Nice articles goldenmember.
[B]Introduction to drawdown statistics and maths[/B]
I have written this post out of request, and it was one of my most enlightening moments in trading. It will consist of several parts since it is a lengthy topic. If you ask retail traders what statistics they use, the extent of statistics are percentages ā pretty much the same level of mathematics as nine to ten year olds are taught at elementary school. They continue to use this level of mathematics into their trading and its not really suitable. I was fortunate enough to study maths up to high school advanced level, although I do not consider myself a patch on anyone who has done a college degree in maths. If you vaguely remember the maths, then you will know that when maths teacher said that maths was useful in every day life she was lying, but it is useful in trading.
Statistics are useful because they can tell you how likely results are due purely to chance. They can also tell you the expectation of drawdowns and losses per 1000 trades or per timeframe. You can then fit a strategy or audit your strategy to ensure that you do not succumb to a margin call. In fact, in 2011 there was a movie released called Margin Call. The premise of that was the risk manager and mathematical whizz kid worked out that the risk/drawdown that the company was taking was beyond the expectation that the maths showed ā ie: they were living beyond borrowed time already! This meant that they had to get rid of their positions before they would blow up! It amazes me that a lot of retail traders have seen the movie, but have no real idea what they were talking about, except that the Spock from the New Star Trek was in it, and that it was āpretty cool.ā
Using the correct statistics you can take your strategy, or your results and apply the worst possible scenario to it (most losses/biggest drawdown etc). You can find out how many trades it will take for you to encounter a certain drawdown. Given infinite time of course, all systems will fail. Given 1000 years, the most robust systems will fail. Statistics will tell you how many trades you can expect to trade before you drawdown 20%, 40%, 60%, 80% (margin call). For example, the statistics can show you that you require 20 000 trades before you can expect an 80% drawdown. In the movie margin call (2011), the statistics already showed that they were way beyond the number of trades required to get a margin call at their current risk (which is why they dumped positions). You can apply this to your own trading. In reference to the points I made before, people who trade 20% per month, a significantly higher risk of the margin call than a 5% per month trader. The risk is NOT just 4 x as high (this is elementary school maths if you think this) ā the risk is much higher, and in another post I will discuss it. Again, if this post makes you yawn or fall asleep, do let me know and I will change topic.
I agree with this as well. The signal-to-noise ratio on the internet is pretty awful, especially with trading. And be careful of ābear pornā (gold bug forums, conspiracy theories etc).
This is a quality thread. Thanks goldenmember.
I am always looking for something to readā¦I just read the first page and it sounds good so far.
Thanks for thisā¦ It will keep me busy for the next hour or so 
I just feel the need to put that in BOLD letterā¦ just saying lol
I disagree with you on thisā¦If 5%-8% ROI is what other traders are comfortable with gaining every month, is okay too it is probably because of what they are capable of doing or the risk tolerance. However, 20% ROI is still achievable to some without so much drawdown and high risk. I have seen it someone does it and I am now testing it to myself. I just needed timeā¦but it can be done.
I assure you- Iāve read them all. 
Youāre very welcome.
Iām very much a fan of the saying, āEveryone knows something you donāt.ā So I spend a lot of time listening to and reading the words of others. And your latest stream of thought isnāt boring at all. We are all working with numbers here. It would be a bit silly to decry short articles about various mathematical principles. Keep up the great work.
I totally agree with what you are saying - its a problem with the internet - everyone and anyone can get exposure. With the right SEO, you can get your opinion on the Egypt crisis above the opinion of respected broadsheets if anyone was inclined on search engines.
Thank you!
Well, you are a womanā¦ and as I said they make better traders! :49: But on the serious side you have given me an idea for what to write on my next post (donāt want to cram everything into one post - someone said it was already a wall of text).
Thanks for your kind words!
Continuing with my previous posts:
[B]Part 2 of drawdown statistics ā a brief look at permutations[/B]
There are many ways to work out drawdown statistics and I shall just list a few of them, as well as what NOT to do. The most common error that I have seen (I have to clarify that I do not mean everyone does this as some people assume I mean when I mention examples) is where people trade for a month to 3 months, assume that drawdown is the maximal drawdown and adjust expect to continue. One example of taking this to an extreme is where a trader I spoke to was trialing a system which had live tested for 2 months. He then increased his lot size based on those 2 months to maximise his gains assuming the biggest loss in those 2 months would be the biggest loss he would ever had. That did not turn out well as you would imagine.
Myfxbook has a statistic called ārisk of ruinā which is based on your win rate but it is flawed since it assumes that all your losers will come in a row. This is actually uncommon. lets go back to the coin flippers working for the investment bank as an example. They each are given $5 million accounts, and bet 20% or $1 million on each coin flip since that is the minimum bet. Guess wrong and they lose $1 million. Guess correctly, and they gain $1 million. To simplify things they always bet 20% so they are always 5 flips away from blowing up (management requires high standards). Given that each coin flipping event is independent and fair, the chances of losing is 50% or 0.5. Losing 5 flips in a row would cause the coin flippers personal account to be blown and he would be sent home in shame, never to work in banks again. The risk of ruin as soon as they sit at their desks as given by myfxbooks stat would be given as 0.5 x 0.5 x 0.5 x 0.5 x 0.5. This is 0.03125 or around 3% who lose 5 flips in a row and get sent home. This is the risk of ruin as given by myfxbook. You could extrapolate this to say to say that it would take 32 coin flips for a coin flipper to be sent home in disgrace. Thatās not too likely you might thinkā¦
HOWEVER this is not the whole picture. As well as being sent home for guessing 5 coin flips in a row (LLLLL where L is a losing flip), the coin flipper can lose in many different sequences of events. For example he may get the following sequence LLWLLLL and be sent home after 7 coin flips. The probability of this occurring is 0.5 x 0.5 x 0.5 x 0.5 x 0.5 0.5 x 0.5 or about 0.8%. However, he can also lose by LLLWLLL (another 0.8%) or LLLLWLL (add another 0.8% chance of being sent home). All the different sequences of how the coin flips may end up need to be added up to see his chance of failure. Just with those 3 losing permutations above, the chances of ruin increase from 3% to 5.5%, and the expectancy of flips they will last fall from 32 to 18. Working out the different sequences and permutations where the coin flipper can blow his account actually tells you that the chance of blowing the account is significantly higher than you might think.
Learning this maths is quite time consuming ā I recall it was an entire module of my maths exam a long time ago (approx 8 weeks of 4 hours lessons a week), so its not something you can just pick up by reading a blog post, but I hope you get the general idea. A website link is included here for anyone who wants to read more: Combinations and Permutations. But if you really wanted to learn then getting a cheap maths book and working through the examples is the easiest way. You will also benefit from a scientific calculator ā although you can find online scientific calculators easily enough.
Lolā¦ Donāt be haten! Donāt be jealous! I know itās hard to be a woman lol
In fairness, we learn those strategies and techniques from menā¦ and of courseā¦ The what NOT TO DO
I will take credit then of your next post
So this one is for you Pip N Roll: basically its about the value of lower risks and longer lasting gains (maybe the true meaning of turtle trading as opposed to the āturtle trading technique.ā)
[B]Part 3: Probability and drawdown[/B]
Let us imagine for now that you have gone back to your math textbooks and you now know how to work out the chances of failure of a system (note there are weaknesses to this using just permutations that I will come onto in another post). The next topic is about applying probability and risk to drawdown. Again, we are looking at the coin flipper in particular and of course, we do not think that he has a very high survival rate. What if he cut down his risk? Instead of risking 20% on each coin flip, he had a bigger equity size and decided just to risk 10%. He goes and talks to his manager and they agree. We can then work out the risk compared to his coin flipper neighbour who has also been given a raise (investment bankers (or read hedge fund if you prefer) are fair to their employees). Thy both give their boss their trading plan and objectives for the next few months.
Lets simplify and say that we discount the different combinations and say that only 5 in a row losers will blow an account. The 20% coin flipper has 1/32 per flip chance of blowing up, whereas the 10% coin flipper has 1/1024 chance of blowing up. All things considered, the lifespan of the 20% flipper is 32 flips, whereas the lifespan of the 10% flipper is 1024 flips (ignoring combinations which would reduce both flippers lifespans).
The 20% flipper starts with $10 million and ends up with a potential of $3 418 000 000 at his 32nd flip where he is past his time to blow up.
The 10% flipper starts with $10 million and ends up with a potential of $24,328,178,969,536,839,355,491,975 ,986,536,468,22 0,739,584, 000, 000 after 1024 flips. Of course at 32 flips, the 10% flipper only has a potential of $211 million and feels a fool compared to the 20% flipper, but in the end has a far superior plan.
Applying this to trading directly - I realise few people trade 20% risk, but there are plenty of people who trade 2% risk as opposed to 1% risk. The calculations would be very similar in how much would be made overall, and the lifespan of the trading account. I was messaged by someone recently who asked if I provided trading signals (I do not) and I mentioned that signals were a bad idea because money management was a large part of trading, and that signal followers would multiply up their risk without understanding the consequences - the underlying assumption is that if you double risk you just double the drawdown but the consequences are far more far reaching as I have posted.
Talking very roughly (you would have to do the maths to be more exact, although even then it is an approximation) you are far better off reducing the risk from 2% to 1% because that will increase the ālife expectancyā of your trading system which in the end will get you the results. Of course a lot depends on your investment goals - do you want to get rich in 6 months, or incredibly rich in 3 years - reducing the risk allows you to make the latter more likely.
support this thread!
Thank You for your sharing your knowledge Goldenmember . Im sticking with this thread
Iām glad you like what I have written - the next post is a bit on the statistical side as well - I shall be done with the statistics overview in the next couple of posts so I should be onto more interesting things soon.
[B]Getting significant statistical results[/B]
An analysis is also useful for working out whether systems are entirely due to chance or have an edge on the current market but there are limitations, especially if you have small dataset. One of the most applicable uses for statistics is to find whether a trading system is successful solely by chance, or whether there is an edge. If you log your trade results you will have a record of your wins and your losses. Traditional statistics would have you input all your results and see of they beat the ānull hypothesisā of the trades being exclusively down to chance. Our examples of the coin flippers would given enough time have a 50/50 ratio of wins vs losses and would not be able to achieve their plans of 200+ million in a few flips. A probability assessment would state that the statistics support the outlook that the results are exclusively down to chance. Many traders will have good statistics and good win rates for periods of time because their systems are by chance have fit the market. They are dip buyers in a rallying market, sell the rally types in a bear market, or are grid traders on a ranging market (I have to make the point that there are many different types of rallying market, different types of bear market, and different ranging market in case someone brings up that point but I will talk about that later).
The statistics for when they are in the right market are good, but the snapshot that is taken is not indicative of the greater market - there needs to be a significant sample. Trading for 20% gain per month for 3 months tempts people into drawing out excel charts of 20% gain compounded for years (eventually hitting millions from a small account) but ultimately I have never seen this happen despite seeing many accounts have promising starts. I have seen many systems be successful over a period of months only to flatten and disappear - you can see this on zulutrade, myfxbook, fxstat and everywhere else. I only tend to look at systems that have been trading over a year to see whether their system is down to chance or actually has some edge behind it, otherwise the statistics may only be down to chance. Also it is possible to ājukeā the stats somewhat by only closing winners, and letting the losers run - after all - they are not counted in the loss rate until they are closed. Again, where do you draw the line? 6 months, 1 year, 2 years, 5 years? 100 trades, 200 trades, 1000 trades? There is no fixed answer - it just depends what how significant you want your statistics to be. The strictest is to do a statistical test which has the highest power and has the strictest probability or p value. By doing numerous tests you will be able to find the limit of where your trades are valid. This is quite similar to how confidence intervals are managed in the monte carlo simulation. If anyone wants to do anymore reading on how to do these tests here is a good overview: Statistics Glossary - hypothesis testing
When you see statistics with a great monthly gain, or a win rate for a month or two, you have to be aware that the population that the statistics is drawn from is not great. The probability of results being down to chance is a lot higher the fewer results there are. Getting good statistics and plenty of results is important for finding out whether systems work. I would caution over being wowed by statistics with a short lifespan, they may seem impressive but do not come up well against a robust test.
[B]Population statistics in trading[/B]
As mentioned, the markets are not random, some traders do not have set stop losses and take profits. Many close on an decision unrelated to strategy, or hold in hopes of getting a winner, double up on trades, alter the risk on a trade or decide to miss trades. This makes perfect paper trading not be so perfect when it comes to real life. Another vital aspect for statistical tests is epidemiology or population studies. Although it is nice to think of ourselves as a unique special individual trader that can work miracles, it is best to have a realistic view of ourselves and what can be achieved. If you want to see what a good trader is capable of, then you should take a look at a top trader and what it takes to get there. If you are able to access their trading record then you will have information on what sort of drawdown to can expect as well as knowing what returns you can get. There is a ready source of this information on sites like myfxbook which depending on the individual trader gives you ideas of drawdown, trade size and trade selection. There are also other sites such as investegate which covers hedge funds and gives the equity growth. There are lots of traders who claim they make millions, but these sites are the only indication they do - plenty of people talk big, but cannot back up their statements. Of course, boasting that you make 25% per month sets a very large precedent for others to look up to, which is why it should not be looked upon as a competition when you have no idea how the others are running.
If you aspire to making a certain amount per month via a certain number of trades and via a certain amount of drawdown you should vie to find someone who has achieved similar statistics. A lot of traders have come and gone, and if you are chasing for a trader who has a risk/reward ratio of 1:5 and a drawdown of <5% with 30% gain a month by scalping, and you canāt find someone like that then the chances are that you will not be able to do it. I am not saying that it is impossible. If you can find a significant amount of people who are able to do it for a month, then you can probably manage it for a month. If you can find one person that can do it for 3 months, then it is unlikely that you can do it for 3 months. If you cannot find one person who has been able to manage it for a year, then you are not going to be able to do it yourself, unless you consider yourself above and beyond everyone else.
There is a reason why many people are not forex millionaires, because it is a hard job with a high failure rate. If you think about a career you generally look at what a realistic salary you can achieve with 1 year, 5 years, 10 years etc. For instance, if someone was to look at becoming a lawyer, they could look at earning $20k per year initially, $80k within a few years, and $200k as they became a partner within 10 years (this is in the UK). You do not immediately assume that you will be earning like the UK top lawyer (see this article: Revealed: Britainās best paid lawyer | Mail Online). If you worked in the civil service in the UK, you would expect $30k initially, followed by incremental increases each year with about $50k after 5 years, and $80k after 10 years. You not assume to be earning the same as the Prime Minister. In trading, performance is even more highly related to success, so do not automatically assume that you will head and shoulders above everyone else - it is not realistic, not humble and can lead to arrogance, over trading, over competitiveness which I have mentioned is one of the downfalls of traders.
If you are a scalper then follow the best scalpers and see what they can achieve. If you are a long term fundamental trader then follow them and see what they can achieve. If the best scalpers are making 200% per year, the chances of you making 500% per year consistently are so impropable and divorced from the real world, that you should re-examine the way you look at the world.
When I was at school there was a envelope making/selling job at the local postal service that paid per envelope that you made/sent. The average wage for this was minimum wage ($9/hr at the time), but my fellow pupils eagerly added up the potential to make an envelope every 10 seconds (based on how fast they could do one) and thought that it was going to be an incredibly well paying job paying over $100/hr just for making envelopes incredibly quickly. Donāt have unrealistic expectations - great things are theoretically possible but the wiser trader looks at things as part of a larger, more realistic scheme.
The initial reaction to this thread was no surprise. People want the method without acknowledging the fact that their mindset is more important than the method. Trading success is nearly 100% psychology.
Thanks for that - I had posted up a broken link which wasnāt much good. I am glad someone corrected me
Thanks for your reply. I think that psychology is important, but its not 100%. Lots of people try and look for psychology as the missing link, but I think that they are missing a lot more than psychology. Risk management, fundamental understanding, technical understanding, psychology, equity management, goal setting and many more factors that are also commonly missing.
Hello, nice thread.
It seems like you assume there is same risk reward (since you attribute same 200$ for both trades), but I donāt see a reason why you should assume this. Take for example 4 pip stop loss to get those 200, then assuming trading costs to be around 1 pip you get 1:40 R:Rā¦ you are going to need very tight stop loss to achieve same R:R for that 40 pip tradeā¦ But one thing for sureā¦ trading costs will play much bigger role on that 40 pip trade.
Also you shouldnāt use such an ambiguous word like āāsafeāā (same goes for āperfect tradingā) without elaborating what you actually mean here. Whatever you meant, I doubt you can really argue for safeness without knowing what stop loss and success rates both strategies have.
If you are attempting to learn by chart watching ask yourself: what have you learned this week that you did not know last week by watching the chart? If you can write 2 or 3 new points that you did not know the previous week I would be amazed.
I certainly could write at least one every day, but donāt be naive and expect it to be some groundbreaking discovery. For example it might start like like this: hmmm, I have seen very similar price behavior in the pastā¦ then you go back and try to find that and other similar occasions etc.
I asked him what he learned in ONE YEAR, and his learning consisted of 1) always use a stop loss, 2) donāt be emotional, 3) let profits run. Three points that he could have learned in an hour, he took a year.
1&3 are equivalent to āāmarkets trendāā. Anyway, it is hard to impossible to learn things like this in an hour as you sayā¦ there are certain things that one must experience and realize by himself to really understand how important they are.
Hi, thanks for the reply ARTjoMS. Many of the examples are very broad examples and illustrations rather than specifics which try and get across a general point. I didnāt want to elaborate on each example since my posts would end up being far longer than they already are and pretty unreadable!
[B]Conclusion to statistics posts[/B]
As cliff notes to previous few posts on statistics. I have made the following conclusions that I follow in my own trading. You may disagree with them, and apply other thoughts, but they have been instrumental in driving the way that I make money. There is a lot more in depth that you can go into - there are various books and online resources that can help. There is also software that is a shortcut for calculating odds but I recommend that you understand the principles behind them rather than just feeding your results into a computer. The interpretation (as in anything not just statistics) is very important if you are going to draw a conclusion. The conclusions I drew are this:
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Losing an account/blowing account is far more probable that what win rates and loss rates indicate (see permutations)
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Survivability grows accounts (with constant compounding) more efficiently than high risk systems
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Despite systems repeatedly having an edge over the market, single systems or techniques are short lived and need to replaced to maintain an edge
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Population studies show us other factors outside of mere win/loss rates and statistics influence profitability and drawdown and that these factors are very significant. Any trading should be taken on the side of caution.
Of course statistics are necessary to tell you whether your system will work or is worthwhile continuing with. Its incredibly important with technical trading but it equally tells us that winning 80% of the time with 2:1 win rate is not all there is to it.
My trading system is based a lot on surviving as this is what makes money as an investment.
Why have I emphasised this point? The issue is that even if you have a 75% win rate system with a 2:1 reward/risk ratio (which no one I have ever seen has achieved) it will still eventually blow up given enough time. If you trade 50% risk on that system it will blow up very quickly. If you trade 1000 times per day, it will blow up in a matter of months. No matter what system you use, no matter how great it sounds, if you do not understand that all systems have finite lifespans in the matter of trades that are rapidly shortened by trading many times per day or by increasing risk per trade, then you have missed the point. I have also made the point of looking at your own statistics and relating that to the theoretical statistics (either given by a guru or by backtesting) and questioning why there is a discrepancy. Is there something you are doing wrong, or is the fault of the system itself?
You might ask - why have I spent several posts discussing what I could have posted in one post - its because it serves to illustrate and emphasise certain points. You can quibble about small points but rather than discuss those I want to put forward my general ideas and I hope you find them useful.
This concludes the āstatisticsā part as I want to move onto talking about other subjects in further posts.