Math can prove NOTHING about the real world without first scientifically proving the assumptions and axioms that underlie the mathematical model. This is the great weakness of math. The weakness of mathematical logic is best illustrated with the 2300 year saga of Euclid's fifth postulate. (and yes, it does mean something for trading) <b>Euclid 5th Postulate and the Errors of Intuition:</b> The history of Euclid's 5th postulate illustrates the problem of trying to apply the abstractions of math to the real world. For those that do not know, back around 300 BC, Euclid created 5 postulates (core truths) that underpin all other developments in planar geometry. The first 4 postulates are short, simple sentences that defined points, lines, circles, angles, etc. The fifth postulate was uglier -- a long-winded, inelegant definition of parallel lines. For centuries, mathematicians have sought to prove the fifth postulate from the first 4. Their arguments for their efforts had been that: 1) the properties of parallel lines are obviously physically true; and 2) the fifth postulate is too kludgy to be a postulate (even Euclid himself did not like this postulate). But, try as they might, these learned souls could not find a way to PROVE the fifth postulate from simpler axioms. One tack taken by the mathematicians was to show the outrageously absurd implications of assuming that Euclid's 5th postulate was false. The result was a counterintuitive world with "curved" straight lines, parallel lines that diverged or converged, and angles that did not add up. Thus, mathematicians invented a bizarre world of so-called non-Euclidean geometry. Although non-Euclidean geometry grossly violated the physical sensibilities of everyone, it did not violate the logic of the other 4 postulates. By the mid 1800's non-Euclidean geometry was a oddity of only academic interest. Then along came Einstein, whose work on relativity and the nature of space-time used Riemann's work in non-Euclidean geometry. Einstein's theory suggested that the physical universe might be non-Euclidean! This was first proved in 1919 -- showing that "straight" lines of starlight curved as they passed close to the gravitational influence of the Sun. Thus, the patently absurd became the scientifically accepted. The evidence that the universe is non-Euclidean is evidence of how wrong mathematical and physical intuition can be. <b>Conclusion:</b> My point, for those that have stuck with me on this long essay, is that math and the real world have nothing to do with each other until science connects the two (and science is a fickle matchmaker because it can easily disconnect the two at any later date). Math is a virtual world populated by assumptions, idealizations, and their implications. Mathematical constructs are abstractions -- convenient mental artifacts that may (or may not) bear a passing resemblance to reality. (At some level, I would argue that ALL applications of math to the real world are mere examples of the curve-fitting that traders know to avoid.) In the case of geometry, all of the mathematical PROOFs that everyone learned in high-school geometry are true in the mathematical world but NOT true in the physical world. In the physical world, they are only approximations (admittedly, they are extremely good approximations). The math of the markets is the same. And in the gap between the assumed mathematical ideal of the market and the actual physical reality of the market lies the potential for profits for traders. Postulating high profits for some traders, Traden4Alpha
Traden4Alpha, That's a great post. Mathematics dominates every aspect of our lives in far deeper ways than we could imagine. I remember one of my favorite mathematical puzzles was that of the "traveling salesman." Assuming a salesman had to visit 50 cities, what would be the most efficient route for that salesman to take? To this day, I believe that this is still one of the great unsolved mathematical puzzles. Brute force can solve it, but it becomes exponentially more complicated as the number of points becomes larger. Actually, I correct myself. It appears they have found new ways to reduce the time required. Here is a map for Germany and thousands of cities: http://www.math.princeton.edu/tsp/d15sol/d15map.html When it comes to market movements, they apparently do trend. The problem comes with knowing how long a trend will last, how long a retracement will last and several other factors. The longer we watch a trend to observe that it is, in fact, a trend -- the more trend we waste in that confirmation. The less time we give a trend to confirm itself, the higher the probability that we could be entering on a random spike up or down within the noise itself. You could sit down all day and apply all the math in the world to the markets and still be no better off than a 5 year old playing it like a video game (in my opinion). There are generally several good high-probability setups within markets that, if you can recognize them, you can exploit them and come out ahead over a given amount of time. You could take a trade with a +1.0 ES target and a -1.5 ES stop and enter LONG or SHORT from the flip of a coin. You might do really well for days, weeks or maybe even months -- but this doesn't mean the system is viable over an "extended" amount of time. I'll just as well take my 5k and the system I've developed and go trade. If I lose it, oh well. If I scrape by, then maybe I'm onto something. However I have long since abandoned trying to apply esoteric mathematical principles to trading.
aphie, Excellent points! <b>The Traveling Salesman Problem</b> is another really good example of the gulf between theory and practice. In THEORY, this optimization problem becomes exponentially harder as the number of sites grows. In PRACTICE, programmers keep coming up with clever ways to solve the problem for cases that the theoretician said would take a supercomputer the age of the universe to solve. You can prove that the problem gets harder in theory, but cannot prove that the problem is hard in practice. <b>Exploring vs. Exploiting Trends:</b> I also liked your explanation of the trade-off between the wait for confirmation that wastes the trend vs. the exploitation of every wiggle that exposes the trader to false-moves. This logic also applies to system development -- do you paper-trade a system for so long that the market changes before you actually use the system to make money? The trade-off between exploration and exploitation is found in all adaptive systems -- and if a trader is not an adaptive system then they won't be a trader for long. <b>Abandon Math? NOT!</b> I, personally, would not go so far as to abandon "esoteric mathematical principles" in trading. Math can provide extremely powerful insights into the markets and trading systems, if one can stomach the assumptions that one has to make to use that math. The key is to understand the discrepancy between the real markets and the idealized mathematical model. These discrepancies come in four flavors with respective implications for using a powerful mathematical tool: 1. If that discrepancy is unfavorable, the mental leverage of mathematics will amplify it into a seriously losing situation. 2. If that discrepancy is relevant, but random, then one can apply the powerful tool under the proviso that the results & risks will be somewhat worse than expected. 3. If that discrepancy is irrelevant or negligible, then one can apply the powerful tool to legitimately optimize a trading system. 4. If that discrepancy is favorable and systematic, then one look for even more powerful tools to model and exploit that new-found structure in the markets. <b>Esoteric Math is like an F-16:</b> I would never put a novice in the cockpit of an F-16, but that does not mean that a trained professional cannot exploit the awesome power of the plane with an acceptable level of risk. I'm working on my pilot's license while I'm Traden4Alpha
some great posts in this thread! I haven't seen the interview since I don't get Fox over here in Switzerland but my theory of markets is the following. Let's assume that the average performance per year of a certain Index is 8% per year. And this 8% represent the economic growth of the companies that are represented by the index. Now if someone just buys the exact same stocks that are in the index and bought them when the index is established then he will be able to get the same performance as the index. Well over the years he would also have to adjust the change of the index and this would be the only activity in his portfolio. Now on the one hand it lies in the nature of the markets that market participants don't hold a stock for this long period of time. As a fact most people buy a stock when it has already an established trend and in this way it will never represent the performance of the index. On the other hand most market participants hold a loosing position longer than a winning position and therefore they ride with their investment more of the down trend than on the up trend. Well this is a very practical reason why most are not able to outperform an index. Now I want to come back to the zero-sum game. When we have an yearly average performance of 8% in an index then someone who would be able to generate 12% over the same period of time with the same stocks that are part of this index then he would either have to exit the markets at times of a down trend or he would have to select the companies of the index that perform the most. Now when selecting single companies a higher risk is being involved so we only take the example that someone buys every stock of the index and combined with a market timing strategy - he exits in a down trend and enters again on a lower level. The point is and that's where aphexcoil was right is that for the time you are not loosing money and the market is in a downtrend someone else has to loose it. So if you make a 12 % average yearly return over a period of 30 years and beat the index by 4% then someone else has to loose this 4%. Compared for example to the futures markets where there is always one winner per looser and always the same amount of money in the market. In the stock market indexes there is also the same amount of money in the market but this money increases yearly by 8%. So the zero-sum game starts at 8%. hope anyone understands my english... little fuzzy today.. because I'm little tired. I just got home from a 11 hours hike in the swiss alps... Was a beautiful day and on top of the mountains there is already a lot of snow.
Traden4Alpha, I'm not suggesting one abandons esoteric mathematical principles. Well, actually I guess I am -- but here is how I see the difference. Most everyone has a good grasp of the power of the human-mind knows that it makes very complex calculations all the time. If you're running around on the field playing a sport, your brain is working out very fine calculations to become better at the sport. Take golf for example. Most people who start playing golf when they have never played before outright suck. Why? Because they have no grasp of how be correctly aligned with the target, correct posture, address, stance, grip, takeaway, etc. All of these things are very important for a good golf swing. Now, after taking lessons, the individual learns what it feels like to be addressed properly to the ball and how the correct posture feels. Soon, they learn how to take the club back and how to coordinate their muscles to hit a good shot. This is training of the body and mind, but it translates into mathematics at some level. The mind has to constantly be aware of where the arms are in a three dimensional plane at all times. It must make specific power calculations for hundreds of different muscles. What does this feel like to you? It feels like you're doing what you've always done, but with more practice you ingrain those correct calculations into your mind and your swing becomes better. Now lets go into trading. Obviously, not everyone is a math wizard -- but this doesn't mean that they aren't doing differential equations within their heads subconsciously. So when you apply these theories to trading, experience is golden. The more you trade, the more your mind begins to subconsciously take in patterns, probabilities, statistics. What does this feel like to the trader? It feels like intuition. This is why a mechanical system could never defeat a true experienced intuitive trader. Your mind is taking in information from many sources -- price, volume, direction of trend, tick, trin, futures, etc. To a new trader, none of this makes much sense. A mentor might tell the trader, "When A happens, B usually happens, but not if C occurs." Just like teaching someone how to golf, a golf instructor can show a student all the correct principles behind a good golf swing but only the student can devote the time needed to practicing to become better. So, it is my belief that, at some point, one doesn't need to apply "outside" mathematical approaches to trading. Everything that must be done is done in real-time on-the-fly via the training the mind does subconsciously. It all seems so confusing until, at some point, it just clicks. That's why a lot of people like Gordon are still in that "show me the picture of a good golf swing" mode. What needs to happen is that you go to the range and start hitting shots, see where the ball goes, and then progress your training from there. You won't become a good golfer by watching the Ryder Cup and you won't become a good trader by reading books.
aphie, that's exactly what I always try to tell people that are asking me how trading works... most people are able to catch a ball even they don't know Newton's formula of gravity. But that formula exists in a complex format in the brain of a person. The format of connections between synapses. A biological memory that has the outstanding ability to combine information in a creative manner... and this creative ability of the brain enables someone to combine information in a non mathematical approach.
aphie, before i started trading, if i had looked at someone like me, i might have said the same thing. how many people open up their trading accounts thinking they're going to lose? we all think the losers are someone else and it can't happen to us. i did as well. who here doesn't think they're going to be the 5-10% of traders that succeed? my point is, don't be surprised if a year from now, you're in my shoes. i bet after you trade for a while, you'll be like, "what the f$@#?!" "i didn't think i would do this bad!" "why am i not making money?!" "what am i doing wrong?" here is the major issue i have with you on this. you speak as if you're a great trader with many battle scars. it's as if you think you have such great trading knowledge that you can look at me and see everything i'm doing wrong. i loved this quote: "What needs to happen is that you go to the range and start hitting shots, see where the ball goes, and then progress your training from there. You won't become a good golfer by watching the Ryder Cup and you won't become a good trader by reading books." how many times do i have to state i've been trading actively for 3 years? what makes you think i have not gone to the "range" and hit a few shots? i've hit many. you also said: "It all seems so confusing until, at some point, it just clicks." has everything clicked for you already? have you mastered the markets? if so, where's all your money? let me know if you are up $1 after 2 months of trading. i'm not trying to be an asshole. you know i'm on your side. i just don't see how you understand what my problem is when it seems we're in the same boat?
I'm not trying to knock you at all. Believe me, I've taken some hard knocks -- I've lost a few thousand from not using stops in my past. Although that is a stop loss for some, it was a good chunk to me at the time. You may be right! We will begin to find out next week. Ass-kicking or not, it will be nice to get back into active trading.