statistics and standard deviation

I had made a few posts regarding this topic in the buy/sell line system thread which can be found here. However I began to realize that it is really a very broad and complex topic that really deserves it's own thread. I also couldn't find such a thread on FF.

It started with a theory of mine that when a system or trader is successful, higher risk will pay off better in the long run. I wrote a small program which more or less proved this to be true however there is a psychological issue that is not factored in which probably is out of the scope of what we are looking at. The logic is explained below for those interested. For some it will be boring.

Anyways by accident I happened upon something very interesting that I think we all know but don't accept. Even a winning system can lose for a while and a losing system can win for a while. How long is a while? Well first I need to define some terms so it will be easier to explain. A test is a certain amount of trades and a series is a certain number of tests. As it turns out about 13% of the tests (each consisting of 100 trades) of a losing system of (45% win ratio-1:1 r/r losing lol) turn up as profitable. That's right you have a 13% chance of being profitable after 100 trades while trading a losing system. After 250 trades the number is less than 1%. This has extreme ramifications since most people will deem a system successful after just 50 trades and surely after 100 trades if the system is profitable then that's enough. I would interested in what people think about this topic and if they have done similar things.

The program which is attached will pick a random number (it's not truly random but about as random as is possible) between 0 and 99. It uses the dot net cryptography class. If the number is below your predetermined win loss percentage then it's a win and if the number is above or equal then it's a win. It's a good way to derive randomness for a given chance. Each time it chooses a random number this is like a simulated trade. It uses this information to determine the rest. I will attach the source code. It's quite simple for an experienced programmer I think.

I would love to hear any feedback good or bad on this. Also if you don't understand what I am talking about or whatever just tell me. I would love to help. For me I don't that bothered by losses now that I really understand what's going on.

Hi bfis! It is very interesting topic and also very important one. I think that most of the traders don't understand importance of statistics and probability in trading since at the end of the day all the finance including fx trading as more sophisticated gambling. If they new something about statistics they could probably arrive at good insights like this.

Do you have interest in quantitative finance? I plan on studying financial mathematics when i join university in about 1.5 years. I think that quant finance can help a lot retail traders to be profitable, especially when they have statistical edge on their side.

All the best.

Gov

First of all this thread was in the trading section. I don't know why it was moved. It has a small program but that is just to support the idea just like you will see indicators in a trading system thread. Anyways I must admit that I have no idea what quantitative finance is. I a no math genius but I do know how to program. It basically just simulates scenario where you have placed trades that have a certain % of winning. Think of it like a coin flip program where the coin has more of a chance of landing on one side than the other. Even just a simple coin will demonstrate what I am talking about here. If you flip a coin 20 times it will not land on each side 10 times. This should be an eye opener for most people. I know it was for me. It has soo many ramifications. For one most people will test a system for a few days and if it doesn't work they quit. The reality is that this is not enough. Maybe even a month is not enough. Anyways I could ramble on for a while but for me it has helped e deal with losses a lot better. I now know that a few losses does not mean anything. Or as I recently posted in another thread, if you are hitting at 70% on a 1:1 r/r you could probably attract many many investors. You would be the dream trader. Even at that rate though you would still expect to have somewhere between 15-21 losing streaks of 3 or more over the course of 1000 trades. Granted you should also have about 100 winning streaks of 3 or more but that's not the point.

Yes exactly one should not test system for small amount of time. Couple of months or years is good. Also backtests are important but nothing trumps live trading for long period of time. Plus when you have system that works you should try to improve it and update it. For whatever reason people connect trading systems and EA as set and forget things. Most models stop working after couple of years if not updated simply because market changes and we all now that markets are not constant things.

Yes 70% 1/1 r-r ratio is a perfect trader! I would be satisfied with at least 50% 1/1 ratio or even better 50% 2/1 ration.

When it comes to quantitative finance i mentoned it because you seem to be interested in probability in finance. If you have knowledge of Calculus, Differential Equations and Partial Differential Equations go read Paul Wilmott on Quantitative Finance . People say tat it is nice introduction to quantitative finance. I am still pushing my way through all the maths needed to understand this but i think it will be worth it. Also book that talks about quant trading is Quants. Really interesting book.

definitely quantitative finance background would be a good start for any trader, and exponential research on other asset classes, risk management is also very good to have as well as psychology and so forth.

just by a trader being aware of
political events
monetary policies
fiscal policies
macro economics
as well as............

probability theories
volatility calculation and models as the black scholes, standard deviations and statistical price ranges, variances
kurtosis, skewness, and type of volatility such as heteroskedastic

being aware of other trading methods like Digital options, futures, equities, and market class correlation.

the more knowledge one has the better, but statistics and probabilities are definitely a big boost to trading, however one needs to know its short comings.

Here is my 2 pips for those mathematical minds.

Let me rephrase the question. What is the probability that a losing system (45% win rate with 1:1 RRR) will be in profit after 100 trades?

In this scenario we need at least 50 profitable trades in order to be profitable. So we can actually solve it by using binomial distribution. If you are using excel then you may key in this formula:

You will find that the answer is about 13%.

Actually this kind of question had been discussed many times. You just need to dig it out.

Let's just say that I didn't do so well in math class but interestingly to note that I also came up with the same result using my program. How many trades would you say you need to test before being able to say a system is successful? I have come to about 250 trades will give you about a 1% chance of success with such a failing system. At that point I think you might just be getting into an issue of roi considering your investment is your time. Sound about right?

IMHO all systems eventually fail. No matter how many trades in your historical backtest or even live forward test, there is always a market situation that you never encountered therefore make your system fails.

Personally I think what really matter is how you identify that your system is failing so that you can stop the system before too late.

hm, interesting point of view. I would say that probably most systems eventually fail. But if your system exploits a human trait that doesn't change over time, then I don't think that the system will ever stop working (except of course more people start using similar systems).
Well, so you are suggesting that the market will in future create market conditions which haven't happen before? That might of course be the case, but I think the markets already have shown any kind of market condition within the last 10 - 100 years.

I think it isn't so difficult to recognize when your system is failing. You can use the max historical drawdown as a cut-off point or an MA applied to the equity curve, and when the equity curve falls below the MA, then you have an indication that the system might have stopped working.

if you encounter a situation that you never seen before does not imply that the sistem is failing. if this situation happens once or twice a week then you can substract from the profits you make and the sistem lives on. if the new situation/situations become the standard and overcomes the profits that's where you will be taken out. by the way what is the statistics and backtesting periods of the best system that you encountered/ discovered?

thanks @bfis for this thread ...I had tested100 trades and I thought they were representative.I now will test 300 before making conclusions.
personally I believe not all systems fail especially if it is a simple system.....complex systems that involve taking advantage of a particular market inefficiency are the ones that go bust.
the markets will always trend and constrict and this is all you need to create a system...I have read reminiscences of a stock operator and I am struck by the similarities between now and then ....the way Livermore describes the actions of the locals, always gunning for the stops first before continuing with the trend....so we can assume the markets never change as human behavior never changes .....otherwise speculation would just be like reading chicken intestines.

The idea of failing systems is a completely different topic. I believe that there are no systems but there are only traders. Give the same system to 10 traders and you are likely to get 10 different results. When I am talking about probabilities I am really speaking of a system traded by a specific trader. After 250 traded bob trader traded some system and got 67% win rate. These statistics are only for bob and not for anyone else. However this data can be useful for Bob.

van tharp in his book definitive guide to position sizing recommends a minimum of 100 trades to derive a sq. no. he also says too many trades will skew the results.

I think doing Monte Carlo simulations on the 100 trades will point in the right directions and show whether the system is really worth trading.he recommends a sq no. of 1.7 and above.I am sure the 45% 1/1 win/loss system can't cut it.

my 2 cents.