive edge. The greater the MFE in respect with the MAE, the more pronounced and favorable the edge of your entry logic. This is the basis of what is called a Mathematical Expectancy Analysis.

Important: When you do a Mathematical Expectancy analysis of an entry logic, you are not evaluating position sizing, or exit logic or anything. You just determine what would have been the entry point and direction of a trade, and then you calculate the MFE and MAE a number of bars later. If you want your study to be more thorough you calculate the MFE and MAE 10 bars after the entry, 15 bars after the entry, and 20 bars after the entry. Or any number of bars for that matter, and that will show you whether your edge is more significant right after entering the position, or if it is expressed after a while being in the position.

Let's say I have a system with an entry logic that after 10 bars provides an average MFE of 50 pips, and an average MAE of 40 pips. And let's say the study was carried out for a 10 year period during which the entry logic materialized 1000 times. Well, this is a good candidate, and apparently an entry with a positive edge. Judging by the MFE and MAE values alone, you can design a simple exit. If you put your Stop Loss at 45 pips, that is five pips beyond the Maximum Adverse Excursion, and Target Profit also at 45 pips, that is 5 pips below the Maximum Favorable Excursion, then on average this system is bound to reach Target Profit more often that it reaches Stop Loss, and over time it should result in a growing equity curve.

Now, in terms of system design, you should never define a static, hard number of pips as target or stop loss. The reason is that over time, the volatility of a currency pair might and will change. For example, maybe the EURUSD usually moves 120 pips a day today, but in 10 years, days of 200 pips could become the norm. Nobody knows. That's why it is dangerous to set TP and SL with hard numbers of pips assuming the currency will be as volatile in the future as it is right now, or as it has been in the past. You need to determine you targets and profits based on the current volatility, and your Mathematical Expectancy Analysis, should also be done using a measure of volatility rather than hard numbers of pips.

How to include volatility in your Analysis.

One of the most efficient ways to measure the distances is to use a percentage of the Average True Range (ATR) to calculate your MFE and MAE, and likewise, your system would determine Target Points and Stop Loss levels dynamically based on entry price plus/minus an appropriate percentage of the Average True Range that is beneficial according to the Mathematical Expectancy Analysis.

The Average True Range measures the average size of the most recent bars in history. The usual configuration is the last 14 bars.

Now, if a trade moves 50 pips in your favor, when the Average True Range at the time was 80 pips, you wont report a MFE of 50 pips, instead you will report a MFE of 62.5% of the ATR.

Now, you run your analysis for 10 years again and you obtain that your entry logic has an average MEF of 60% of the ATR, and an average MAE of 40% of the ATR for all the entries after 15 bars.

Well, at this point you can determine that if you put your Targets not 60% but a little below, say 55% of the ATR away from the entry price, and Stop Losses 45% of the ATR away from the entry, your system is bound to hit TP more often than SL and also your winners will be bigger in this case, as the TPs are larger than the SLs. When the entry logic presents itself your system verifies the value of the current ATR and calculates the number of pips necessary for TP and SL. In this case let's suppose we have a signal to go long, and current ATR is 100 pips. Well the Target Point will be 55 pips above the current entry price (55% of ATR) and the Stop Loss should be set 45 pips below entry price (45% of ATR). Obviously, for other trades, the number of pips for TP and SL will be different because the numbers will always be calculated based on the volatility at the moment, reflected by the current ATR.

Well, I hope this explains part of the mystery of the phrase: "you need a system with a positive edge". It took me a while to find information about it and a lot of reading to grasp the concepts and put the different pieces together.

In future articles I will evaluate and discuss whether an entry based on some indicator's behavior has a positive edge or not. I will begin by analyzing the MACD Divergence Indicator built by me a few months ago. I will demonstrate whether it is possible to create a system with a positive edge, based only on MACD Divergences, and I will also evaluate which MACD Divergences are better to trade,Hidden or Classical Divergences, or whether they are useless and do not offer a positive edge over a significant number of trades.

The Lazy Trader
A site to discuss Options trading, Forex and Long Term Investing.

An expectancy analysis of Regular MACD Divergences for the EURUSD currency pair

This article is a study about the effectiveness of trading Classical MACD Divergences on the EURUSD currency pair. My goal is to evaluate whether Classical MACD Divergences offer and edge and to somehow quantify the edge of the indicator that could lead to the development of likely long term profitable automated strategies.

A Classical Divergence or Regular Divergence is the one where price makes a higher high but the indicator makes a lower high, or when price makes a lower low and the indicator makes a higher low. For more information visit http://www.babypips.com/school/regular-divergence.html.

I will be making use of the MACD Divergence Indicator implemented by me a few months ago.

Before going any further, I want to alert you that I will use some terminology such as the Maximum Favorable Excursion (MFE) and the Maximum Adverse Excursion (MAE). Please read the article How to measure a system's edge in order to understand the study presented here.

As explained in that article, the idea is to simulate entries on every regular divergence signal that took place, and evaluate the MFE and the MAE over a number of bars later. If, over different period lengths after the entries the MFE is greater than the MAE on average for both long and short trades, then it can be said that the strategy of using entries based on Classical/Regular MACD Divergences has a positive edge that can be exploited and result in an automated system with a positive mathematical expectancy and likely long term profitable.

The study was made from January 1, 2000 to December 31, 2009. That's ten years worth of data. The time frame used was H1, that is one hour bars. The data set was obtained from Alpari UK by direct contact with the broker. That is, this is not the free data downloaded from the Meta Quotes servers which is known to have problems such as holes of several days, sometimes months with no candles, candles with only one tick of data etc.

There was a total of 1434 MACD Classical Divergences detected in the H1 time frame. 682 of them were bullish divergences and 752 were bearish divergences. Now let's see the MFE and the MAE for different numbers of bars after the entries.

5 bars after entry
Buy trades MFE = 25.2% of the Daily ATR
Buy trades MAE = 29.0% of the Daily ATR
Sell trades MFE = 27.8% of the Daily ATR
Sell trades MAE = 26.1% of the Daily ATR

10 bars after entry
Buy trades MFE = 33.8% of the Daily ATR
Buy trades MAE = 35.3% of the Daily ATR
Sell trades MFE = 37.3% of the Daily ATR
Sell trades MAE = 34.8% of the Daily ATR

15 bars after entry
Buy trades MFE = 41.2% of the Daily ATR
Buy trades MAE = 40.4% of the Daily ATR
Sell trades MFE = 42.9% of the Daily ATR
Sell trades MAE = 39.9% of the Daily ATR

20 bars after entry
Buy trades MFE = 47.7% of the Daily ATR
Buy trades MAE = 46.4% of the Daily ATR
Sell trades MFE = 49.8% of the Daily ATR
Sell trades MAE = 45.4% of the Daily ATR

25 bars after entry
Buy trades MFE = 54.6% of the Daily ATR
Buy trades MAE = 53.2% of the Daily ATR
Sell trades MFE = 55.5% of the Daily ATR
Sell trades MAE = 53.0% of the Daily ATR

Pretty interesting results. As you can see, short trades offered a positive edge over the whole spectrum. Long trades didn't offer an edge early after the entries, but started to offer an edge 15 bars and more after the entry. Overall, Classical MACD Divergences seem to offer a positive edge. This edge is not shown immediately after the entries but a little while after: 15 hours and more in the position. It can also be said that it is a small edge, as the MFE is only slightly greater than the MAE around 3% greater.

Looking at the 15 bars study, we could design a very simple strategy without any optimization. By simply trading all the signals, using as Target Profit a distance equivalent to 41% of the Daily ATR, and a Stop Loss of also 41% of the ATR, we could create a system that will hit TP more often then SL, resulting in a profitable strategy. The strategy would automatically be adjusted to current volatility by not having hard numbers of pips set as TP or SL, but always calculating them on the fly based on current volatility reflected by the Average True Range (ATR).

A simulation using such a strategy was made on the H1 time frame, using a fixed spread of 2.0 pips, which is an unfavorable spread compared to what is mostly offered out there by the majority of brokers today. This is a necessity so that we don't deceive ourselves using very favorable spreads that might not be available under real trading conditions.

A risk of 1% of the capital per trade was used:

(Click on image to enlarge)
http://3.bp.blogspot.com/-OJkrHdqUoQ...uity-Curve.PNG

(Click on image to enlarge)
http://2.bp.blogspot.com/-xPjVqxHIQ8...-Draw-Down.PNG

The capital grows 74.67% over ten years, and it does so at the cost of a maximal draw down of 27.98%. Nothing spectacular. The equity curve is not soft and smooth, but keep in mind this is a very raw version of the system. The edge exploited by trading all the signals is very small because the average MFE is only slightly greater than the average MAE, less than 3% greater. So, it is a small edge, which can obviously disappear with ease if the behavior of the currency changes slightly in the future. It is not advisable to trade based on such a small edge. If we could get a significantly greater MFE, let's say at least 5% greater than the MAE, then trading based on that market inefficiency should be safer and more likely to persist in the future because the nature of the currency would have to make a greater mutation in order to completely destroy our edge.

The system can obviously be improved. Some ideas are:
- Only use signals where the confirmation bar of the divergence is significantly powerful (large).
- Do not take signals generated during the Asian session, where bars are just too small due to lack of volume.
- Only trade signals in the direction of the long term trend by analyzing the behavior of a long term moving average.

Those are just a few ideas. Of course you can come up with your own. The important thing is that once the idea is conceived a new Mathematical expectancy analysis must be carried out to verify that the added filter improves the edge. By improving the edge, the positions will have larger TPs and smaller SLs while maintaining or improving the win/loss ratio, and that should result in smaller draw downs and better returns.

I will evaluate some of these ideas in order to come up with a likely long term profitable mechanical system entirely based on Classical MACD Divergences, with better returns and significantly smaller draw downs. I want to obtain a smooth growing equity curve based on simple trading principles, a larger statistical edge and without getting to curve fit.

If you liked this article stay tuned for the evaluation of the edge of Hidden Divergences on the H1 time frame for the EURUSD currency pair

Design of a EURUSD Donchian breakout strategy with proven statistical edge

This article appeared first on The Lazy Trader at http://www.the-lazy-trader.com/2012/...-strategy.html

This article is about a Forex strategy that I designed for the EURUSD currency pair. In this exercise I would like to share with fellow Forex traders the concepts and ideas to take into account in order to design a "likely" long term profitable trading system. Steps to follow in the design process, and methods to find the answers to questions such as "Is there statistical evidence to believe this system has a positive edge?" or "How do I choose a reliable parameter set?" or more important yet "How do I know in the future that the system has possibly stopped working and shouldn't be used anymore?"

The basic idea

The initial idea behind the system is to exploit breakouts. And this is not new at all, many successful methods in the past have successfully exploited these inefficiencies where instead of trying to "Buy low - Sell high" we attempt to "Buy high - Sell higher" or "Sell low - Buy to close even lower".

For example, analyzing the daily time frame. If the price of a currency makes a close today that is higher than every close in the previous X days, then we can say that the currency pair is in an uptrend. At that point we could argue that chances are in favor of a continuation and then we could enter a BUY order betting that we will be able to sell higher in the future. The same for a SHORT trade. If the close today is the lowest close of the last X days, we are in a downtrend and we could enter a SELL order hoping to buy back later at lower prices for a profit.

Of course X, which is the number of days we are going to look back for the lowest close and highest close is a number we need to optimize. The greater the value of X, the stronger the trend has been, but presumably the closest the time for such a trend to be over.

For example X = 80 means we would enter a LONG order if the close yesterday is the highest close of the last 80 days, or a SHORT order if the close yesterday was the lowest of the last 80 days.

X = 80 represents a stronger trend, that is more mature, but also probably coming to an end, we don't know.

A smaller value, for example, X = 50 represents a young potential trend that has been formed. it is not so mature, so chances are lower that it is over, but it could also mean a trend that is not solid yet, and could easily be a fake out.

So, both aproaches have a benefit and a drawback. In the first case, chances are higher that it is a solid and strong trend, but it could also be coming to an end soon, so I might get smaller profits. In the second case I risk entering many fakeouts but if I catch one good trend I'm going to be riding it from the begining, or closer to the begining, thus potentially obtaining more profit from it. But the cost of failing many attempts could affect my overall results.

Profitability of the Parameter space

In any case, what is important to understand is that whether X = 50 or X = 80 give positive results in a back test, that doesn't mean that the idea of designing a strategy based on this principle has any merit. For the idea to be truly validated as potentially good, positive results need to be obtained for the neighborhood of surrounding parameters. Let's say X = 80 gives you positive returns on a 10 year backtest, but X = 78, or X = 82 give loses? That means, you probably just curve fitted your system and the system will fail at the slightest market mutation in the future.

That's why we need to verify that surrounding parameters of the space also yield positive results. So, below is a simple Optimization Test from 01/01/2000 to 31/12/2009 run in Metatrader 4, entering trades for 50 day break outs, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100 day break outs combined with time based exits 6 days to 12 days after the entry.

(Click on image to enlarge)
http://2.bp.blogspot.com/-iWx98Caqd4...ion-Report.PNG

The darker the rectangles the higher the profit obtained in the ten year back-test. White rectangles mean negative profits, that is loses. As you can see all the combinations of parameters yield profits in 10 year back-tests (All green rectangles and no white ones). This means, if you were to choose a given combination and the market mutates, you won't be drastically affected in the future because you have a strong parameter space to withstand market variations. So even though you might not trade with the optimal parameter set in the future you are still bound to have odds in your favor because you are likely trading a parameter set that although is not the optimal anymore, at least it is a profitable one.

I like the combination of 70 day break out with 6 days time based exit. It is not the one that yields the highest profit in the 10 year optimization report, not at all. But it is the one with the best ratio of AverageAnnualReturn/MaximumDrawDown. That's the AAR/MDD ratio. It combines a decent return with one of the smallest Drawdowns in the parameter space and I like that, small draw downs whenever possible.

Positive Mathematical Expectancy of the Entry

We need to make sure that our entry logic is better than a random entry. For that we analyze every single entry in the ten year period and compile the Average Maximum Favorable Excursion (MFE) and the Average Maximum Adverse Excursion (MAE). For more information about what MFE and MAE are, how they are calculated take a look at my article How to measure a system's edge. It is all explained there.

The Mathematical Expectancy Analysis reveals that for the 70 day break out with 6 days time based exit there were 363 entries (363 trades). The Average Maximum Favorable Excursion (MFE) was 160.84 and The Average Maximum Adverse Excursion (MAE) was 121.77. That means, on average trades went in our favor by a distance of 160.84% of the daily ATR and against us by a distance equal to 121.77% of the ATR while we were on the trades (6 days for each trade).

We can see that MFE is greater than MAE, so our entry has a positive edge. Trades went, on average, farther in our favor than against us. This edge can be measured with the Edge Ratio dividing MFE/MAE = 1.32

A truly random entry has an Edge Ratio of 1.00. Our entry has an edge ratio of 1.32 which is a signifficant edge. Our entry logic has a positive edge.

Analyzing our Exit's Edge

But we also need to verify that this is not a lucky occurrence. So, ideally the Edge Ratio is higher than 1.00 not only for the 6 days exit, but for the surroundings. For example the edge ratio should be > 1.00 for 4 days exits and for 8 days exits as well. Back to the calculation again and we obtain:
MFEMAEEdge Ratio
4 day exit125.29100.261.25
6 day exit160.84121.771.32
8 day exit189.41138.551.34

We now have a strong evidence to believe that both our entries and exits have a positive edge and that the parameter space is wide enough to show profitability with different parameter sets. We won't be simply choosing a set of specific unique parameters that happened to yield positive returns in the past.

Setting Targets and Stop Losses with Walk Forward Analysis and Rank Parameter selection

Now, we need to define a Target Profit and Stop Loss for our trades. These values won't be a hard number of pips, because hard number of pips won't be useful when the volatility of the currencies changes. Our distance to Target Point and Stop Loss will be variable and based on currently volatility. That's why we will set them as a percentage of the Average True Range (ATR) at the time of the entry.

We run another optimization where we combine possible Targets from 180% of the ATR to 600% of the ATR combined with Stop Losses from 100% of the ATR to 300% of the ATR. And we cover theparameters space coarsely, using 20% steps.

(Click on image to enlarge)
http://1.bp.blogspot.com/-kVi9ofswfQ...top-Losses.PNG

We run several optimization reports in two year intervals as follows:

1/1/2000 to 31/12/2001
1/1/2001 to 31/12/2002
1/1/2002 to 31/12/2003
1/1/2003 to 31/12/2004
1/1/2004 to 31/12/2005
1/1/2005 to 31/12/2006
1/1/2006 to 31/12/2007
1/1/2007 to 31/12/2008
1/1/2008 to 31/12/2009

The idea is to obtain the parameter combination of TP and SL that yields the most stable dradown values and the most stable yearly returns. We don't care about the highest return, because there is no guarantee that such parameter set will give the highest return in the future. We want to prioritize stability (Smallest standard deviation of the yearly returns, and drawdowns). We simply want the parameter set with the smallest variability.

We have a bunch of good candidates but the two most stable parameters sets are:
Target 320 % of the ATR, Stop Loss 200 % of the ATR
Target 340 % of the ATR, Stop Loss 200 % of the ATR

The first one is a bit more stable, it has a slightly higher return and a slightly lower maximum draw-down so I'm sticking with that one.

Finally we run a back test of our most stable parameter set for the optimization period 2000 - 2009 and this is what we get:

(Click on image to enlarge)
http://4.bp.blogspot.com/-Pydl4cAVdd...D-Strategy.PNG

Yearly returns

2000 +8.55%
2001 +3.40%
2002 +17.28%
2003 +19.69%
2004 +10.60%
2005 -0.96%
2006 +12.27%
2007 +8.09%
2008 +12.42%
2009 -2.28%

We have obtained a strategy with a positive mathematical expectancy, a wide profitable parameter space and we determined the most stable combination for setting Targets and Stop Losses.

The strategy enters orders with a 70 day break out of the highest close or the lowest close. We set a Target equal to 320% of the ATR which we calculate in terms of pips at the time of our entry based on the value of the ATR at the moment, and we also set a Stop Loss at a distance of 200% of the ATR. This way our strategy is flexible to volatilty changes in the currency pair. Finally if our TP or SL is not hit, we exit the trade 6 days after the entry.

Some additional statistics:

Average Annual Return : 8.90%
Maximum Drawdown : 9.75%
AAR/MDD : 0.91
Ulcer Index : 3.23
Sharpe Ratio : 1.13
Martin Ratio : 2.38

When to stop trading the system?

This is perhaps the most important question because it will give you confidence to stick to the system in the inevitable bad times, and only stop using it when there is evidence that the strategy stopped working. And obviously realize it before your account has suffered a significant draw down.

The fact that the system had a maximum draw down of 9.75% doesn't mean that a higher value won't happen in the future. But we need to decide how much more pain we are willing to suffer before we decide that the system stopped working.

In order to accomplish this we use Monte Carlo simulations. Essentially we distribute all the outcomes of our past trades in different orders. All the losses and winners distributed randomly and not in the particular order in which they took place in the past. We distribute all 363 trades randomly and we do it 100 000 times. That introduces enough randomness in the possible orders or combinations in which the sequence of losses and wins may happen. Then for all 100 000 combinations we analyze final profits and draw downs. We then assume that if our trading in real life reaches the worst Monte Carlo scenarios in terms of profits and draw downs the system has stopped working and it is not safe to use anymore because presumably, the market inefficiency that it exploited is not present anymore.

After analyzing the 100 000 iteration Monte Carlo simulation we obtain the following values:

Worse Case Draw-down 17.63%
Worst case consecutive losses 19

If our system reaches a 17.63% draw-down we can stop using it with evidence suggesting that most likely it has stopped working. As well as if it reaches 19 consecutive losses.

At this point we are done designing our likely long term profitable system. Which we designed and optimized using 2000 - 2009 data. Aren't you curious to know how the system performed during 2010 - 2012?

2010 - 2012 will be our out of sample testing period. Essentially simulating how the system would have traded life from 2010 to 2012 which is a period totally alien and unknown for a system designed using only data from 2000 to 2009.

According to the characteristics of the system, we can expect an average yearly return of 8.90% with a standard deviation of 6.83.

That means there is:
- A 68% chance that our yearly return will be between 2.07% and 15.73%.
- A 95% chance that our yearly return will be between -4.76% and 22.76%

Without further ado here are the results:

2010 +6.12%
2011 -4.27%
2012 +7.83%

Our yearly returns are within the expected intervals. We have one negative year in 2010 but there is no evidence that the system stopped working given that our worst case draw down scenario hasn't happened. The system performs better in 2012 and we obtain a 7.83% return for 2012. Overall a 9.54% equity growth is obtained between 2010 and 2012 with a maximum draw down of 8.51%.

Of course if you want to increase your returns you increase your risk per trade. All the simulations were done with 1% risk per trade, calculating the position size accordingly so that if SL was hit, only 1% of the account was lost. If you increase the risk level to 2% per trade you can expect to double everything, both profits and draw downs. You would have achieved 17.80% average yearly returns in the 2000-2009 period but also a 19.50% maximum draw-down and the worst Monte Carlo scenario would be a 35.26% draw down. What matters in the end is the AAR/MDD ratio (which is always 0.91). It is up to the trader to decide how aggressive he wants to be with his risks per trade levels.

The strategy doesn't use unsound trading principles such as Martingale or Grid trading. It has a positive mathematical expectancy and a wide parameter space of consistently long term profitable parameters. It is not the flashiest or most spectacular strategy in the world, but it is a profitable one nonetheless and a strategy that has been working for the past 12 years, with evidence suggesting that it hasn't stopped working. For sure, I will revisit it at the end of 2013 to analyze its trading results from January 2013 to December 2013.

I hope this article shines some light on the design principles of mechanical Forex systems, or any mechanical system for that matter and that it helps some one out there.

Download source code of the Expert - Lazy Trader Breakout EA

This article appeared first on The Lazy Trader at http://www.the-lazy-trader.com/2012/...-strategy.html

- The simulations have been run in Metatrader 4, with AlpariUK data directly provided by the broker.
- A 2 pip fixed spread was set using the Spread Fixer tool implemented by Asirikuy.com
- The Mathematical Expectancy Analysis was carried out using Asirikuy's Mathematical Expectancy Analysis tool
- The Walk Forward Analysis along with the Parameters Rank Analysis, the Analysis of yearly returns and draw-downs as well as the system's characteristics were obtained using Asirikuy's Draw down Analysis Tool.
- The Monte Carlo simulations were run using Asirikuy's Monte Carlo simulator.

Results - 2014
Results - 2015

Bass

Absolutely fab posts of late. This thread is fast turning into a one-stop shop for me. Thanks greatly mate.

C

Turtle Trading System Automated. Method 2. (Forex Expert Advisor)

The legendary story of the Turtle Trades. Pretty intriguing isn't it? If you don't know about the Turtles and the story behind them, you can read here. My question always was, are the mechanical systems that they used still valid today? Are those systems still profitable? Are they applicable to Forex?

The Turtles traded several markets with 2 systems (System 1 and System 2). These systems didn't have any discretionary rule. Everything, from entries to exits, position sizing to money management, everything was clearly established to the very last detail. This document is the most comprehensive guide I have seen about the Turtle Trading Methods and I used all that information to automate System 2 in Metatrader. I automated System 2 first as it is simpler to program. My plan is to eventually do the same thing with System 1. Let's see if System 2 still works and if it is applicable to the Forex markets, in particular the EUR/USD pair.

The Rules
The system uses the daily timeframe and the rules are surprisingly simple. These are the rules for entering Long positions:

1. Buy when the current price is higher that any other high in the previous 55 days.

1. Put a Stop loss 2 Average True Ranges away from the entry (by using the ATR the system is flexible to current volatility. When the volatility is higher the Stop Loss will be set farther away and viceversa). The ATR used is evaluated over 20 days. So ATR(20).

1. Don't put any Target Profit on the orders. The goal is to let them run as far as possible in your favor.

1. Dynamically calculate position size so that if Stop Loss is hit you only lose 2% of the account. So, if you have a farther away Stop Loss, the positions size will be smaller, and viceversa.

1. Once inside the trade, if price moves in your favor by half the ATR, then add another long trade. And you do this until you have a maximum of 4 open trades in the same direction.

1. Every time a trade is entered, move up the Stop Loss of the existing trades, to the same price of the Stop Loss calculated for the new trade just entered.

1. Exit all the trades when the current price is the lowest price of the last 20 days (This may happen at a profit or a loss). Or exit when Stop Loss is hit.

For short positions the rules are the same but the other way around. You enter when the price is the lowest it has ever been in the last 55 bars and you exit when price is the highest price seen in the last 20 bars. This trading system has all the ingredients recommended by professional Forex traders: it cuts losses short, it lets winners run, it adds to winning positions.
https://1.bp.blogspot.com/-Wmdcef0ab...ble-EURUSD.PNG
Notice in the above picture how all 4 trades were profitable. However, notice how much of the profit was lost. With some optimization that I will explain in this post, the system can be much more profitable and let fewer portions of the profits slip away.

Pretty simple system but incredibly powerful. Also mentally hard to trade. Buying at a 55 day high is tough as that's the point where most traders think the move is done and start fearing a reversal. Same for shorts when you initiate a short position at the 55 day low. Entries are definitely hard to digest psychologically speaking. Exits are even harder. Waiting for the price to reach the lowest point of the last 20 days is painful while you inevitably watch part of your profits evaporate. But this is the best way to ride a trend as far as possible without arbitrary target profits that cut your winners short. This mechanism allows the strategy to ride monster trends once in a while that skyrocket profits.

I ran a mathematical expectancy analysis of the entries and verified that both Short and Long entry signals have a significant positive edge. This is good as a first step to trust the system. Then I coded the rest of the strategy and started to have fun with back tests.

Here's the result of the back test for the EURUSD currency pair from January 1, 2000 to November 14, 2012 (Fully trust worthy paid data from AlpariUK obtained through direct request to the broker). The spread used was 2 pips which is worse than what most brokers offer today.

(Click on image to enlarge)
https://1.bp.blogspot.com/-Q6IWEc485...ults-Forex.PNG
One note here about the draw down. The 31.69% relative drawdown is calculated by Metatrader taking into account the biggest drop peak to valley in the equity curve considering floating profits and losses (of non closed trades) in the calculation. That is why the draw down is reported as a higher number than what it actually is. When considering only closed trades instead of temporary unrealized profits and losses, the Maximum Relative draw-down is 21.34% in almost 13 years.

Some more statistics:
Average Annual Return: 13.19%
Ulcer index: 12.06
Sharpe ratio (Compared to S&P500): 0.70
Martin ratio (Compared to S&P500): 0.89

This performance easily beats the returns of audited professional Forex traders reported on the Barclay Currency Traders Index. A high Ulcer Index of 12.06 reveals what we already know: The system is hard to trade. But who said profitable trading was easy? Also, the Turtle trader must be patient as he will not be trading every single day. The system can stay inactive for weeks waiting for the expected Donchian Channel Breakouts in either direction.

Some further optimizations
The Turtles applied this method using the 55 & 20 days combination to all the markets they traded. The system was not optimized for specific instruments. It is more of a "universal", a "fit all" approach, which is great because it exploits a more universal market inefficiency that seems to work across multiple instruments. It is a more fundamental occurrence and therefore you would assume it is a market inefficiency that is harder to disappear. But that doesn't mean the parameter selection can not be improved for specific markets and that's what I wanted to do for the EURUSD pair.

First I ran an Optimization test to make sure that the Parameters space provides good results even though parameters were drastically changed.
https://1.bp.blogspot.com/-sGtOycX75...s-Method-2.PNG
A coarse optimization was run only for two parameters (days for entry signal and days for exit signal). The great news is that the Parameters space is very solid and profitable across the board (All green). Meaning the 55, 20 set is not the only profitable one. Any combination of days for the entry between 40 and 80, along with any selection of days to exit between 4 and 20 consistently yields positive results. Which is great because it means that even if you are not playing with the most optimal parameters, you still have a high chance of seeing equity growth over the long run.

Once I was confident the Parameters space was that wide and good, I ran a Rank Analysis for the parameters selection. The idea is to obtain the parameters that yields the most stable draw down values and the most stable yearly returns. It looks like the 70 day entry with an 8 day reversal exit is the most stable parameter set, which offers the most stable draw-down values yer after year along with the most stable returns. Here's the back test using the 70 & 8 combination.

(Click on image to enlarge)
https://1.bp.blogspot.com/-ZNISIiEhd...ults-Forex.PNG
Now the maximum drawdown according to MT4 (which as I said, considers floating unrealized profits and losses) is 25.20%. But in reality it is only 15.66% considering the equity curve based on closed trades.

Average Annual Return: 18.33%
Maximum Drow-Down: 15.67% in 13 years
Ulcer index: 8.98
Sharpe ratio (Compared to S&P500): 0.74
Martin ratio (Compared to S&P500): 1.77

This is, in my opinion, a far superior version. The essence of the system hasn't been changed. We simply came up with parameters that consistently deliver superior results and that are likely to be profitable going forward regardless of market mutations.

Beyond any doubt, the Turtles Trading System 2 has a positive edge. It is profitable and applicable to the Forex markets (you can test it on other currency pairs as well). Although profitable, the method is psychologically hard to trade. The hardest part is letting profits run indefinitely without a predefined profit target. That factor explains why some Turtles were not profitable in spite of the fact that they were all taught the same system. Letting your profits run, as originally sated is what ultimately separates the great Forex traders from the amateur ones.

Thanks for your interest. I hope you enjoyed this article and I also hope that if you make the Turtle Trading System EA part of your trading arsenal, you can benefit from it. For any inquiries and support of any kind feel free to contact me at [email protected].

Update
As a proof that Long term Profitable automated trading is possible, the Turtles Trading system continues to deliver good results after this document was written. +35.6% in 2014, +22.8% in 2015 Read the articles below for more details:

Results - 2014
Results - 2015

Profitable Forex strategies - a follow up (2015 results)

Just like I did last year, I now want to go over the results of 4 Automated Forex strategies that have been discussed on this site in the past. The results last year were pretty good across the board, putting to rest the notion that "Forex robots don't work... wah-wah-wah".

Of course I have discussed several other Forex trading strategies in the past. Most of the time just exposing trash, scams and over curve-fitted junk, especially during the early life stages of this site. Just like I said last year, after a while, I realized the amount of garbage was insanely beyond my reach and it didn't make much sense to keep exposing charlatans and endlessly picking fights.

So here we are, focusing on robust Forex trading strategies with long profitable track records and great likelihood of being profitable in the future. I say great likelihood due to the fact that they exploit a very simple principle of the markets: trends exist. These are systems with simple rules, few degrees of freedom and strong and wide sets of profitable parameters, which suggest low degrees of curve-fitting.

I purchased high quality data (FXDD broker) to run all these tests on the MetaTrader4 platform. Bid-Ask spread used of 2 pips in the simulations, which is higher than what most brokers offer nowadays, putting our tests at a disadvantage. I adjusted the time zone of each quote by adding three hours so that the weeks only have 5 daily candles (Monday through Friday), all of them full 24 hour candles, instead of the shortened Sunday night and shortened Friday.

The currency I'm using, just as last year, is the Euro, or else this article would be and endless orgy of back-tests. Let's look at the results. (By clicking on the name of a strategy, you can visit the original article where it was first discussed)

EURUSD Donchian breakout strategy with time based exit

This strategy enters on a 70 day Donchian Channel breakout, sets a Stop Loss 2 ATRs away and a Profit Target 3.2 ATRs away. If neither Stop Loss nor Profit Target is achieved in 6 days, the system will simply automatically exit the position as it assumes the initial momentum after the break out may be fading. 3% capital allocation per trade on this test.

(Click on images to enlarge)
http://2.bp.blogspot.com/-7ijoFS6id-...chian-2015.PNG

http://4.bp.blogspot.com/-WDTCtfga0j...reak%2Bout.gif
Solid +38% return in 2015. Very strong year. This is on the back of a +16.79% return in 2014. The Max draw-down in the equity curve was 23.66% (Like I have said in the past, Metatrader over estimates the draw-down as it assumes floating profits and losses instead of just closed positions). 34 trades in total, 23 winners, 11 losers. This is a pretty aggressive system, and not every single year is a winner, but when it wins, it usually wins big.

50 Day Breakout system with 50 SMA - 100 SMA crossover confirmation

A strategy kindly shared by portfolio manager Pavel Kařzek, who trades this mechanical system on several currencies and futures. For simplicity, again we just show the results on the EURUSD in 2015 or else this article would be infinite.

Because the strategy is applied on so many instruments at the same time, Pavel trades each one with very low risk settings. Let's see how it did for the Euro in 2015, max risk per trade of only 1%.

(Click on images to enlarge)
http://3.bp.blogspot.com/-mPqts11pjm...akout-2015.PNG
http://2.bp.blogspot.com/-_rdJOvGYG4...nfirmation.gif

A +1.79% return for 2015 (Euro only) on the back of a +3.86% return in 2014. Very small 1.39% draw-down experienced. Although this is a small return, take into account the insignificant draw-down and also the fact that this strategy is traded in a portfolio with many other instruments, including not only currencies, but also futures, metals and grains.

The Turtles Trading System (Method 2)

The legendary Turtles Trading system doesn't need an introduction. This beauty has been killing it since introduced back in the 80's. For more details, click on the link above and enjoy.

By the way I recently finished programming a prototype for Method 1 of the Turtles, which was insanely more complex to program. The results of Method 1, when applied to currencies leave a lot to be desired in respect with Method 2. It is profitable as well, just not as attractive, and highly correlated (draw-downs of method 1 tend to coincide with those of method 2, and this is why the Turtles used "either or"). I don't think the Method 1 Robot is even worth publishing.

Back to Method 2 in 2015. Starting from December 15, 2014 instead of January 1, 2015. This is because on January 1, there were positions open since December 15 that had not been closed yet. So, in order for those results to be included in 2015 (which is when the positions were closed) this run has to start a little earlier than Jan 1, 2015.

So, how was 2015 for the Turtles Trading system (method 2) applied to the EURUSD currency pair?
Simply another excellent year.

(Click on images to enlarge)
http://4.bp.blogspot.com/-iDwZjIRzUM...ry-results.PNG

http://1.bp.blogspot.com/-5oKYJi7syi...-live-2015.gif
Very strong +22.80% return in 2015 after a spectacular +35.60% the previous year
Draw-down (closed positions only): 5.62%.
10 winners and 6 losers in 2015 (vs 7 winners and 15 losers in 2014, yet the winners were larger in 2014).
When combining 2014 and 2015 in a single run, the strategy has returned +62% in just these two years, with a maximum draw-down of 11.62%. Unbelievable how a system with simple rules for trend following is still killing it 3 decades later.

The Turtles Trading System is not the Holy Grail. It is in fact extremely hard to trade and very few individuals would be able to mentally handle it. During years of good trends it will kill it, but in other years it can and will have extended draw-downs in both depth and duration.

LT Trend Sniper

My Darlin. From yours truly, the LT Trend Sniper system: my premium strategy designed for following 2 - 3 month long trends on currencies such as the Euro (EURUSD), the Sterling pound (GBPUSD) and the Australian dollar (AUDUSD). I have recently tested it with success in Gold as well, as I could finally get my hands on decent quality 1-minute Gold data going back to January 1, 2001.

So, here's the Sniper with the EURUSD in 2015. Also starting the test on December 15 to avoid disregarding positions that were closed in 2016 but which were initiated in 2015.

(Click on images to enlarge)
http://2.bp.blogspot.com/-h0DURHBaIA...ry-forward.png
http://1.bp.blogspot.com/-VxV4Axf8Eu...ts-forward.gif
+8.20% return which is near its historical yearly average. The result differs a bit from what I achieved in my personal account because I was using a small $2,000 balance. Position sizes on my small account could not target the exact desired risk with the same granularity as a large account would have, like the $100,000 used in this test. Max Draw-down: 7.02%.

Many people have asked me whether I prefer the Sniper or the Turtles system and my answer is: The Sniper. My opinion is based on the Average Annual Return to Max-Draw-down ratio. The Sniper has historically obtained better returns for the draw-downs that it experiences. We could increase the position size, to match the historical returns of the Turtles and it would experience way smaller draw-downs at those risk levels.

When it comes to the portfolio of EURUSD + AUDUSD + GBPUSD, the system had a mediocre result, mainly due to the under-peformance of the Sterling Pound (GBPUSD) which had a -11.62% year and brought the portfolio down 1.02% for the year 2015.

Other symbols like Gold (XAUUSD) and the Canadian Dollar (USDCAD) had positive results of +1.50% and +14.70% respectively.

Euro +8.20%
Australian Dollar +2.19%
Sterling Pound -11.62%
Canadian Dollar +14.70%
Gold +1.50%

All those instruments combined in the same portfolio would have resulted in a +15.33% return with a 12.67% draw-down.

I have met so many traders entirely opposed to 100% automated trading systems. If automated trading systems truly don't have a chance, then why do those same people always complain that the markets are dominated by "algos".

Profitable automated trading is possible. It has been done. It is happening every day in the markets and it will continue to happen.

But, just like I said last year, be careful. There is an extraordinary amount of useless garbage out there. Especially in the world of retail Forex trading where automation is more prevalent and unscrupulous vendors distributing curve-fitting junk just to make a quick buck by selling the get rich overnight dream.

Let's let the "algos" work, and see how they perform in 2016. It would be cool to show extended track records of fully automated systems over 10 or 20 years. Let's see if I'm alive by then. As long as I am, results will continue to be shared year after year no matter what.

I am loving that Lazy Trader blog Bass. Definitely worth a bookmark. :-)

Yeah, it seems that this guy fairly knows what he's talking about when he talks about positive expectancy, MFE, MAE and quantifiable edge of your system.
Simple tried and true systems with follow up on the results in plain english that we mortals understand, not like most of the quant geeks out there .

Watching the Champions league : Barca - Atletico ; Bayern - Benfica

Alpha generation platform.

An alpha generation platform is a technology solution used in algorithmic trading to develop quantitative financial models, or trading strategies, that generate consistent alpha, or absolutereturns. The process of alpha generation refers to generating excess returns.[1] Alpha generation platforms are tools used by hedge funds, banks, CTAs and other financial institutions to help develop and test quantitative trading strategies. Alpha generation platforms support quants in the creation of efficient and productive quantitative trading strategies.[2]

Traditionally, quants have used tools such as MATLAB, R, C++ and other computer programming languages to create complex trading strategies that help them perform high-frequency trading. However, as market data volumes increase and more traders create financial models that deal with multi-asset class data, news sentiment data and more, quants must spend a large amount of time programming models, debugging code, and integrating multiple market data sources. This is why some firms have begun adding alpha generation platforms to their quant infrastructures.

These platforms are often seen as a complement to traditional quantitative tools as they can help quantitative analysts process huge volumes of market data. With many of these platforms, users can write out models in English, program models using the platform's supported computer languages, or import strategies written in MATLAB, C++, R and other languages. Alpha generation platforms also often include data integration and storage capabilities through built-in database solutions that capture, standardize and store massive volumes of financial tick data.

Methodology[edit]

Alpha generation platforms are used to locate excess return in the capital market.[1] They enable the development of mathematical and statistical models that help determine whether or not a specific investment may be profitable. In some quant-driven funds, these models make the final decision on whether to buy or sell an investment.[3]

These systems cannot be fully trusted[4] and require qualified quantitative analysts to try to prevent massive drawdowns. The dangers of relying upon a platform as illustrated in the paper by Andrew Lo.[5]

The average quantitative strategy may take from 10 weeks to seven months to develop, code, test and launch.[6] It is important to note that alpha generation platforms differ from low latencyalgorithmic trading systems. Alpha generation platforms focus solely on quantitative investment research rather than the rapid trading of investments. While some of these platforms do allow analysts to take their strategies to market, others focus solely on the research and development of these highly complex mathematical and statistical models.

Agreed ..

Bass, I need more time for your thread

Take all the time that u need buddy, i'm just building my Digital Library.

Thanks for the vid Bass. I like the look of Nick Radge's Bollinger Band Breakout System and will give it a go shortly across my universe.

Below are the specs from his book 'Unholy Grails'. I hope you don't mind me adding it to your library. Cheers mate. :-)

Feel Free to do whatever you like C.

3 Systems In one Research.

Tuesday, April 12, 2016
Taming the Beast - Profitable Gold trading strategies

A complete Gold trading system with positive expectancy. Metatrader Expert Advisor included.

In order to diversify my trading, over the past couple of years I have been researching strategies to effectively trade Gold. Gold is an extremely emotional market that can move several points in a day in one direction, and in the same way it can quickly give it all back. These wild rides, the noise and volatility make it sometimes harder to trade in a discretionary fashion. There is a huge emotional component that ends up hurting Gold traders more often than not. That, and the fact that it is a 24-hour market, makes it more suitable in my opinion for fully automated trading through a robot, a.k.a expert advisor.

At this point, I have developed three Gold trading strategies with a positive edge: a Trend Following strategy, a Volatility based breakout strategy that uses Bollinger Bands and a Counter-trend strategy. In today's article, we'll explore the Trend-Following strategy.

STRATEGY DESIGN

Using pure price action and no indicators, we can determine that Gold is in an uptrend if today's closing price is higher than every closing price over the last X days. We can also say that Gold is in a downtrend if today's closing price is lower than every closing price over the last X days.

I started testing this simple hypothesis with X values between 50 and 120 to determine if there was momentum in favor of the trend, by measuring Maximum Favorable Excursion (MFE) and Maximum Adverse Excursion (MAE) after all the entries. This allowed me to quantify a positive edge. For more information on calculating MFE, MAE, what they represent, etc, read How to measure a system's edge.

I finally settled on 100-day break-outs, as they provide a solid and clear edge. Meaning, if Gold closes today, higher than it has closed in all of the previous 100 days, then it usually has some upside momentum that carries it higher over the next few days. The beauty of this is that, this is not only true for 100-day break outs, but also for 80, 90, 110, 120 and all the values in between. That's to say, we have a reliable entry parameter that just "didn't happen to yield positive returns in the past". If all the surroundings (80, 85, 90, 95, 105, 110, 115, 120), or even some of them had yielded negative results then our 100-day entry rule would not be reliable and we would just be curve-fitting our system to past history, with fewer chances of survival in the future.

After this, I decided to set a Stop Loss at two times the daily range using the Average True Range indicator (ATR). This distance is usually enough to give your trades enough room to work out the noise while at the same time we protect our capital against unlimited risk. 2xATR is a common rule applied by many mechanical trading systems that use the daily time-frame and it was pioneered by the popularTurtles Trading system. A 2xATR move against our original assumption is usually a lost cause. Better to take a manageable loss at that point and move on.

So, now, we have a 100-day breakout entry combined with a standard 2 ATR Stop Loss. Time to think about exits. With the LT Trend Sniper system, we sometimes follow trends for 2 months or more. The Average holding period is 21 days. For this strategy I wanted to do something different. I wanted quicker exits, which is why I thought about a simple time-based exit and started testing automated exits 4 days, 6, 8, 10, 12, 14 days after the entries. All the time based exits showed positive results in the 12 year back-tests performed (2001-2012), which is a great sign. By choosing a simple 10-day time-based exit, we are not choosing a parameter value that just "happened to be" profitable in the past. We are indeed choosing a value in the middle of a sea of profitable possibilities, with good solid returns also in the surroundings to withstand future market mutations. By the way the 10-day exit DOES NOT yield the best returns in the back-test, but it does have a solid neighborhood which is what I like the most about this particular value. There is no guarantee that the parameter value with the greatest return in the past will continue to be the most profitable one in the future. The main concern is always the robustness and future reliability of the system.

In addition to the 10-day exit, the trades are entered with a 2:1 reward to risk ratio. In other words, if during the 10 days of life of the trade, a reward that is twice the risk is achieved, then we will be satisfied and will close the position for a nice profit. Therefore, upon entry, the trade is set with a Target Profit (TP) of 4 times the ATR. So, now we have Stop Loss at 2 x ATR and Target Profit at 4 x ATR. By the way, here, once again, we obtain positive returns regardless of whether we use a 1:1, 2:1 , 3:1 and other reward to risk ratios (3:2, 5:2, etc) , which is again a great sign.

With these simple rules all that was missing was our capital allocation. I wanted to keep a constant risk per trade so that results are not skewed by a few occurrences with greater weight. Because the Stop Loss distance is dynamic, our position size is also going to be dynamically calculated. Meaning, if the Stop Loss distance is small, we can afford a slightly larger position size. However, for larger Stop Loss distances we have to use smaller position sizes. This way we keep a constant risk throughout all the trades. For more information on this, read How to risk a percent of your account per trade.

SYSTEM'S RULES:

Buy GOLD on a 100-day closing high.
Short GOLD on a 100-day closing low.
Stop Loss at 2 x ATR
Target Profit at 4 x ATR
Close the position 10 days after the entry if neither SL nor TP have been hit.
Risk 5% of the account per position. Meaning if SL is hit, the account loses 5 percent. Of course, this risk level can be reduced for more conservative traders.
Never trade two positions at the same time. If a new signal is triggered while in a position, it simply means that the trend is progressing in our favor. We won't increase our capital exposure at that point. Instead, we just ride the original position.

Ok here are the results of this simple, yet effective strategy from January 1, 2001 to December 31, 2012. We are assuming a 0.40 point spread throughout the test. (Most brokers offer better spreads than this nowadays. Anywhere from 0.20 to 0.35 is common). The simulation starts with a $100,000 account balance:

(Click on image to enlarge)
https://1.bp.blogspot.com/-iGhNke3a5...Day%2BExit.gif
(Click on image to enlarge)
https://1.bp.blogspot.com/-uuxE6I5jF...ld-results.PNG
Not too shabby. The strategy achieves a +9.83% Average Annual Return, which easily beats the S&P500 Index and the Barclay's Currency Traders Index. The worst draw-down in the equity curve was 19.06% and it took place from October 2008 to February 2009. Of course, by using a smaller than 5% max risk per trade this draw-down can be reduced, but at the expense of also smaller Average Annual Returns. Still, with a 19.06% max draw-down, the strategy easily beats the 55% draw-down suffered by the S&P500 benchmark during the financial melt-down of 2008.

Reducing the magnitude of losses

Despite the positive initial results, we can still explore more approaches to control our draw-downs. For example: Trailing Stop Loss mechanisms. Now, usually, when you bring Stop Losses closer, you expose yourself to getting stopped out more often. As a consequence, you start taking smaller losses BUT more frequently and this may result in a null net effect in many cases or even worse outcomes. For this reason, we must be careful and not trail stop losses too aggressively. We will always keep a 2 x ATR Stop Loss distance, and we will move the Stop Loss by 0.5 ATR whenever the position moves in our favor by 0.5 ATR. For example, if our original Stop Loss distance was 32 Gold Points (ATR = 16), then we will move it by 8 points once the trade has gone in our favor by 8 points and we will keep doing that indefinitely. Once the trade has moved 2 ATRs in our favor, we have moved the Stop Loss four times and it is now at the break-even level, the same price at which we entered the position. As the trend progresses in our favor, we keep trailing the Stop Loss level in 0.5 ATR increments, or 8 Gold Points in this hypothetical case.

Let's look at the results now with the addition of the Trailing Stop Loss mechanism.

(Click on image to enlarge)
https://1.bp.blogspot.com/-Ac-B-k1SH...Day%2BExit.gif
(Click on image to enlarge) https://1.bp.blogspot.com/-Ga7l3bHOt...-stop-loss.PNG
A much nicer equity curve now and improved statistics. Average Annual Return is now +10.94% and the Max Draw-down ever suffered is 15.94%. (Meta-trader over-estimates it with 18.17% because it assumes higher equity peaks and larger losses as it considers open positions' balances). My preference is to only consider closed positions in the results.

This is now a more respectable trading system with very few degrees of freedom and a very low degree of curve-fitting to past data. We have a strong parameters space with many combinations of entry + exits and reward to risk ratios, all of them yielding positive long term results, which speaks of the robustness of this approach and the huge mutations the Gold market would have to endure in order for this simple trending principle to entirely stop working in the future.

How did the system perform in the Out of sample period (January 1, 2013 - January 1, 2016)?
Well, here you are:
(Click on image to enlarge)
https://4.bp.blogspot.com/-YrPaZXQIp...Day%2BExit.gif
(Click on image to enlarge) https://3.bp.blogspot.com/-GB8XGk0Hz...-trader-EA.PNG
In the three-year Out of Sample period, the account grows +25% and behaves within the expected parameters. This is important, because this period was not taken into account at all during the initial design of the strategy. In other words, this is Gold data that the system had never seen before and it is what would have resulted from trading the strategy live during those 3 years.

Combining both the Back-test and Out Of Sample periods we have 15 years of trading history from January 2001 to January 2016.

(Click on image to enlarge)
https://4.bp.blogspot.com/-IrKoELjD_...Day%2BExit.gif(Click on image to enlarge)
https://3.bp.blogspot.com/-LLtagWG0v...stem-rules.PNG
Beautiful and rather smooth equity curve. The original investment is quadrupled in 15 years, representing a +10.29% Average Annual Return. Max draw-down is 15.94% (closed positions only, not open floating profits or losses). Notice how the Average winner is much larger than the Average Loser and the system wins about 50% of the time, resulting in an excellent 2.01 Profit Factor.

As my free contribution to the trading community, in particular those who specialize in Gold trading, the robot will be shared here in a few days, so it can be downloaded and used by anybody. I'm still organizing the documentation and fixing a small execution issue in the software.

Exploring Other Instruments

Once the system was entirely conceived, I started to wonder how the strategy would perform in other instruments. Same break-out principle, same 10-day exit, same Stop Loss distance and 2:1 Reward to Risk ratio. It was a very nice surprise to see this system showing solid results in instruments other than Gold. The simple edge it exploits is more universal than I thought.

With the Euro for example, we obtain even better results than with Gold. We have good results whether we trail the Stop Loss or not, and whether we trail it indefinitely or just until the break even level and not beyond. Here is a 16 year back-test from January 1, 2000 to January 1, 2016:

(Click on image to enlarge)
https://2.bp.blogspot.com/-2WrD85aP9...BBreakEven.gif
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https://3.bp.blogspot.com/-NONl40O6C...rt-advisor.PNG
Solid +13.94% Annual Return (AAR) with a Maximum Draw-down (MDD) of only 13.60%. A great 1.02 AAR to MDD ratio.

So, now if we want to diversify our risk a little more, we can combine both GOLD and EURO in the same portfolio. GOLD and EURO are not historically strongly correlated instruments. They don't inherently move in the same direction all the time. This is great as it provides us with some built-in risk diversification in a context of a trading strategy with a positive expectancy. By combining both instruments, the draw-downs in one of them can be slightly mitigated by positive results in the other instrument. Of course, we also have the risk of increased draw-downs if they happen to coincide in time.

Here's the GOLD + EUR portfolio. 2000-2016:
https://1.bp.blogspot.com/-Zu03CxJOb...strategies.PNG
https://2.bp.blogspot.com/-PO7mW-v1_...profitable.PNG

Here is the break-down of returns per year:
https://2.bp.blogspot.com/-q5WNRI213...er-results.PNG

A 23.37% Average Annual Return is nothing to sneeze at. It turns a $100,000 account into 2.48 millions in 16 years and this is without ever injecting additional fresh capital into the portfolio. It comes however, at the expense of a painful 23.35% draw-down and a period of 536 days during which the portfolio failed to reach new equity highs. It is therefore, a psychologically difficult system to trade. Imagine going through a 20% account draw-down, more than a year without achieving new equity highs and it just looks like you are wasting your time. Profitable trading hurts. For more on that, read my article The Torture.

Personally, I prefer less aggressiveness when trading more than one instrument simultaneously. Using a3% position size per trade instead of 5% better fits my pain tolerance. This results in still nice +14% Average Annual Returns, but with a much more manageable worst historical draw-down of less than 15%.

This is a nice example of a simple long term profitable system. I will consider it in my own trading and will follow up on the results at the beginning of every year.

Thanks for reading, and I hope that by studying this system you become a better trader whether you end up using it or not. It might help you explore and develop similar ideas on your own, and if that is the case, I would be glad to hear from you in the future.

Cheers,
LT

Notes:
- Back-tests run assuming a 0.40 Bid-Ask spread in Gold and 2 pip spread for the Euro (0.0002). Both numbers are pretty unfavorable by today's standards.

- The data was purchased at forextester.com and it is 1-minute data. No need to purchase tick by tick history when we are dealing with long term trend following strategies that use distances in the hundreds of pips for both Stop Losses and Target Profits, unlike other strategies such as intra-day, short-term scalpers, where tick data becomes more necessary.

- Back-tests performed on the Metatrader 4 platform, build 950, powered by GoMarkets, an Australian Forex broker regulated by the Australian Securities and Investment Commission (ASIC)

- Portfolio simulations performed through the Asirikuy Draw-Down Analysis Tool, version 1.41a.

http://mechanicalforex.com/free_ebook.pdf

Mathematical Expectation in Multicurrency Forex Trading
JUNE 9, 2014 BY EDDIE FLOWER

Some forex traders use the same trading strategy for all currencies, while others use entirely different strategies depending on the currency pairs being traded. Or, traders may use multiple strategies with multiple Forex pairs, in order to perhaps increase profits while reducing the risk of drawdown resulting from over-concentration on a single strategy.

Expert advisors (EA) make it possible to optimize the input parameters, yet they don’t necessarily make it easier to put separate strategies together into a single system. And, testing may show increased risk from overlapping or correlated drawdowns when disparate Forex strategies are merged together.

Using algorithms, a trading system can check currency pairs and perform specific operations according to input parameters. A multicurrency, multi-system EA can be crafted in order to assess all trading strategies side-by-side. This may be helpful in case only a single EA is permitted to access a given account.

It can be challenging to develop a forex trading system that works well across different currency pairs under a variety of conditions. Most of the widely-known systems for multicurrency trading are based on trend-following strategies, such as Donchian-channel breakouts, and are designed to profit from very long-term trends. Yet, a multicurrency strategy must show clearly show a winning “edge” over the typical time horizons for forex traders.

For example, in order for a system to work well with both EUR/USD and USD/JPY the signals must have a high likelihood of success in spite of volatility and potential correlation between the two pairs. And, trades must become winners during fairly short time periods. If not, then trading correlated pairs may create a risk of over-concentration and excessive drawdown.

There are many profitable opportunities in trading the four major currency pairs — EUR/USD, GBP/USD, USD/JPY and USD/CHF. I’ve been enjoying good success by using a strategy based on Mathematical Expectation (ME). I use ME to analyze data and spot comprehensive trading opportunities and calculate entry/exit points for trading the four major currency pairs.

Mathematical expectation predicts the likelihood that a Forex trade will win

A well-programmed EA can use ME tools to help build systems that work across multiple currency pairs. I’ve helped developed a couple of systems that work in real-time and show long-term profitability through back-testing.

Recently, traders have become more aware of the drawbacks that arise when using data-mining techniques to back-test and fine-tune strategies for Forex trading systems. Alternative system-development methods like System Parameter Permutation (SPP) are now available and can help traders avoid the issue of data-mining bias.

If done carefully, SPP or data mining will help build a set of good-quality indicators to generate signals across the four major currency pairs. Then, the expert advisor calculates Mathematical Expectation to see whether the trade is likely to be profitable or not.

Finally, it’s a matter of specifying filters and testing to find precise strategies that consistently result in winning, profitable signals. Entry and exit points are calculated by the mechanical trading system using mathematical expectation adjusted for current volatility.

Calculating the mathematical expectation of success

Mathematical Expectation (ME) is a statistic that measures the greatest temporary profit that a trade experienced the entire time it remained open. It was first popularized under the Optimal-F position-sizing and money-management rules developed by Ralph Vince. The equation is:

Mathematical Expectation = MFE – MAE

The mathematical expectation tool gives multicurrency forex traders a predictive “edge” in developing winning systems. ME is defined according to the concepts of Maximum Favorable Excursion (MFE) and Maximum Adverse Excursion (MAE). ME’s value can be calculated in real time by the mechanical trading system.

Maximum Favorable Excursion is the greatest balance on a favorable trade before a forex trade is closed out, regardless of final closing price during the time period, whether daily, hourly or minutely. MFE is the highest positive balance achieved while the trade was open.

Maximum Adverse Excursion is the largest unrealized or temporary loss during a trade, regardless of whether the trade was closed out as a loser or not. MAE is the lowest negative balance on the trade while it was open.

In order to quantify and analyze the ME from a given forex pair, traders can simply calculate average MFE and average MAE for a large number of past trades. Mathematical Expectation equals Maximum Favorable Excursion minus Maximum Adverse Excursion.

If average MFE is larger than average MAE, then the Mathematical Expectation is positive. The larger the ratio between MFE and MAE for a given currency pair, the more favorable is the outlook for a potential trade.

Multicurrency forex trading strategies based on Mathematical Expectation

When trading EUR/USD, GBP/USD, USD/JPY and USD/CHF with a multicurrency strategy based on the Mathematical Expectation, this metric is usually positive and generally high, and similar among the various currency pairs.

It’s important to avoid evaluating position size, or trade-exit rules or any other parameters while the expert advisor analyzes the entry points. Those parameters can be set independently by the mechanical trading system based on ME adjusted for volatility, as discussed later in this article.

After determining the entry point and trade direction, the mechanical trading system calculates MFE and MAE values generally first at 10 bars beyond the entry price, then 15 bars beyond, then 20 bars beyond the entry price.

In addition to signaling entry points, the ME also shows whether the forex trade’s advantage is best immediately after opening the position, or at some average interval after being in the position.

My simplest multicurrency trading strategy uses daily charts and relies on a combination of three price-based rules, and only a few parameters that use mathematical expectation to predict success.

The rules for long and short trades are as follows:

Trade long (and close out a short trade) when:
Close > Previous Close
Open > Previous Low
Previous Close > Prior Close

Trade short (and close out a long trade) when:
Close < Previous Close
Open < Previous High
Previous Close < Prior Close

This system reverses the trade when the signal changes. So, if the system has a “long” position open when a “short” signal is received, the system will close the long position and instead go short. Likewise, if the system has an open “short” position when a “long” level is received, it will close the short and immediately go long.

Another parameter of this system is the stop-loss trigger which is set at a value just slightly more than the fifteen-day or twenty-day average true range (ATR). This value is updated each time a new signal is received in the same direction.

Nevertheless, if there are new signals in the same direction, my system does not add new positions, since I’ve found that drawdowns outweigh additional profits when doing so.

Finally, regarding position size the system allocates a maximum 2% of account equity to a single high-ME trade. If there are multiple signals in several currency pairs, yet the ME calculations are showing correlation among the signals, the total position sizes will be no more than 2% of equity.

Trading results

This simple multicurrency forex trading system has shown decent results in real trading, and back-testing over a twenty-year period shows that it would have enjoyed profitable results for at least sixteen out of the twenty years tested. It has shown a reward-to-risk ratio of about 1.7 and winner percentage around 45%, while the profit factor was nearly 1.4.

Still, the drawdowns can be lengthy – The longest drawdown seen under back-testing was more than 1000 days. The ratio of profit-to-drawdown when using this strategy is similar to that of buying-and-holding stocks, and during back-testing the ratio was about 0.35 with a total return of more than 500% during a twenty-year back-test.

Risk management for multicurrency trading strategies using ME

By knowing the average MFE and MAE values, a forex trader can program a multicurrency mechanical system to exit a trade at a profit target or stop-loss point determined by adding a calculated number of pips beyond the Maximum Favorable Excursion or Maximum Adverse Excursion values.

On average, in order to win over time the forex trading system must reach the profit goal more often than it touches the stop-loss exit level.

For example, if my system is seeing an average MAE of 35 pips and an average MFE of 55 pips, there is a tradable opportunity. The profit target may be projected for 50 pips, which is 5 pips less than MFE, and the stop-loss exit can be set at 30 pips, which is 5 pips beyond the MAE.

Regarding system design, it’s important to program the trading system to define profit targets and stop-loss points according to volatility instead of setting a fixed number of pips.

Volatility helps determine exit points for multicurrency trading

As mentioned earlier, a mechanical trading system can easily use Average True Range (ATR) as a volatility-dependent tool to calculate MAE and MFE in order to set exit points. The system determines the entry price plus or minus a percentage of the ATR that is workable according to the ME analysis. To have a large enough sample, I usually set the ATR to calculate the previous 15 or 20 time frames.

For example, during a market when the EUR/USD is moving an average of about 100 pips per day, the system should calculate target profit points and stop-loss points based on current volatility and the analysis of ME.

So, if a trade moves in a favorable direction for 55 pips, and if the current ATR is 85 pips, the move is not reported as 55 pips; instead, the MFE is reported as 64.7% of ATR.

Over time, I’ve seen that the MFE for the four major currency pairs EUR/USD, GBP/USD, USD/JPY and USD/CHF seem to fluctuate around an MFE value of about 60% of ATR, and average MAE around 40% of ATR for the typical entry after 15 time periods.

In order to fine-tune forex trading results according to volatility, the mechanical trading system can set the profit targets and stop-loss points at varying levels. For example, the system may set the profit target exit point at 55% of the ATR value away from the entry point, not at the MFE full value of 60%.

And, volatility may require setting the stop-loss exit points at 45% of ATR value beyond the entry point, not at 40% of ATR. Still, this system is likely to reach target profit levels more often than stop-loss levels, and winners should be larger as long as target profits are set larger than stop-losses.

For all trades, the calculated number of pips for target profits and stop-losses is always based on volatility just at the moment of the trade, as reflected by the ATR.
When a signal arises, the trading system checks the value of current ATR, then calculates the exact number of pips to reach target profit and stop-loss levels.

As an example, assume there is a signal to go long in EUR/USD,and the current ATR is at 100 pips. So, the target profit point will be at 55 pips over the entry price (55% of the ATR value). And, the stop-loss will be at 45 pips under the entry price (45% of the ATR).

A few more thoughts about Mathematical Expectation

The mathematical expectation is generally lower for “short” trades, and some traders have seen ME increase by as much as eighteen bars after the open, then decay during price swings by as much as eighty bars after open.

For “long” trades, the ME generally has a longer lifespan, with values that may increase quickly up to the thirtieth time period, and then continue slowly onward up to about 75 time periods. Using this system, my average trade duration is about 25 days.

The best upside when trading EUR/USD, GBP/USD, USD/JPY and USD/CHF seems to accrue by about 30 time periods. If the favorable movement continues onward past that average point, then it’s likely that some sort of fundamental bias in the market is prolonging the move.

In summary, this basic multicurrency forex trading strategy takes advantage of a positive, high ME shared across the four major currency pairs. The entries, profit targets and stop-loss points are all based on ME.

When the Mathematical Expectation indicators are predicting success, the four major currency pairs — EUR/USD, GBP/USD, USD/JPY and USD/CHF – can be successfully traded either together or separately.

Have you tried ME in your trading?

Worth Downloading and Viewing.
http://www.slideshare.net/TomaszWasz...xt_slideshow=1

Thanks Bass..