Beyond of average
I do financial software development for twenty years already, and from different peoples I always receive one and the same, very obvious question: "If I buy your software what profit can I expect?". I always fee myself uncomfortable when they ask me this question. Usually I answer very straightforward (like this: http://www.timingsolution.com/TS/Articles/10pc_above_Chaos/index.htm ) - you will get 10% above Chaos. Some people liked that; others asked for more details.
Some months ago I have suddenly figured out how I should answer this question. This is what this article is about.
I have already mentioned many times that the usage of standard mathematical statistics methods does not give any significant results. Automated trading systems that proved working well and, from statistical point of view, expected to be working well forever, - they suddenly stop working the same way, which breaks all statistical laws. As Mandelbrot mentioned, the drop like the one occurred in year 1987 can happen once in so many years; however it happened in 1987 and then, 30 years later, in 2008 it happened once again.
Does it mean that statistics is not working here? Usually it is not easy to figure out that it still works, and nobody is cheating you. Simply the statistics that really works in finance (or any science that deals with phenomena that involve active human behavior - like sociology) and the standard statistics are two totally different sciences. This subject is very popular now, there are specialized University seminars and research regarding financial mathematics, there are special books on this subject.
As I see it, the main difference between these two branches of statistics is: the standard statistics analyses/try to reveal the most common case(s) while the financial statistics deals with the chance, the chance to outperform the stock market. For example, if you work for some government department, you will definitely apply standard statistics, as you need to cover the maximum amount of cases. The average household income, GDP per year, life expectancy - all these are the statistical averages that give you the averaged portrait of citizens of your country.
Financial mathematics analyses chances: we want to make some money, build our wellness. Any trader will tell you: you have to work with news, not gossip, just NEWS FACTS. You need to find your system, and have enough DISCIPLINE to follow that system. Chaotic and emotional behavior is not acceptable here. IMHO if we would like to specify the most common characteristics of a trader, this is seeing a risk as a native environment. This is not an averaged person. Averaged persons are described by standard statistics that represents majority while the financial mathematics deals with the minority behavior. In other words, we are more interested in out of range behavior. This is still the same statistics, though concentrated on a different subject - standard and non standard behavior.
Why I write all of this? I think we can apply this knowledge practically.
Firstly, we should always remember that applying standard statistical formula for estimation of trading systems we are practically always underestimating the risk. I wrote about that several years ago here: http://www.timingsolution.com/TS/Articles/cds/index.htm
The second issue is finding a mathematic/technique that is the most suitable for building financial models. Actually, as it is now, I see more questions here than their solutions. Consider this example: to estimate the workability of some projection line, we use Pearson correlation criterion. This criterion is proven to be good when we analyze normally distributed oscillated processes. However, I always have a feeling that some other math should be applied here, and we will be more concentrated not on common/averaged but on something exceptional, something that brings us profit.
Look at Quantum models in Timing Solution. There I tried to build trading models based on this new statistics. As an example, let's Annual cycle, the most reliable cycle in finance data as so far. If we calculate this cycle following classical, standard, statistics, we get a composite diagram like this. It shows the averaged movement for IBM stock within a year:
Q Annual cycle works differently. We are not interested in general knowledge of how this Annual cycle works within a year (it may be not working at all). Instead, the only thing that we need to know is the time to open and close a position. This is how Annual Q cycle for IBM looks:
This cycle reveals two trades only, one long trade (buy this stock October 7 and sell October 21) and one short trade. As you see this cycle is not working for trading all the time, it works within some restricted time intervals only, a kind of pearls in the sea of Chaos.
A classical Annual cycle shows the general Annual tendency, and this is good as Annual patterns really exist, exist from the point of view of average values. It is useful when you do some analysis of markets in the past, for some magazine, as an example. You may make some good finds there, why not? But - if you decide to trade this stock using Annuals, it means that you will actively dealing with the future. What you do now affects your future, positively or negatively, and your good finds in the past may not be so good to you. You are entering here a different territory that needs a different math. This is why for some last years I mostly work with quantum or a-la quantum models.
And here is the answer to the initial question about expected profit. The question has been asked in terms of classical statistics, statistics that covers maximum amount of cases. Accordingly you receive the answer in terms of classical statistics - if you use this system blindly, you will receive 10% above the Chaos accuracy. The question asked this way totally excludes the human behavior, your behavior, from our consideration. I believe the question asked this way excludes the risk management idea from our consideration as well. IMHO the involvement of human activity demands necessarily a good risk management.
PS. I wanted to stop here. And I decided that some words have to be added in regards to risk management.
Yes, there are a lot of sources that teach you how to reduce your risks with different tools (like different order types, stop-losses, diversifying your portfolio, etc.). However, I believe that the main problem is not in those. It is much more important HOW the trader applies them (as opposed to WHAT tools he or she uses). Some call it "intuition", some call it "karma". I prefer "common sense" or (better) "gut feeling". To me, it is a continuation of our basic instinct, the survival instinct. IMHO, actively applying risk management methods, we activate the parts of our brains that were developed by first animals 400 millions years ago. It is a part of a brain responsible for the orientation in the surrounding world. Thousands generations of dinosaurs developed it trying to avoid being eaten by ugly tyrannosaurs :) A trader, reading news and analyzing various charts, tries to avoid being beaten by the Market. I really do not have a better explanation.
August 17, 2015