Perspective is what prevents it. Everything is already either 1) perfect for something or 2) will be perfect if ...

I am in the camp of 1) everything perfect for something. I believe perfection is simply finding the right tool for the right task.

perfection seems to be more obtainable in small test samples, and as the data amounts increase inversely the reliability of the results will typically decrease. einstein faced this problem when leaving worldly math and venturing into mathematical permutation of celestial orbital bodies.

most likely with a staunch belief in the power of math einstein came up with the theory of relativity. now we are into super computer required research, however man has mostly failed to catch up with providing the correct inputs to discover anything absolute so far.

so we trudge along with moderate solutions that are to trading what the most popular paint color (white) of cars is - boring.

truly our acceptance of perfection could be the one rock not overturned yet most likely because we are standing right on top of it.

@Mark, I find breaking the issues/problems down into small manageable pieces that can be refined over time is best for me. I have long had the basic infrastructure but there are always new requirements, improvements to existing approaches and even completely new algos.

Having said that, I allocate some time (not as much as I would like) to pure research. I read a lot of academic papers just to see if I can find a nugget that will allow me to look at an issue in a completely new way.

I think this is indeed a hunt for the Holy Grail. Personally I do not know Sir Launcelot, so I think it will be a very long time indeed until he resurrects at the end of everything...

Now, taking my tongue off my cheek, I am going to state my firm belief that mathematics are never perfect. Math approximates goals in asymptotic fashion, always closer, never there. There is some really weird kinds of math that produce really weird kinds of results. But none of these will never ever be perfect.

If the object is to trade we can approximate perfection well enough to do so. By well enough I mean well enough to develop a good edge and to be able to trade profitably. Will we ever be able to trade with perfection, not so although we may approach this goal asymptotically.

if math is merely an expression then perhaps it is the observer who has fault. man can only gain advances by a belief that is not yet based on proof. how mundane for one to follow and regurgitate what is already known, this is called higher education! asymptotic: the devil's invention.

It's like as the cuantum paradox.

Math is kind of fiction. Perfection is anemy of good.

@Mark, it is like everything else. Higher education benefits some more than others, and overall only a small fraction of postgraduate degree holders will be capable of doing truly inventive, original research and discoveries. What I am describing is the right side of the familiar bell shaped curve, the left side also exists among those with postgraduate degrees but I would rather not talk about them.

higher education should come from practical in the field experience which promotes a positive attitude to succeed at a task. not in a classroom being dictated to and tested on memorization.

back to perfection for me it is the absolute knowledge that if a labeled event happens i can depend that another labeled event will occur. not all events observed in life are predictable in their outcome, but i have found those involving math are far more dependable.

Math is the only universal language we currently have. You can state in any language on this planet: 2 + 2 = 4, and everyone will agree. Oops, not everyone, twice I've seen in this very forum someone having stated the “opinion” that it did not hold, one of them presenting himself as a mathematician!

With math we can understand how things are related, how things work. It is with a mathematical formula that we can understand and measure gravity, force, quantity times price... The math is out there, not only to model our world, but to help us observe, measure and predict the outcome of a multitude of phenomena. But it still remains a tool, just like a shovel. Even if I have a formula for a stochastic process, it does not mean that everything I'm looking at is stochastic.

So the question is not if math is perfect, but can it be useful? The answer is an unequivocal yes. As a matter of fact, if you don't use it in trading, you are doomed.

The original question was: The answer to this is very simple. You are dealing with a quasi-random phenomenon. And to the extent of my knowledge, I still have not seen anyone systematically beat a simple game of heads or tails. It's only if the game is inherently biased that you could design a betting system that will make you win, not all the time, but on average, and end up with an almost assured positive outcome. Effectively, designing an edge which at first will be extracted from statistical data observations. A bias that then can be transformed into programmable gaming procedures.

The notion of “holy grail” in trading, to me, is a silly one. Should one wish to estimate the odds on finding it, they should start using words, and mathematical expectancy measures, that go way way beyond infinitesimal, and give themselves some time like billions and billions of years to find it. A more modest “successful” trading strategy would be kind of more appropriate, at least you will find some of those.

All you can do is observe what is out there. Try to design a mathematical expectancy model that reflects part of what you see and then test it on past data to see if it's worth its salt. From my observations, if you come out with a positive result, it already starts to be a feat. You might have found a winning edge.

Yesterday, I had a university professor, in an attempt to close a discussion state: everyone has their own truths. To which I argued: no, not at all. As this would imply that there are 7 billion shades of the truth and I can't accept that. In math, there can only be one. An equation stands or it does not. It's not a matter of opinions. However, does the equation used depict what is being observed? That is another question altogether.

guy as always your post are enlightening and i appreciate your input. there is much discussion at the university about math failure and always it is actually the application. such could be said for market data as well, which is really as you mentioned a quasi-random phenomenon.

i endeavor to complete a holy grail system because i see traces it could exist. there is pure math which can be allied to a normal market and more fuzzy math which is useful in an emotionally driven market. the recognition of these separate events and the ability to switch methods adaptively are where i have focused.

i find comfort trading events out of the normal market rhythms and so i spend allot of time in a dreamy artistic math fringe area which would seem ridiculous to most. but i am ok with that because the results prove my addiction worthy of the risk. I believe in math's absolute truth and honesty, and that my inability to properly express the problem is where most say math fails.

if the holy grail exist it would be dependant upon properly identifying all the variables which make up the pulse of the markets.

There is no holy grail in trading just as there is no holy grail in poker. However, you can use math and algo's to gain a large advantage in your probability to make winning trades.

Hello Guy, I had not heard from you for a while. Agree with you, math is a tool and it is not designed to be perfect, it is designed to do something, some action, which it does do well within its design parameters. The problem comes math is applied beyond its design parameters. Or like what you called the market, quasi random phenomena. What does this means? It means that the math we know and we apply to the market is not designed to deal with issues like these quasi random phenomena.

For example have you ever given any thought as to why it is impossible to control the violent corkscrewing of hydrogen plasma inside magnetic containment bottles used in fusion research? Most likely it is due to the fact that we cannot predict what the behavior of the plasma will be inside the magnetic containment bottles with the math currently available. So, quantum mechanics does not work for this application, we need something new. Great! When we find this something new we will advance a couple more steps forward and then find out something else that does not work as expected, and get something new again and over and over.

Is this applicable to the market, yes it is and always has been, the market is not predictable. It is a complex system of infinite complexity, it is likely that the hydrogen plasma inside a fusion reactor containment bottles is more predictable than the market is (ie less variables and therefore less complexity than the market's).

As you state, the tool does not fail, it is being used for a purpose it plainly cannot do. This will lead to a better tool for dealing with that purpose. If you wish this will be a step closer to perfection, something we will never achieve simply because we cannot design a universal tool to work without fail regardless of what we throw at it. In my opinion therefore, looking for the Holy Grail of trading is like looking for that mythical health pill that cures all, a pill that will take care of your cancer, make you better looking, and improve your sex life all at a very reasonable price...

I agree and disagree with your point about the variation in "truth". We all perceive things differently, even when we are looking at exactly the same thing. The truth inherent in whatever it is that is being observed may be very complex and therefore there may indeed be many shades in the way this "truth" (of the outside event) is perceived. These differences or shades are not differences in the "truth" of that one thing we all look at and study, but differences in individual perception (and you should add the bias of the observer because we all have biases).

I look at the market as a personal thing. It is really not personal at all, it is shared with millions of other people, but my individual perception of the market is very personal. Events mean something to me that they may not mean to others, data is used and manipulated by my methods which no one else may use. Ultimately what I get is a collection of gains and losses to guide me further into the market. Is this right in an absolute sense?, most certainly not, but it is good enough for me. The important point here is the "me" centric view of the market, which I am willing to gladly accept is different in many shades of variations with the views of the market (the same object that we are all looking at and studying) of innumerable other people. As long as what I perceive and I do with my market perceptions are acceptable to me, all is well. I do not disagree or find it upsetting that others may have different perceptions or different approaches to the market than I do.

The perfect tool for trading would be time travel.

Guy, I agree... "everyone has their own truths" ... haha! No. As the Lone Wolf of Wall Street (Bernard Baruch) is credited with saying in 1946 "Every man has a right to his own opinion, but no man has a right to be wrong in his facts."

http://www.barrypopik.com/index.php/new_york_city/entry/everyone_is_entitled_to_his_own_opinion_but_not_his_own_facts

Hi Mark, I think we have a different definition of what could be considered the “holy grail”. I prefer the term used in academic portfolio management literature: “atlas strategy” to represent the ultimate strategy. The atlas strategy is the one that supersede all others. It's the best solution of them all. And that's the one I consider out of reach. However, if you are looking for a “holy grail” definition that signifies an assured future positive outcome, then that type of strategy abound. It won't be the case of one strategy anymore, but of many.

In matrix notation, I can write: A(t) = A(0) + Σ(H.*ΔP). This formula covers any trading strategy H applied to a portfolio of stocks over any time interval. The atlas strategy is usually expressed simply as: H*. And when ordering strategies, performance wise, it would get first place: Σ(H(*).*ΔP) >>> Σ(H(S#n?).*ΔP) > Σ(H(S2).*ΔP) > … > Σ(H(B&H).*ΔP) > 0; where H* exceeds your, or my, best positive trading strategy H(S#n?) by an extremely wide margin.

The atlas strategy exists. It's simple logic, there has to be one. It's just that the probability that your, my or anyone else's strategy is it is really really really small as expressed in my last post. Personally, I don't think that any of my positive outcome strategies could ever even come close to the atlas strategy. It requires perfect information. I can add that I don't even search for it. The reason is also simple: going forward I'm faced with a quasi-random phenomenon. I can't outguess the future at every turn, but I can “outsmart” the averages over the long haul. Meaning that I can design an H(S#n?) strategy, which could only be viewed as my best effort. This does not mean that your trading strategy is less than mine, only that what I could do was my own limited best effort. Yours could do much better than mine; I have no problem with that. And I would provide accolades.

If you remember, I've used a strategy you originally designed and made public in 2002 on Weath-Lab. It was later modified by someone in 2006. I transformed it again to do more in 2011 by changing its trading philosophy and long term perspective to adhere to my vision of things. The 2011 portfolio simulation was done on totally out of sample data since it was only considering the previous 6 years of daily prices. Not only that, the stock selection was also totally different. If there was something in the improvements to the strategy design, it would definitely have to show it, performance wise.

I'd like to take that as an example that a strategy by itself can be made to be a dynamic process which can be improved upon, time and time again, by changing its environmental decision making process and coded gaming procedures. I viewed making the improvements as just moving the strategy up the ordered performance list. I can't say that it approaches anything close to the atlas strategy, only that it was on my way to my best effort.

@Guy why waste time looking for perfect information or for perfect strategies. All you need is something that works for you. You need to improve it with time and you need to apply it in a way that any drawdowns will not destroy your ability to stay in the market. Everyone has to develop a way or a path that leads to improvement of his/her efforts. There is no perfection there is only approximation, you can always get closer and closer to perfection but you will never get to it. Perfection is not a valid goal, but there is always room for improvement.

Hi Oscar, nice to hear from you. As usually, direct to the point. I appreciate that.

You say: Yes. And that's the whole point. We don't have the same notions. We don't give them the same weight. But when we use a mathematical formula with the same input variables, we do get the same answer.

The way we interpret the answer is where we will find the differences, within the nuances we can bring to the analyzed problem. But first, the interpretation we make will have to agree with our own respective perceptions, opinions in some cases, and value systems. It will all have to make sense and stand tall within all the knowledge acquired over the years.

In an automated trading strategy, the math is not the problem. It's the decision making process that is. The logical conditions we apply to trigger entries and exits. The what makes our stock inventory change or not. We both face the same stock price series, it's just that we will time slice them, and manipulate the traded volume, differently. Technically, we will simply manage the stock inventory differently for the duration of the do while loop.

If the math in a strategy did not give the same answer every time, I would throw away the program. I don't want a computer program that will, only on a whim, answer 4 to the 2+2 question. It has to have the correct answer every single time or else.

A trading script is structured as an endless do while loop with statements (equations) and conditional variable tests (logic) to do such and such, including issuing trading orders. I want each coded statement to do exactly what I've programmed it to do every time I run the program. I don't want to have the program feel sentimental, fuzzy, indecisive or opinionated.

You use more sophisticated techniques in your programs than I do, things like AI. So I expect that our respective programs will be very different. But we still have the same objective: to do the best we can with our respective trading scripts.

A lot of stuff add up to opinions, educated guesses or preferences. But when it comes to mathematical equations, there is little choice available. To an equation, one can only answer true or false. Does a square have 4 sides? That too can not be resolved with an opinion and one could hardly argue the point. A program statement: A := B is not open to interpretation either. However, an if this then do that, could trigger a trade or not.

All the things you have said in the past concerning your own trading style showed an intricate system adapted to your perceptions and needs. I find that great. You do have a well balanced view of trading. You know what you want, you know what is available, you know what you can do to achieve your goals within the market limitations presented to you, and you have the tools to do the best you can. Your strategy might not be the atlas strategy, just as mine, but it will be good enough for you; until you design a better one if desired. It is also a strategy you will understand quite well, after all, it's your own design. It's the same for me.

In that sense, it is a personal thing. We extract from our respective perception of the problem what make sense to us. From the data we observe, we will synthesize and design a programmable long term edge.

The quest remains not of a “holy grail” but just to do the best we can within our respective limitations. This should not stop you or anyone else from doing better than most. We do the best we can with what we have. That's all we can do.

Hello Guy, as usual I am enjoying this. Everything you say is correct. However there is what I consider to be a very important factor that has been left out. That is the broad selection of what to trade and under which time frame.

For example what security do you wish to trade. The choice of securities is very large. You need to select what it is you are going to trade and how you are going to focus that trade before any math calculations take place. Do you require high volatility or high stability of price? Do you prefer a specific sector for this particular trade, and how do you choose the sector you wish to trade? The market is complex, there is sector rotation going on at all times. A trade that breaks down when using a given sector may be entirely applicable to a different sector. I do not know of any specific mathematical way to profile what I want to trade, my approach is to run simple tests with a variety of securities I am interested in and I follow, and based upon these preliminary tests choose the security I will trade using whatever approach I am planning to use.

There are stocks that go back and forth between a high and low values, in a tight range, and have been doing so for quite a long time. These are good securities for trading in weekly time intervals. There are sectors that are very sensitive to the newsmedia, others not so much. This can also be used to define a trade.

The point I am trying to make is that there are very important issues requiring the use of opinion, educated guesses, and individual perceptions at every step of the way in the setting up of a viable trading system. This is something that is highly personal and will vary from individual to individual.

Another point I want to make is that you may use math or mathematical techniques that do not provide the same exact answer in every run. This is, in my opinion, a desirable and attractive feature offered by AIs and NN's. It must be understood that because of the way AIs and NNs are designed, they yield very different results in repeated runs using the same data and the same basic analysis. All you have to do to obtain these different results is to vary the AI/NN defaults used for each run.

One of the simple demonstrations that can be done using AIs or NNs is to feed the system paired values of radiuses and circumferences of a random sample of circles. The system will resolve this data to yield approximations of pi, the constant. None of the approximations will be exact unless you allow the system to run to completion. Limited runs always yield approximations. The same data may be run repeatedly varying run times, or other defaults which produces a scattershot of results around the value of pi. In my opinion being able to obtain a scattershot of approximate answers is more valuable when dealing with the market than obtaining a single invariable number.

As you described before, the market is a quasi-random system. Why should the mathematical solutions to such a system be fixed? A cluster of approximated and related solutions obtained as described can be valuable in dealing with such a quasi-random system as that provided by the market.

Hi Oscar, yes to all your premises and conclusions. And again straight to the point: <...selection of what to trade and under which time frame >. One sentence and you are opening up all the academic literature on portfolio management of the past 60+ years. In a way, it is asking for what will be the best ultimate solution? I don't know!

All I can analyze is from what I see, making some assumptions on how the data is interrelated and try to extract from it some long term viable trading strategies. A simple and honest quest to find better and better methods within my trading philosophy. I've modelled this philosophy to be a variant to Mr. Buffett's investment methodology.

In this variant, everything is governed by the math that can help realize my objectives which can be resumed in one sentence: accumulate shares for the long term and trade over the process. It does not say: I know the future. But I do make the same long term bet as Mr. Buffett: a bet on America. In fact, a bet on humanity, that living standards will continue to improve for all.

So the assumptions are easy. I'll be looking for stocks like MA which I think might survive for a long time to come and which I can trade under any time frame (meaning no preset time frame). It's not the same answer for everyone naturally, but these are the premises my programs look for and adhere to. Everything within this methodology can be easily explained. I view it more as a compromise of sort in the face of future uncertainty.

You have this mess, this ever changing swarm of buzzing equity prices fluctuating quasi-randomly in this erratically pulsating sphere having for centre of gravity the actual prices agreed upon by the majority of participants at that very instant. The activity within this sphere is unbelievable.

You can only track, by hand, a few stocks from the multitude; a little more with a computer. You don't want any of your selected few to be squashed into bankruptcy. Nonetheless, should you ever have one, your strategy design made it so that it will have only a minor impact at the portfolio level. So technically you need to design the best you can and still plan for the worst.

If you want to outperform the averages over the long term, you will find some limiting factors. Academic literature with its efficient market hypothesis abound with these. No one seems to see, or accept, that they can easily cross over a portfolio efficient frontier. Naturally, if one accepts this limit and design his/her strategy to live within it, they should not be surprised if they do achieve their goals. You don't see index funds outperforming their index by much, they most often underperform their index. They wanted to live within their efficient frontier boundaries and they got it. Wasn't this their very nature by design?

You will need to do more to escape the gravitational pull of market averages, this pull is very strong. Most achieve long term portfolio performance results below their defined efficient frontier, below market averages. See Jensen's paper for instance where he showed that long term average alpha generation was negative at about -1.7%. And thereby confirming that the market averages were quite hard to beat, on average.

Yet, you will find Mr. Buffett having escaped this gravitational pull. He outperformed for the last 50 years, a remarkable feat (about 10 alpha points). That's A(0)*(1 + 0,20 )^50 compared to A(0)*(1 + 0,083 )^50; 9,100 times initial investment compared to 54. This amounts to a doubling time of about 3.8 years compared to 8.65. It all comes right back to achievable long term CAGR levels.

Much finesse in Mr. Buffett's methodology. It deserves to be studied. I see it worthwhile to extract its best qualities. And then try to do better.

@Guy - have you read all the recent articles regarding the differences between what Mr. Buffett says he does and what he actually does? He apparently possesses quite the public relations machine and the principles (ethical primarily) he espouses are not how his companies act.

These are quite interesting reads on the order of Flash Boys and come not from one disgruntled competitor or ex-employee but from a multitude of sources complete with facts and figures.

I would be interested in your take on it since I know you know a good deal more than the average person about him and certainly infinitely more than I do.

@scott. Where can you find those articles on buffet?

@Tyler - I read them on Bloomberg but my understanding is they were in various places. I think I also saw mention of some on zerohedge.

@Hello Guy, I agree that you may indeed start with the principle that governs your trades and work forward from these principles. I completely agree that modeling your approach upon the actions of someone credited with being a really superlative investor is not a bad idea, as a matter of fact it is a very good idea. This decision to model your procedures after Buffet's is nothing to apologize for. Combined with portfolio theory of discrete investment, none of which (should a particular investment fail) will be a major blow to the overall portfolio, and the rules of diversification, etc... should give you a portfolio that may be expected to grow instead of dwindle.

You are making personal assumptions in a number of these decisions. Buffet may escape the gravitational pull of market averages but there is no certainty that you or anyone else trying to emulate his investments principles will do so as well as Buffet goes. However making the assumption that a portfolio constructed upon this basis should be expected to grow (although perhaps not as well as Buffet's) appears to be a fairly safe assumption. Indeed after retirement most of my funds are kept in portfolios actively managed by myself.

Now again, going to the issues that interest me the most, you speak of "this ever changing swarm of buzzing equity prices fluctuating quasi-randomly in this erratically pulsating sphere having for centre of gravity the actual prices agreed upon by the majority of participants at that very instant." This is a very nice broad description of the market. What this means to me is that nothing and no one has a certain, well defined methodology to predict market prices.

As I have indicated, this is entirely fine with me. After all I worked over 30 years dealing with determinations of life expectancy, something which cannot be determined a priori but can be estimated in a reasonably approximate fashion. If you look around, the world is full of workable solutions based upon well informed assumptions. Actuaries make all kinds of assumptions in pricing blocks of business. These assumptions work fine in the real world. Please remember that there are trillions of dollars placed upon the validity of these assumptions. Assumptions are used everywhere in risk estimation, whether it is the risk of death, or the risk of material loss due to natural events. Do I need to say that these assumptions have a long history of being proved correct in the long run?

Going into different fields, less widely used in business but important nevertheless, differential equations oftentimes do not provide definite answers. Quantum mechanics require assumptions to be made about any number of issues. All of these work well within limits. If these techniques are used to deal with issues that exceed their capability, once some hard to determine limit is passed they do not work very well. So, why should it be different with the market? Assumptions are fine and they are workable. Assumptions on the way that Buffet's methodology works (based upon public relations statements) and assumptions made in adapting Buffet's methodology to your own purposes are fine as far as I am concerned. No need to reinvent the wheel.

Scott, whichever way the Berkshire Hathaway team achieves their results, as long at they do so within the boundaries of the law, should be OK for others to emulate.

@Oscar - I agree with you completely; that has always been my position. With regard to HFT in particular many seem not to agree with you though; they somehow think HFT is a special case and it is "unfair" for one set of traders to be faster than another set of traders.

If someone doesn't like the results because they don't like the rules they can either try to have the rules changed, learn to live with them or choose not to play.

Thank you Scott. I firmly believe that you have to play according to the rules, as long as the rules are followed you can do whatever you can imagine or devise and use whatever methodology you wish (yours, purchased, or kludged together from whatever it is you read in the media), The thing I absolutely love about the market is that you are the final determinant of whatever outcomes come your way. No one forces you to do or to believe anything in any particular way. You and only you determine where to go, what to do, and how to do it. You put your money where your mouth is and take the rewards or the consequences. I absolutely love the freedom this gives me.

it's my belief that few mega sharks made their money following the rules even in trading. many consider hft as not following the rules at least of ethics. i too love the total freedom that trading gives you to let your mind run wild, and so i will continue to pursue and believe in perfection.

the evidence that such could exist is what drives me day and night, the trading finances the pursuit. i want to live in a brave world of absolutes and permanency. if good enough is to just make money, i would give it all away to start again with nothing.

perfection is when it's good enough for me and nothing else will substitute. if i did not know this goal is obtainable i would have no life to live.

@Mark - I have known plenty of what you term mega sharks and you are correct, few if any, followed the rules, at least as those rules are commonly understood. Interestingly enough, if you asked them, most would be incredulous at the thought anyone could think they hadn't followed the rules.

I think many of us trade more to support our research habits than for any other reason and it is the continual quest for perfection that drives us.

@ Guy, Scott, Mark. My dear Lord, this is starting to sound like the odd couple, only that it has become the odd multiple, I am including Guy, perhaps there are others as well.

Mark the way you define perfection makes it very much an attainable goal. It is absolute perfection in all cases and at all times that is not attainable.

All the best to everyone, I believe we are all very similar in what we love to do.

@Oscar - good points across the board.

Oscar, yes, yes and yes. The actuary can make long term probability assumptions on population data. Estimates that can be use to write long term insurance policies.

We can view the long term centre of gravity of this travelling and pulsating sphere of random-like moving prices just like a market index. We can estimate the long term general drift of the swarm, or a sub-group of stocks which will navigate near its future gravity centre.

It's why you take a group of stocks in the first place. It's not just diversification, it's like taking some insurance that we won't be too far away from the average. From my previous posts, you may surmise that I expect the long term drift of the swarm to be positive as it has been for the past two centuries. Not much merit in such a forecast!

Following the swarm will give us about average long term performance. Technically, we should not even expect to generate alpha from this process. The selected group of stocks would tend to move toward this far away centre of gravity.

To get more, you need to do more. So let's look at the equations that can govern and guide an alpha quest. In a way, they will say what can be done.

As said before, you already have good trading practices in place. Therefore, what's needed is to go a step or two further. The following formulas give a progressive and over-simplified story, if you will, of what I look for. It always ends up to be about boosting the CAGR level beyond r, beyond the average long term trend. It's about generating alpha and reducing doubling times.

First, let's start with the classic: A(t) = A(0)*(1 + r )^t : where you have portfolio management without skills (index funds, r > 0, and trending to historical market averages). No alpha. No outperformance, but you win the game. Requires a simple program: buy.

Adding alpha, skills: A(t) = A(0)*(1 + r + α )^t : adding portfolio management skills (active funds, α > 0) the result of better stock selection, better timing and even luck. Most don't succeed: α < 0. But those that do raise their CAGR. The quest of mutual funds for instance.

Going a step further: A(t) = A(0)*(1 + r + α + λ )^t : adding paper profit reinvestment ( λ > 0) to the mix will boost CAGR.

Going for even more: A(t) = A(0)*(1 + r + α + λ + φ )^t : adding stock accumulation with overlaid trading ( φ > 0). The stock accumulation contribution φ can grow over time. It's a matter of choice and procedures. The accumulation being financed by the trading profits and cash reserves.

To push even further: A(t) = A(0)*(1 + r + α + λ + φ + ξ )^t : adding a covered call + naked put program on the accumulating inventory ( ξ > 0).

Note that because you are accumulating shares over the long term, the added option component should be viewed more as an administrative procedure and not necessarily as outright speculation. I see it more like renting out the accumulating inventory, collecting covered call premiums while the naked put provides a premium and a discount on the next intended long term purchase on which I will be able to issue an additional covered call and naked put.

All components contributing to what amounts to an oversized alpha: A = α + λ + φ + ξ.

This is one way one can increase performance over the long haul and escape the gravitational pull of the averages (r). It's doing more with the excess equity instead of leaving it idle as in a Buy & Hold scenario.

You will make more because you will be doing more. It's that simple. It's what you see detailed on my website with the long term back tests to demonstrate this as viable solutions.

Mr. Buffett outperforms because he has skills, uses profit reinvestment and stock accumulation. It gives him 10 alpha points. And it makes a huge difference over 50 years of portfolio management. If he added trading, covered calls and naked puts, he would gain even more alpha points which is what my methods are designed to do.

@Guy, it sounds so simple when you explain it like this. However getting the alpha is not that easy, maybe it is taken over a spectrum of stocks in the portfolio. Getting multipoint alpha is yet more difficult. I guess it may be achieved by following a multipoint, somewhat formulaic set of actions. Believe me that I have seen what you have in your site and I am impressed.

@Tyler - I just saw another article like I mentioned - below is the link you asked for. As Oscar pointed out - if it is within the law...

http://www.zerohedge.com/news/2015-05-18/more-buffett-hypocrisy-eco-friendly-billionaire-seeks-squash-nevada-rooftop-solar

the comments on Buffet are so dead on that are poster on zero hedge. soon though the world will be left blank with any sort of actual facts and knowledge, to be replaced with what they want you to here. it's why the world is in the shape it is now, so back to my little perfect math world i go hope the markets will be here to trade tomorrow.

Oh I do not know about this Mark. You cannot abandon the world to go hide in your little place where math provides all the security you need. The world is full of equivocation and spinning of the truth. Locking yourself in a small environment where things make sense does not correct the situation. In my opinion, you should face this situation, reject it and embrace what you know is the truth. You may be able to go ahead and determine the rules that will regulate the type of world you want to live in and work in. If you do this correctly you may wind in a very good place, very much suited for your likes and dislikes, and not far from the outside world with all of its misinformation and spinning. Hope you land there and enjoy it. Remember, you cannot eliminate the garbage that is thrown at you in a daily basis but you can re interpret this garbage in a way that makes sense to you. All the best.

i do think that one reason most systematic traders have problems keeping faith the holy grail exist is because their models keep failing. imagine a airplane manufacturer who keeps failing because they only fly their planes in caves or a indy car team who only run their cars on a wet dirt track. the airplane and indy people will testify that while they have moderate success that perfection is impossible. yet you and i know that the application of their technology may be sound but the application all wrong.

such is the way i feel about those who have succumbed to failure when modeling the markets, i too know that the application is at fault not the technology. i only know of one other systems developer who exclusively runs automated trading systems on non time based data. i migrated to this conclusion after continual failure using time based data. now the technology looks a whole lot better that it did in a cave or on a wet dirt track.

@Mark - you may be thinking of William Schamp and if not, you should track him down; he trades volume based (as do I).

I have said for years that every single thing can have two states (which are not mutually exclusive). A given thing (formula, physical object or situation) is perfect for a given purpose or can be made perfect for a stated purpose. It is perfect for... or would be perfect if...

Oscar, thanks for the kind words. You say: True. But far from impossible. If it was so easy, everybody would do it. But look around, you will find very few that even attempt to do steps 4 and 5. Step 4 can have quite an impact. Step 5 can be viewed more like an added bonus, icing on the cake since you would be simply renting out your accumulating stock inventory while preparing your next purchase at a discount.

To show that alpha could be easily generated, I did test after test, showed summary performance reports, numerous charts and analyzed the results. Most often, each one of these tests doing better than their predecessors. All those portfolio tests went back at least 6 years. Some were looking 20, 25 even 50 years back. The underlying trading methods varied, none of the test were the same, except when needed to make a point. Some used strong trend definitions, some milder ones right down to none at all. Some strategies used various degrees of random entries, from a small fraction up to totally random. Some used indicators to none at all. Some known strategies were transformed to adhere to my vision of things. By all this, I was trying to show that the methodology could be adapted to about anything. At the same time improving my strategy designs and software procedures.

But at all times, the underlying stock accumulation principles with it overlaid trading component were at work. In a few cases the trading itself was performed as some byproduct of the methodology. At times, to improve a strategy I would crank up the degree of trade aggressiveness, just like turning a knob. You wanted more, so you had to do more. It was, for me, a way to try to find out where the limits were and where stood my preferences.

If I run a trading script on my machine, it will do the same on anybody else's. It is just code after all. It's a pity that the old Wealth-Lab site has been shut down. It had a library of some 1,800 strategies frozen in time since 2008 that anyone could test. Almost all of them failed their 6 years out of sample tests showing so many ways of not to do things. There was much to learn there.

I've provided the mathematical background and the underlying principles to support the methodology, from quadratic equations, stochastic differential equations, to matrix equations. All reaching the same conclusion: if you wanted to generate more alpha, you would have to do it yourself. And most of it would be from the adopted trading strategy. The strategy that you would use going forward would make all the difference between executing the very best strategy you could program and a so-so one. Note that step 1 and 2 already made someone easily win the game over the long term.

Anyone could duplicate or come close to the strategies I've presented. If I could do it... then... My hope was to have people start designing their own trading strategies their own way. How hard could it be with all that was provided? I naively thought that all would find this interesting, would find their own way of doing this, and win over the long haul. It's within the nature of this kind of methodology for everyone to win. All anyone had to do was to do their best, prove to themselves that what they programmed was not only understood but acceptable to their own newly adopted view of things.

It's like building an expert system. A what to do should this or that happens knowing that most of the things you will see going forward are very random-like in the short and medium term but as the time interval increases you can have more confidence that the swarm of stocks you selected will approach the centre of gravity, the mass centre of the market averages. So the strategy design will be the important point, the how you move the inventory as the swarm moves over time. It's all about strategy design and seems so simple from this side of the fence.

@Guy. Thank you again there is really great information in your site. Now, let's add a few things to the Alpha maximization discussion if you may. Please keep in mind that I am doing this from a retirement point of view. To summarize, retired people have time to think and to develop. However, they tend to have a fixed amount of funds and their main concern about this fixed amount of funds is to grow it. I am of the opinion that from this point of view (although some of these points may well apply to long term portfolios started much earlier in life).

First issue is taxes. If you have to pay taxes on investment profits, these will by necessity reduce the alpha of the portfolio. There are ways to deal with this which are perfectly legal and available to most people.

1. Deferred income. Deferred income which is set aside and invested should be kept deferred for as long as the rules of the deferral program allows. It is amazing how much more money you can get out of deferred income invested this way. Of course when withdrawals occur you must pay taxes on the whole amount withdrawn.

1. 401k and IRA accounts. These are both perfectly fine and legal ways to maintain significant amounts of invested deferred income in your portfolio. Every 401k may have different rules as to when withdrawals must take place, minimum amounts of withdrawal, and restrictions in the types of investments allowed. If you can maintain the account (which belongs to the company you worked for, not to you) with no limits upon the age of withdrawal, then you might as well do so. If they force you to start taking RMDs (required minimum distributions) at age 70 1/2, then you are better off switching the funds (tax free) to your own IRA which has no investment restrictions. The ability to maintain significant amounts of money invested in a tax free environment is very good for a healthy alpha.

1. Stock options of various kinds. When these are part of your portfolio, it pays to wait as long as you are allowed to do so before you exercise the options. That is, as long as your prior company is healthy and its stock price is increasing. Otherwise it may be best to exercise them. The proper time to exercise options is complicated, however proper execution timing can add alpha to the portfolio.

You see Guy, it is not a matter of considering a portfolio and its alpha as a segregated portion of your fiscal picture. Every portion of the fiscal arrangements have to work together and contribute to the overall alpha. If you can fund a great big portfolio in a self directed IRA to which you have transferred your 401k funds much the better. If you use fully taxable accounts to provide the cash you may need to exercise options this is just fine. Since retirement I have been developing in my own mind a concept of a self alpha that integrates my total return and my total outflow (paying taxes, living expenses, etc...). Each of the pieces should contribute to the overall alpha or (as far as the outflow is concerned) not cripple the overall goal. Taxes have to be taken into consideration in these calculations, don't you think?

@Guy. One more thing I may not have been clear about in my prior post about the self alpha concept. You can have a number of staged goals for it. Most basic is the ability to live out of steady income and not touch the portfolios. Depending on how much is generated by the portfolios and how much I personally spend this may result in an acceptable level of income from the portfolios with no alpha (due to personal expenses). Then come the real alpha test, the ability to generate more out of the portfolio than the fixed income provides. And then, of course would come the ability to not only generate a surplus over the fixed income (which is assumed will be spent totally), but to generate enough over the fixed income to equal 50% of the SP500 performance for the year, Then the ability to generate a surplus equal to the SP 500 performance for the year, and finally and most satisfactory of all, the ability to generate true alpha and gain a surplus that beats the SP500 performance for the year. These goals may not be reasonable, I would like your opinion as to whether or not this is a reasonable set of graduated goals to aim for.

Oscar, as usual, all valid considerations. But these considerations apply whatever trading methods one might wish to use. They are part of the: all other things being equal clause. Things that are the same for everyone, things that you have to live with whatever the outcome of your portfolio and its trading methods.

To account for these, you could write step 5 as: A(t) = A(0)*(1 + r + α + λ + φ + ξ - e)^t to account for expenses, fees, withdrawals, and taxes. Mind you, this needs to be done for the other steps as well, so step 2 would look like: A(t) = A(0)*(1 + r + α - e)^t. Sure it will reduce the aggregated alpha. But the portfolio could still outperform depending on the extent of these withdrawals. And as you said, withdrawals could be large enough as to effectively reduce the overall portfolio.

Note that my preferred strategy not only accumulates shares for the long term, it also has a tendency, a propensity if you like to accumulate excessive cash reserves. I usually classify it as a side effect of the methodology when in reality I need to design more functions in order to better control this long term affinity the strategy has to accumulate cash. I'm not that efficient after all, I could do better, still room to improve.

Not being able to predict the future makes it hard to formalize the needed equations and is partly why I haven't taken the time to solve the problem yet, even though I know how I would do it.

That strategy can have its controlling function parameters set up as an external file and be under human control as time goes by. Meaning that from the outside you could control the general direction you want the strategy to take, just like turning knobs. Increasing or decreasing the share accumulation process for instance. Slowly converting the portfolio to cash if needed. Some of the cash could be extracted from excess reserves for personal or whatever other reasons instead of leaving it idle doing nothing in the trading account. Many types of adjustments could be made (withdrawals) with minimal impact on the trading strategy itself.

What has been demonstrated is that: these strategies were designed to survive for a long time, were scalable up or down and were able to reduce the doubling time. They also very much depend on A(0).

I would point out that the alternative may look like this:

http://www.marketwatch.com/story/stock-pickers-still-have-catching-up-to-do-2015-05-20

which says that being an active or passive player in this game turns out to produce about the same overall results. In matrix notation: Σ(H(active).*ΔP) ≈ Σ(H(passive).*ΔP). Both types of strategies being about equivalent with a doubling time of about 8.4 years. This looks like step 1 in action: A(t) = A(0)*(1 + r – e)^t. The no alpha scenario: the expected outcome.

It is why you need to do more, it's not easy, but it can be done.

Let suppose a tool what trades automatically, generates Open/Close market trades and executes it on an account.

Let suppose that after T time periods it was N positive trades and M negative trades.

Let P = Sum(profits) / (Sum(profits)+Sum(Abs(losses))).

A tool is an absolutely perfect if P==1 for unlimited T. A tool is realistic and possibly applicable if 0.5

Some ratios else to characterize any sequence of profit/loss values might be calculated. This output values and ratios are applicable for a portfolio too what is a combination of any assets and tools because of its additivity and there are some productive ways to decrease portfolio risk on its basic.

http://www.slideshare.net/yurimartemianov/predictive-automated-marginal-trading-technology-pamtt-part-1

Perfected trading is a subjective concept in the reality. A profitable trading with minimized risk is accessible. I suppose that only market price dynamic and tool's ability to predict it defines trading or asset management performance firstly. Price data is a raw material for any tool what we are speaking about. The price data simulation using the classic time series models is unusual often. Using Machine Learning with some modern math brunches ideas provides us with optimism. A complexity, multiplicity and high labor intensiveness in a development and testing make difficult a wide expansion of these methods. An advertising of Data Mining and Statistical software and high demand impacts an intensive growing in this field now.

This is all very interesting Yuri. However you must understand that part of this discussion thread deals with the great split in the financial world between long term investing and short term trading. These are two very different animals with different aims, with different techniques, and with different needs.

What you say is true, these automated systems can be done and can operate successfully, however they are dangerous if anything does not work as expected and may bring ruin quickly, depending on how fast the system trades. Plusses and minuses everywhere.

Finally, in case no one has looked this way there is an even longer term form of investment than portfolio investments which Guy has expertly described. This other area is generally left to private capital, the dark pools. Deals are made and funded, and corporations or developments created by groups of people seeking different aims. These deals are hard to evaluate, there is no solid financial information available, only projections, and there may not be a payoff for a long and undefined amount of time. This is a form of investing that is not available to traders or regular investors.

Your post refers to automated trading and your are correct in your assessments. I do not think there is much application for AI (which I use to classify) in investments, and any application of AI to private capital venues is likely to be an attempt to determine probable future trends and markets.

The market is indeed very complex in its nature. One of the reasons why there is no Holy Grail is that there is not a single market which responds to specific rules over fairly well defined time frames.

Oscar,thanks for your attention. There is published basket of 44 strategies what are in the market near 1-2 trading periods in average. The special tool Strategy Designer provides with the ability of very high level of parametrization of designed strategy with unlimited trades duration. It's possible to use this soft as an expert or analytical tool.

http://www.slideshare.net/yurimartemianov/nov5th2013-0000-gmt

It was observed in 2013, Nov looking at PL curve that market situation looks like 2011, March. It was price oscillation at const level some time and essential going down after that. Approx. the same was in 2013, Nov.

and about 1 year then as we can see now.