Forex Statistics and Probability

Thank you guys for your answers! I have to admit, I was expecting to be silenced. You gave me more confidence :smiley:

Thund3r can no more be silenced than l1ghtn1ng can be extinguished. :wink:

I consider there to be three types of probabilities to be looked at in a scenario like this. I call them Hit %, non-hit %, and trade %.

What you have discovered is hit %: the probability that the trade will move in your favor by your criteria (in this case 60%, 20 pips).
The second probability is playing the other side of it. Non-hit % would ask a question like: what is the probability that price will not go down by 20 pips?
The last is executing a full “trade scenario”: what is the probability that price will hit + 20 pips before going down 20 pips?
The combination of hit % and non-hit % is the same as the trade %, but I think you can learn a lot more from dissecting the pieces than you can individually. You can continue to combine them and you can sometimes find some cool relationships.

For example, if your non-hit % is basically the same as your stop loss. The lower the number, the more likely you can go for a position and hold it. The Hit % & non-Hit % (in other words, the probability for price to move 20 pips up then 20 pips down, or vice versa) can you tell you about the “exhaustion” probability of current price.
Stat trading is a tricky route, but it certainly rewards creativity and hard work.

Bottom line is that there is no guarantee. There will be patterns but anytime, the pattern could break.

There is no guarantee of future performance, but professional trading is really about statistics and probabilities, there is no other way to put the odds in your favor if you dont have statistics at hand.

Thund3r, you are raising an incredibly important concept here than underpins the viability and justifiability principles of pretty much the entire usage of technical indicators in forming trading strategies across the whole industry. If indicators do not give an “edge” then they are totally useless.

I don’t think you were actually talking about any “guarantees”, I think you were more interested in relying on “probabilities” and “statistics”? These are so tricky and can be [I]so [/I]misleading!
Personally, I don’t think 60% is a very useful result and indicates an overall expectancy of maybe 50/50. But the question of whether [I]any [/I]kind of historical outcome is reliable for current decision-making depends on many factors, a few examples:

Duration:
E.g. was it for one week or one year data?

Selectivity:
Was it across entire trading days or selective omitting quiet times?

Extremities and criteria:
The result may be 60% in total but what are the extremes in max loss and max gain, do the TL and SL match your own trading criteria?

I think it is also important to study in this way the [I]nature [/I]of the historical data used and compare it with what your future intentions are. For example, if a result of 60% has been achieved over the last 18 months can you expect it to produce 60% over the next 2 weeks?

Another important factor is whether the analysis has been carried out on a backtest/optimising program. In my opinion this kind of backtesting is only best-fitting the indicator to the specific time period concerned. The characteristics of markets do change over time and the “best-fit” scenario from the past will not necessarily continue in the future. This suggests regular backtesting and optimising may be worthwhile.

There are many, many indicators both new and old, some stay, many fade away. Probably the reason why the older established ones continue to survive is because they do indeed give an edge.

But I personally think that one should always remember that an “indicator” is exactly that - an indicator. One must not lose sight of the price action actually taking place and only stare at the indicator. Indicators can help you see the “woods” in spite of all the “trees” and which way the tide might be flowing but if you only stare at the compass and don’t look where you are going well you might just fall over the cliff.

Good thread going here, I just wanna chime in. Most of this is talking about the backtesting of a technical indicator to generate a signal using past data and estimating if that will work in the future and for how long. That’s all well and good, with some really solid info posted above me. In this case we are developing a trading system which happens to use a statistical measurement. And has all of the pitfalls mentioned above and more.

But I want to talk about something much more general. General descriptive statistics about the any market. These can quantify the personality of a market, as well as be used to make determinations on how far the market is deviated from its baseline/ normal state. (I am assuming everyone here knows that markets are non normal distributions and i don’t mean Gaussian normal) An inherent advantage to this type of analysis is that it is not datamined/curve fitted because we are extracting the data we are given and not transforming it or applying additional parameters to it. E.G. like with a technical indicator and settings. It is exactly as the instruments time series has given us, no more no less.

So lets consider a situation in where pure descriptive statistics can assist you. With no data mining but just logical reasoning.

Imagine we know that the average volatility of some instrument is 50, and that any up day is followed by a down day 50% of the time on average through the entire history. We notice that during extremely high volatility days +2 Std Devs that in fact the average up day is followed by a down day only 48% of the time, and the reverse for low volatility days at -2 Std Devs.

This would still net in a 50-50 split average up day down day ratio, which would basically be un-tradeable. However by identify a certain regime in this case extreme volatility, we earn a natural 2% statistical edge. Now the argument can be made that the # of std devs is a parameter, and it is as you could have chosen 1 or 3 etc. But they are still based on the underlying distribution, and you would like to see stability over the choice of std dev anyway. IMHO this would be a much more naturally occurring phenomenon to attempt to exploit as it revealed it self in the underlying time series, the probability of persistence is higher. Rather than attempting to try dozens of indicators to reveal some signals.

I know this example was long winded and used a very simplistic toy example. But I want to put emphasis on the fact that most people are not quantifying the descriptive statistics and general tendencies of the markets as a whole. Instead they are immediately jumping into data mining technical indicators for set ups, where curve fitting can become a much larger issue. Don’t miss the forest for the trees.

I think there is a lot of value in what you are saying here. I guess in a nutshell we could say that most backtesting of indicator performance is not a true statistical analysis at all?

I think, rather than accepting some quoted percentage accuracy of any given indicator or system and diving straight into the deep end, it is far better to run the indicator alongside one’s existing methods and see how it either complements or conflicts with it. Sometimes it may improve on and replace a component part of one’s method, sometimes it may work well but not in the TF or trading parameters that one prefers.

Either way, it is less expensive to run it parallel and test it in your own back yard rather than blindly accepting a stated success rate - afterall, nowadays one can’t even accept back-tested car emissions results as stated! :smiley:

Jack Schwager talking about risk, probability and data.

A possible answer for your question: min. 12.30 & 14.42 & 20.27

I want to say yes and no so bad… so I will yes and no. But seriously, backtesting an indicator is statistical analysis. It is telling you the hypothetical results of some experiment, usually the trading results based on this indicator. The statistics generated are measuring the interaction between the indicator, the market, and the hypothetical trades. Yes this is the foundation of all back tests.

The real question is what are you measuring statistics of? The market itself, in which my example above points that out. A potential set up or strategy, in which case back testing makes sense. Or of something else. Its really about asking the right question. If you can’t ask the right question, how will get know the answer you get is meaningful?

I want to take some time to discuss Technical analysis. 90% of it is based on price data, OHLC. If we take that as a basis, every technical indicator, trend line, fib, candle stick pattern etc. Is some derivative of price. If that’s the case then any statistical study based on an indicator or technical analysis tool is some way of filtering, transforming, lagging or modifying the data in order to be understood by a human being. We need this as no one could fully comprehend tick by tick data in any market.

Now if every TA method is a derivative, then they all are at least 1 degree of separation away from the “truth”. Truth in this case is true price. As you add more indicators, oscillators, etc you add additional degrees of separation form the market price. Same with modifying parameters, the more noise you remove the more lag you add. The easiest way to understand this is look at a simple moving average, the parameter of 1 is the price, 5 is a very fast SMA, 50 slower, 200 even slower. But as you get slower you get smoother.

Lets stack another indicator on that, another SMA making an SMA cross over. Now take a look at the results. Before if price were above or below the SMA as we moved the parameter from 1 to 200 it got slower but smoother. But when we add the cross over, chances are price has already been trading above the original moving average for quite some time. And then after some lag the 2nd moving average will cross over. Yes it removes even more noise, and reduces whipsaw. But we have done that at the cost of increased lag / increase degrees of separation.

Now your thinking jesus Meihua why dont we all just trade price action then? It should be the least lagging method. Well you would be wrong, candle sticks themselves are in fact indicators, so are any bars. You still have to wait for the bar to complete to see if the pattern fits even if its a 1 second bar. That is of course the dreaded lag. The only true price is tick data, which as a human being its very unlikely you will be able to make heads or tails of it.

I am not saying indicators are worthless, and I am not saying that everyone should stare at tick charts. What I am saying is that you need to understand EXACTLY what you are measuring, and why the statistics from these measurements will be meaningful. Price action and Indicators have their use, EAs/trading algos have theirs as well. There is a proper amount by which to remove noise to unearth signal, but its a goldilocks zone. Proper application of statistical measurement, asking the right questions, and understanding of the tool set of different statistics is required.

These two posts should be stickied somewhere.

What’s the other 10%?

Well said. Everyone who trades does so with some kind of bias, be it trend following, S/R, channel, breakout, etc. TA traders measure and test these theories with indicators (tools), and therefore one must make sure their tool is created with the intention with measuring the said theory as accurately (and cleanly) as possible.

Excellent summary, thanks :slight_smile:
Even without the issue of interpreting back-tested statistics it is equally important to understand the indicator or system itself and exactly what it is doing. Nowadays, indicators can be quite complex and not even clearly explained concerning their internal functioning. Even well-known indicators like Stochastics and MACD are used without always clearly understanding what they are actually measuring.

But regardless of how well one examines the nature of the statistical analysis and the indicators concerned that still leaves open the actual question in the OP - how much can one rely on these results in making forward projections and designing and taking new positions on the basis of these results.

One could say that on a purely instinctive basis a historical 60% success rate sounds very weak, but, on the other hand, a 90% success rate would sound very suspicious, i.e. perhaps based on manipulated or selective data.

I guess, in the final analysis, the truth of the matter is in your statement that: “There is a proper amount by which to remove noise to unearth signal, but its a goldilocks zone.”

I left off 10% for volume. The reason why it is so low percentage wise is because you are always looking at the candle that created that volume. So it is not like 50-50%. You are naturally connecting/correlating the volume to a price. So I gave it a lower percentage.

Also good to hear from you in a long time Liquid.

Well there is a whole trillion+ dollar industry based on statistical analysis of financial markets. Consider every hedge fund, market maker, pension fund, investment bank, and the like. Almost the entire financial system is based including central banks use statistics like GDP, PPP, and CPI to determine interest rate moves. So pretty much every professional is using statistics, but this was already stated earlier in the thread.

When we are talking about some trading strategy / algorithmic hedge fund. Its a much similar example and speaks to the OPs question more.

You think 60% win rate sounds weak, I could infact say 90% winrate sounds weak. The reason is win rate is only the half of the equation to estimating a systems profitability. We need to talk about expectancy or expected value.

Expectancy = (Probability of Win * Average Win) – (Probability of Loss * Average Loss)

Why? Because if I have a trading system that wins 90% of the time but has Average Win to Average loss ratio (you can think of this as Reward risk ratio just averaged) of 1:100 it is going to lose money. The 90% does not matter. You said that 60% sounds weak, well on average systematic trend following funds have win rates between 30-40%. Guess what? they are profitable, why because they have win loss ratios of 1:5 or 1:10 sometimes more. It is very niave to think that winrate is a tell all. in fact expectancy is still only a single statistics and not enough to determine overall profitability. But in order to compare apples to apples, it is probably one of the best. Sharpe ratio is also very common.

Regarding the OPs main comment and tying that in. It is not the forward projections that matter necessarily. It is how much do the back test statistics are representative of the future. Rather their stability and robustness. So your backtester must give you results as close to reality as you can. As well as you must as a strategy designer remove all biases like curve fitting, survivor ship bias, look ahead bias etc. The objective of any statistical analysis to be useful is that it must have predictive power or maintain statistical relationships with future market moves. The more robust and stable a statistic the more it will maintain that.

Thank you, MeiHua, once again for your very detailed and comprehensive explanation. I am very sorry that I have given the OP a wrong impression of the value 60% in his question. I certainly didn’t come to this forum to end up misleading people. I will have to review that decision again before continuing posting :confused:

I am aware that such funds do have win rates of 30-40%, but, as you say, they have RR ratios of 1:5 or 1:10. However when I said that I thought 60% is weak, I was trying to keep my focus on the OP’s actual question which was not just a 60% win rate but[U][I] a 60% rate of winning just 20 pips[/I][/U]. ( I also apologise for not making that clear in my post - I have already noticed that I am not very good at translating my thoughts into words on “paper”!) One certainly can’t imagine using with this a RR ratio requiring a SL of 2-5 pips? Even the shortest timeframes or tick charts would surely require a stop of at least 10-15 pips? If I were considering a system that historically produces 20 pips only 60% of the time with a RR that cant realistically be any better than 1:2 then I would consider that a weak system unlikely to produce significant results.

But I really [I]don’t [/I]want to lead anyone astray or give any misleading opinion that might detrimentally affect someone else’s trading decisions so I will say no more! - thanks for your valuable input and corrective evaluation :slight_smile:

Ah good ol volume, I temporarily forgot about it. Seems about right to me.

Nice to see you around as well. I don’t come around here all that often anymore, because as I think you would know, solid stat based threads are hard to find and that’s the basis of what I do now :slight_smile:

Honestly I randomly logged back in here after like at least a year hiatus. Saw this thread and was like wow maybe they are going in that direction. At least people are thinking about it.

But yes i am 100% algo based / statistics based, and have been for a while.

Have you seen any other good stat threads? Maybe you should start one now.

I haven’t seen many of them lately, I’ve been doing my own thing of putting together some pieces for the past couple months. The closest thing I get (which is fine by me really) is for someone to posit an idea with very clear rules or pictures, then someone (or myself) can do the leg work and see if the OP has any merit or not.

I’ve considered starting my own thread, but I don’t want it to be a case of the blind leading the blind. I’m waiting for at least another year to let the consistency work out and see if I’m actually onto something or if it’s just fluke. Most of the stuff I do share is on my blog; if you’d like a link I can PM it to you.

Yeah i obviously gave up on the whole thread thing. It was just a waste of time that I could have spend doing my own thing. Also I am not technically allowed to discuss research any more due to NDA. Either way PM me that info. Wanna see whats up after all this time.