my journal 2

[Yamato]

The Efficient Frontier

Investing Basics- The Efficient Frontier - YouTube

I am going to have to dive into formulas pretty soon. It's going to be heavy.

Pretty much done with markowitz youtube videos. Now I need to read, and there's a lot of formulas ahead, which is like a foreign language to me.

 

[megamuel]

Well this post is going to look very lazy compared to your detailed and well thought out reply to my suggestion. Because there is not much I can add to what you have said, oh and I hate writing and I know you enjoy writing!

I still think that phasing in the systems as capital grows is a good idea. I don't think it has to be discretionary like you say. It can be made systematic and scientific. It's only as discretionary as say, the idea behind a trading system. I'm sure you have historical drawdown information on all of your systems. In which case you can put them in order of smallest to biggest drawdown. When you get some more trading capital you could work out how many systems you can trade based on their combined historical drawdown - this would be done with maths, not discretion. As would the addition of more systems as capital allows. But if you say this is a step backwards then of course, you know better than me.

"The objective is to increase the amount of systems traded, and therefore profit, without increasing the risk". I really do not know how this could be possible. Are you talking about enabling systems when they are more likely to profit and vice versa? Surely that concept is more discretionary than what I suggested. Do all systems trade the same number of contracts? Or different? If the same, maybe you can find away of altering the amount of contracts based on the systems historical drawdown, or the average size of losing trades, or maybe the profit factor or one of the ratios you use.

If you are having problems with systems being correlated and all losing at the same time (I know you were arguing with bbmac about this, not sure what the outcome was) maybe you could have a cap on the number of open trades. So say you only have a maximum of 10 open trades at a time. Yes it might limit profit but it would also limit drawdown when things are bad. Ok, that is not what you want, you want to maximise profit. Just thinking aloud here. But if you could hard code your systems into 1 single system you could test that concept.

Actually, is that an option? To hard code all your systems into one system? I guess not as they trade different instruments plus the code would just be too big I guess.

Anyway, I'm out of my depth here. All the Markowitz work is too complex for me. Are you sure you are not over complicating things? Think I'm going to have to leave it there as I am probably being more of a hindrance than a help but thanks, this is thought provoking stuff. Good luck with it.

Sam.

 

[Yamato]

Replying as I read.

Thanks. Well, actually I don't enjoy writing that much anymore (momentarily). Lately this journal has turned into a full-time job. As i said before, it helps me think, but we've gone beyond that healthy balance. I have to reply though, because such is the nature of keeping a journal here. And I should be grateful for all this feedback from so many readers.

"Put them in order of smallest to biggest drawdown" and so on, yes. Then you're talking about a formula, and then I would agree. As long as you say everything is automated, then I agree. The only thing I cannot agree with is when you say that it is going to be simple. There's a lot more to it than just smaller to bigger drawdown ordering. I would say I know better than you just because of this (besides them being my systems): that you said that it's going to be simple (in the previous post, "could you not just start off with a reduced number of systems?", etc.). It is not simple at all.

It's not possible maybe... you're probably right. Excellent point. Maybe what I meant (and explained wrongly) was that I'll try to increase profit faster than I increase risk. So yes, you trade a system and you risk twice the backtested relativized drawdown, let's say 20k. But then if you add another equivalent system, it's likely you can double the profit without doubling margin (they trade at different times) and without doubling expected drawdown. As you increase more and more systems this should keep happening but the problem is what formula rules all this, and how to avoid mistakes.

For example, with the preceding method, we had come up with the expectation that the 50 selected systems would cause a max drawdown of 40k, and, we could have very well had done everything right and have been very unlucky. But this is not likely to be the case. We did something wrong.

The systems are aways enabled, but they don't all lose (nor trade) at the same time, so this thing offsets/compensates for both losses and margin requirements.

Do all systems trade the same number of contracts? Wait - I can't answer this because lately i have said too many times (even in the reply to your last post), that this is one of the main problems to address (how many contracts each system should trade). So this means you haven't read my posts. And it's not just you, but a general problem here. Everyone keeps asking me questions that i answered within the previous ten posts.

I mean there's a limit to answering each time the same questions, and especially I cannot repeat twice the same answers to the same reader. You need to spend more time reading my answers than asking me questions.

Hmm...

This is it: I guess we've come to a point, with you and all other readers, where i received so much feedback and questions (in the last 2 months) that i can no longer keep replying to questions with my usual "reply as i read" method, point by point.

This is official. I am exhausted.

I need to stop here, not just regarding you but regarding everyone else. Since I cannot use other methods of replying than point by point, and since I cannot ban innocent users, whose only guilt is not reading my last 100 posts, I am going to try to discourage everyone from posting anything longer than 5 lines.

I could have tried to reply shortly and skipping your questions, but it would be more disrespectful than asking everyone to stop posting anything longer than 5 lines and to not post anything unless they've read the last 30 days of my posts.

Ok, so this policy from now on applies to every reader.

 

[Liquid validity]

Counter arguments for MPT theory:

Rethinking Modern Portfolio Theory - Bank Investment Consultant
LOOKING AHEAD: Investing Ideas and Analysis for the Week of November 16, 2009 - Bank Investment Consultant

Worth bearing in mind before putting a lot of work into it?

 

[Yamato]

Thanks for the links and insight into this subject. I will look at them, but I cannot go too deeply into it or I'll get sidetracked.

Thanks for the 5 lines. I will save this link you gave me, to be read later:
http://www.bankinvestmentconsultant...inking-modern-portfolio-theory-2665530-1.html

I will only be ready for it (criticism on markowitz) once I'll know what markowitz says in the first place.

 

[Yamato]

markowitz 1952 paper

Here it is. On page 2 of his paper he starts dishing out formulas, which is good and bad at the same time:



Good because they get quickly to the point and bad because i don't understand very quickly their language. I have a phobia for formulas.

I am going to have to get obsessed with the above page and formulas until i figure it out. It's going to be like when I taught myself how to juggle overnight. I stayed up all night and made it a point to teach myself how to juggle. I might do something like that one of these days. I must focus entirely on some objective and not quit until i reach it.

 

[pecas]

OK, what I'm doing:
1. take the historical series of profit/losses of a system and place them into an Excel column;
2. randomize their sequence 10.000 times (so called Monte Carlo simulation);
3. take note of the max drawdown for each sequence, and create an histogram with the results.

Why?
To estimate if the system max drawdown is likely to repeat in the future, or if the value we have is determined by luck/curve fitting.

Leaks of the method:
a. considers trades as independent events. Example: if success rate is 60%, chance to win next trade is 60%, regardless if you just won 10 in a row, lost 10 in a row, etc. This is a good assumption for my systems, but could be wrong for other systems. Although I could quote Wiley here. He says in his books that more than 99% of the systems he has analyzed, are in this category, and that wins/losses distribute normally. I'm gonna trust him on this, without analyzing my win/loss distribution (math nightmare);
b. considers the success rate as a constant; in the future, it could be worse (or better, but that would not be a problem);
c. uses the past trades like if they could exactly repeat in the future; the alternative is using average trade+success rate+standard deviation of profit, to generate a series of possible future trades (another math nightmare we can avoid for now, also because, if you still assume that success rate, average trade and standard deviation of profit are constant, I don't think you gain that much in generating new trades).

What's next? Do the same experiment with a combo of systems, with the same goal.
In this case, I won't consider the historical series of trade wins/losses, but the daily wins/losses of the combo as a whole.
Reason: even under the assumption that a series of trades is a series of independent events, I can't pretend that trades made on the same day, often at the same time, on correlated instruments like currencies, to make an example, are independent from each other.
So in the end, assumption "a" changes a bit. It's days to be considered independent from each other, not the single trades.

I'll be back to you with results later today.

 

[pecas]

OK, I decided to make 1000 simulations instead of 10000. I want to show the concept here, then I have time to be more accurate.

I used a system on AUD, that shows the following results in the past year:
138 trades
78 wins
60 losses
56.52% success rate
Average trade: +$45.50
Average win: $340.65
Average loss: -$338.19
Profit: $6713.96
Max Drawdown: -$2093.64

So what's the likelyhood that, in the next year, my drawdown will be -$XXXX?
I took the 138 trades, and randomized their sequence 1000 times, taking note of the max drawdown of each sequance, and this is the distribution of results (max drawdown value on X, # of occurrencies on Y):

freakin' 8.40% that max drawdown will be <2100
90.90% that it will stay below 4200 (2x the test max drawdown)
To have a 99% confidence, I can say max drawdown in the next year will be <5500.

To me, this shows this system was a victim of curve fitting, and is probably not worth trading.

Also consider that all this experiment was done with three assumptions (trade result independent from each other; constant success rate; same trade result as previous year), two of which are very favorable, while the first one is neutral.


But, look at this other system:
188 trades
108 wins
80 losses
57.45% success rate
Average trade: +$67.53
Average win: $403.02
Average loss: -$385.40
Profit: $12695.14
Max Drawdown: -$4042.38
It looks quite similar to the previous one... 2x profit... 2x max drawdown... hmmm... I would choose the other one. And instead:
run the same experiment, and find that next year, under the same assumptions:

likelyhood that max drawdown is <4000: 97.80%
wanna be 99% safe? Max drawdown will be <4300

So a completely different result: looks like this second system was not curve-fitting, and more, it was unlucky in the test... most probably, max drawdown next year will be less than we found in tests.


Now imho, this shows how relying on max drawdown found in tests is not only bad for combos, but also for single systems. Not only this, but doubling that number to stay safe could not be enough in some cases, and at the same time could be too much (not efficient) in other cases.

Now on to test a combo of systems.

 

[Yamato]

Wow, pecas. Thanks a lot.

Despite saying to everyone that they should keep posts within 5 lines, I can't avoid replying to you, given that I pretty much gave it to you as an assignment a few days ago.

So, once again I will have to "reply as i read".

FIRST POST.

1. it can easily be done, but we still did not figure out how many contracts I should allocate to each system: it doesn't make sense to allocate 1 contract to each system, and it might not maximize the ratio of proft vs risk.
2. a random drawdown is not the same thing as the actual drawdown because my systems do not interact with each other like many coins being tossed at the same time, so I don't see how "randomizing" the drawdowns fits into my project for automating portfolio selection
3. same as above. And I cannot do something so complex and long unless I first understand and agree with what I am doing

Furthermore, randomizing the drawdowns is actually providing better results than any curve fitting, because... I only wish my systems behaved like many coins being tossed. But their losses are not random and tend to happen together.

Regarding: "Leaks of the method:"
a. Thanks for the work you did, but if I am not convinced I cannot keep going in a given direction. I'd rather do less, and be comfortable with everything and knowing something inside out, than doing more on unstable bases.
b. yes, I agree
c. this one I didn't understand, but we're already far away and I am not following you anymore. I need things to be clear and univocal and here I'm lost.

Of course, given these premises, I won't take it any further and "do the same with a combo of systems".

Sorry, for now, I didn't say "eureka" and this is not clear at all. We need something simpler, clearer and more univocal. Here it's all about approximation.

Of course, I thank you for your great efforts, and I am not saying I have anything better to suggest.


SECOND POST.

Ok, obviously you're much more skilled with formulas and math than me, but this doesn't keep me from having objections to what you are doing. Whether it's because I am not good at math, or because I want everything to be clear, I see too many implications in what you are doing and too many unanswered questions and doubts. You're going ahead with too much stuff without enough explanations. And I think this is over-complex for me, so I cannot go ahead with it. Probably I will say the same about markowitz's formulas, but first I'll have to see what this nobel prize has to say.

I am not saying that I think what you are saying is wrong, but only that I don't understand it, and that it doesn't seem simple enough, and that it seems to have too many implications (for 120 systems). I don't see how I will make it all fit together. Also, I have those objections listed earlier.

We might benefit from a phone call, if you want. Before this escalates into an argument like it has with almost everyone else.

To put it clearly, what I need is a step by step plan of action, from start to end, foolproof, and as clear as it needs to be when explained to a child. It has to look like a recipe for cooking something.

1) you have 120 systems.
2) the objectives are so and so
3) the ingredients (variables) are so and so
4) this is how you will combine them (then a list of sub-steps)

I am not expecting you by any means to come up with such a detailed list today or even tomorrow. What I am saying is that this is the order we have to follow. First we define the ingredients and then we define how we cook this thing. And if any time during our writing of the recipe things become unclear then we have to stop and make them clear and univocal and foolproof. Your posts above instead look like you're getting a whole bunch of ingredients and throwing them into a pot. And I don't even know what you want to cook in the end. So let's start from scratch and address in the next few days:

1) what do we want to cook
2) what are the ingredients
3) what are the steps we will follow in cooking

We will worry about the details later.

Here's my outline.

1) What I want is a univocal method of portfolio selection (combination of systems/contracts) that will maximize profit while reducing potential drawdown and therefore risk.

2) the possible ingredients are: 120 systems, their lists of trades, their sharpe ratios, the contracts allocated to each system, the correlation between the systems, the capital available for margin, the capital available for losses (how much we're willing to lose)

3) the phases of the work are:
a) how do we select which systems to enable
b) how do we select how many contracts to allocate
c) how do we decide when we should disable a system
d) ...

This is my list. We have to start from the general outline and the ingredients to be used (and even before that, we have to look at the available ingredients). We can't just gather two or three ingredients and start cooking without even knowing where we start and where we will end.

Now you could do either of these:

1) keep on writing here and reasoning out loud, whatever you may be reasoning about

2) call me and talk about it on the phone

3) give up because you're tired of debating with me

I will understand if you are tired. For me though this is just the start, so whether tired or not, I have to keep going. If I don't solve this, I cannot invest again.

 

[pecas]

I understand perfectly: we have the same problem (different dimensions), but some days ago we started following different paths, and this stuff is just too much complicated to listen to everything.
I think the best thing is if I open a new thread to explain what I'm trying to do. It's very simple, trust me, just a bit complicated to explain. Maybe I'll get some feedback.
Will send a link to my thread in this post for reference when done.

EDIT: Here's the link:

http://www.trade2win.com/boards/planning-risk-money-management/136608-predicting-future-maximum-drawdown.html#post1691600

 

[Yamato]

Ok, perfect.

I am glad we didn't argue.

Regarding my own direction, what I would add to what i already said is that, as many suggested, the worst-case scenario is that I do not figure out an automation formula and just trade each system after allocating to it a huge capital.

In this case, it would be easy and reliable to say that if we allocate margin + max drawdown to each individual system (and the systems are profitable), then things will be ok. Of course this reduces the profitability by a whole lot.

Let's say I have 3 systems with 5k, 10k, 15k of drawdown, how does this work?

I allocate margin + 5k for the first system, then margin + 10k for the second system, and margin + 15k for the third system.

Of course things will be safe then (provided the systems are profitable). Even without doubling that drawdown, it is nearly impossible they will all happen at the same time.

But they would make little money.

And then more problems already arise right here, even with such a basic solution.

Let's say that the first system is on GBP and has a sharpe ratio of 5, whereas the second system has a sharpe ratio of 2 and it is on CL. Why should we allocate 1 contract to both, when the margin required by CL is a lot higher than the margin required by GBP and GBP is a much better performing system?

So even here, even with such a simple solution, we need a formula to answer the question "how important is diversification and how important is profit?". And I think Markowitz addresses these issues.

There's many more issues than simply the drawdown estimate and the fear of exceeding the expected drawdown. There's also the need for an efficient portfolio. You see, I could easily devise a method to never again incur in a drawdown that I didn't expect, but I would be doing it at the cost of reducing profitability by too much. We want to do both, and much more. That is why it is so complex and that is why we have to first of all define the issues stake and the ingredients, before getting busy with the cooking. First you go shopping and buy the ingredients, then you make the plan and the timing of the cooking, and then you start cooking.

 

[pecas]

EDIT: Sorry if English or tone of this post is not ok, but I had to do it in minutes. Have to run away for a while.

Arguing is my last thought. I want to help and progress myself in the process .

There's many more issues than simply the drawdown estimate

Absolutely true. But isn't it (drawdown estimate) unprescindible? Do you think you're safe with max drawdown x2? That's my point. Because if going with 2x is wrong, you could build a big castle without foundations.

My bad for trying to post a bunch of complicated charts/math stuff, let's try to explain simply here, then the hard stuff will stay in its thread:
You read my three assumptions. The first one is that my chance to win today is independent from my result yesterday. Let's concentrate on this one, because here is the key.
If this assumption is true, my experiment shows that being based on 2x max drawdown can be wrong (can be too prudent, or can be too risky).

But let's say my assumption is false for your systems: then it means you should take steps to improve your systems... because if there's dependency in your wins/losses sequence, you should spot it. Either your systems have more winning/losing streaks than normal (and in this case, you should stop trading after losses, and start trading after wins), or your system has less winning/losing streaks than normal (and in this case, you should stop trading after wins, start trading after losses). But since this suggestion (and similar ones) has been rejected in the past, and with good reasons, I thought this was not the case (i.e. there was no dependency in your trade sequence).
Add to this that even if there is dependency, and you take the necessary steps to improve the systems, not only you will make more money, but you will then obtain a system with no dependency, making my assumption true again.

As for my other two assumptions, they just assume that the past wil repeat, so they're favorable assumptions. If it's wrong to rely on 2x max drawdown under these assumptions, imagine how wrong it may be if even these two are not satisfied.

Maybe I'm just shooting in the dark, but maybe you just choose a "magic combination" which showed a low drawdown, but if investigated further, could have showed a much higher estimate drawdown.

 

[Yamato]

Replying as I read (just for you, because i got you involved in this huge task - everyone else remember not to post anything more than 5 lines).

Oh, good. Careful with me, because I get into arguments all the time.

Yes, we did build such a castle, and the foundations were not crap but almost.

Max drawdown times 2 could be reasonable, provided you didn't over-optimize it.

Wait. I don't have a problem with formulas, but let's take them when they're necessary. First we have to define a general structure of the work ahead. Let's approach it little by little.

Ok, with your first assumption, but I don't understand exactly what it means, so maybe I should not even say that i am ok with it.

The results from yesterday do affect the results from tomorrow, but we do not know how. So I can't agree with your assumption if it is what it seems.

"Drawdown times two" is fine, but the problem once again is how you get that combined drawdown value. First of all it has to be a relativized drawdown according to today's prices, and the investors did get this right.

Second of all, if you get that (relativized) value randomly and at the first try, it is ok, but it is not ok if that value is the outcome of testing hundreds of combinations, and, because of that, it consists of a very low drawdown for a very high return. That miracle is not likely to happen again. And this is the mistake we made. We found a miraculous combination and used it expecting it to hold true in the future. We instead find a univocal and constant method for a balanced portfolio selection, and a realistic appraisal of risk (drawdown).

No, I can't spot it. My systems are simple, they're profitable, and I cannot do any more work on them, or I'd be overoptimizing them. Once they're done, they're done. And they're done. I can only create more systems. Losses may come in trend, and all that, but I won't embark on a task that i cannot solve. So consider the systems something that cannot be changed. They're just as good as they are, and they will not be improved. They're the fruit of 7 years of work, and they'll stay that way. Now I only want to focus on money management, since we only lost because of it.

And, besides, no one can exclude that trades are independent of one another, but for this reason they don't go and try to fix their systems. No one expects to create a perfect system. You're better off creating 10 pretty good systems than spending your time trying to make one perfect system (which will probably not work).

Once again, we cannot exclude there's series of wins and series of losses, but it's another matter to code it into a formula that makes you stop trading every other trade and similar. We cannot assume that the trades are unrelated and yet we cannot go as far as saying "they're so related that i should stop trading every other trade or similar". You make it sound very simple, and i don't know if you're so far ahead of me that i don't understand you, or if I am so far ahead of you that you don't understand me. You seem quite intelligent, but you might not have as much experience with trading systems.

So, once again, I cannot be so bold as to state "there is no dependency" (which is very unlikely to be the case), but I cannot be as precise in the appraisal as to say "let's fix this possible dependency". The same happens when people tell me to use a trendline on the equity line and stop trading when the equity line starts falling. They might have a point, but, since we cannot figure out the formula and the exact relationship in a univocal way, then we just have to let it happen without interfering.

My systems are not perfect, but it is not worth it, to spend the rest of my life trying to make them perfect. If anything, I should just get busy creating more of them. But right now it makes much more sense to focus on money management, which means on finding the best way to use what i've already got.

If i work on my systems any more than i already have, they will become over-optimized and most likely get worse. I don't believe we can work on a system so much as to rule out the possibility that its trades become as uncorrelated as tossing a coin, which should be the meaning of "no dependency". And the problem is that despite knowing this, we cannot improve it.

Finally, I don't understand why are focusing so much on this detail, which does not seem so crucial at all (I never even thought about this thing, until you brought it up on your post).

These things you're saying about "assumptions" sound very scientific but I don't agree with your post, because it's not clear at all what we are talking about. We should talk about simpler things in a simpler way, instead of using this technical language (assumption 1, 2, 3) while we don't know even know the ingredients of our recipe. Too much detail, too much jargon, no clarity, no synthesis. I disagree with this last post your wrote.

And unfortunately you just edited a post that I was replying to, and in my "reply as i read" mode. Now we don't know exactly what i was replying to.

 

[Yamato]

Starting to understand something. I got here so far:

This presumption, that the law of large numbers applies to a portfolio
of securities, cannot be accepted. The returns from securities are
too intercorrelated. Diversification cannot eliminate all variance.
The portfolio with maximum expected return is not necessarily the
one with minimum variance. There is a rate at which the investor can
gain expected return by taking on variance, or reduce variance by giving
up expected return.

But I did not understand some of the formulas. That page felt like translating ancient Greek:

It will take me weeks before I can fully understand those formulas.

 

[Yamato]

Ok, that's it. I suck. I need to gather my remaining forces and embark on a mission to understand formulas.

This whole paper is full of formulas. They're probably relatively simple, but it's like a new language for me.

So I will look for a "formulas for dummies" dictionary or glossary or similar. I am totally lost in this language, and there is no way I can finish this thing if I don't first learn the language he's speaking.

The concepts he's using are not new at all. The problem is I get lost in his formulas.

If I can get past this ignorance/phobia of mine, I will solve all my other formulas problems. And I will be able to accomplish this task, and follow through in my nobel prize route rather than taking another less preferred and less trusted route (trading vendor route). I know the nobel prizes are not out to screw me or scam me for sure. I cannot say the same about the vendors.

Let's start the journey, and let's go back to highschool, and to what they never taught me there. Let's study my enemy:
http://en.wikipedia.org/wiki/Formula

In mathematics, a formula (plural: formulae[1] or formulas[1]) is an entity constructed using the symbols and formation rules of a given logical language.

In science, a formula is a concise way of expressing information symbolically (as in a mathematical or chemical formula), or a general relationship between quantities. Colloquial use of the term in mathematics often refers to a similar construct.

Now, the question is: can markowitz formulas be considered math or science formulas? I think they're closer to math formulas, but I would not call them "math". But maybe I am wrong.

Ok, for today it's enough. I am already exhausted. I will resume from here tomorrow, at work.

As long as I live long enough, I should be able to figure out the 16-pages paper markowitz wrote when he was 25. You see, it is clear to me now that this is like a wall, and it separates me from resuming my investments. The capital is not a problem. It will be a blessing if I get no capital for another 3 months. Otherwise I'll be tempted to resume trading before I am done with this, and I'll never finish it. And I'd probably lose it again.

"Again", yeah. Like bbmac blamed me. Can people still trust you after failing so many times? Damn, was it discouraging to hear that kind of talk. Well, let's list my failures then:

1997-2010: 14 years of compulsive gambling, outside of trading systems: I blew out my account several times per year, year after year. Progress: I learned about the markets and the different financial instruments.

2008-2010: 3 years of system trading with tampering: I blew out my account several times, but I also managed to quadruple it a few times (before losing everything again). Progress: I learned that I could make money with systems (and I built them).

2010-2011: 1 year of non-tampered system trading: Brought profit from zero to 37k, consistently for a year, then quadrupled capital, lost 47k due to money management mistakes, and had to halt the trading due to exceeding the expected drawdown. Progress: I learned that I can make money consistently with my non-tampered system trading, provided that I don't make mistakes with money management.

I see progress as a constant, rather than failure. Correct me if I am wrong, bbmac. In your dreams: I am still keeping you banned for a while. I cannot afford to read any discouraging posts.

 

[Yamato]

From:
Formula - Wikipedia, the free encyclopedia

Such formulae are the key to solving an equation with variables. For example, determining the volume of a sphere requires a significant amount of integral calculus; but, having done this once, mathematicians can produce a formula to describe the volume in terms of some other parameter (the radius for example). This particular formula is:

Having obtained this result, and knowing the radius of the sphere in question, we can quickly and easily determine its volume. Note that the quantities V, the volume, and r the radius are expressed as single letters. This convention, while less important in a relatively simple formula, means that mathematicians can more quickly manipulate larger and more complex formulae.

Yes: this is the part where I get screwed.

Yes! Got it! I found the dictionary I was looking for:
List of mathematical symbols - Wikipedia, the free encyclopedia

Thanks, wikipedia.

Anyway, let's keep reading.

In a general context, formulae are applied to provide a mathematical solution for real world problems. Some may be general: F = ma, which is one expression of Newton's second law, is applicable to a wide range of physical situations. Other formulae may be specially created to solve a particular problem; for example, using the equation of a sine curve to model the movement of the tides in a bay. In all cases however, formulae form the basis for all calculations.

I have gotten this far:
Formula - Wikipedia, the free encyclopedia

Then I'll also have to read the "expression" wikipedia entry.

I can't stop. I need to study some more. Let's not forget I have to read the list of documents in my signature. That's only 20 pages, but filled up with formulas.

So let's read what comes next.

Ok, done. I understood enough of it. I only need to understand enough to proceed to the next step. Now I feel ok about moving on to Expression. Then will come List of Mathematical symbols, and then I will try to get back to Markowitz. And if I am still not ready, I'll practice by reading some more formulas. It has to be like when I was trying to learn English.

This could be good practice:
http://oscience.info/math-formulas/statistics-formulas/

 

[brettus]

From:
Formula - Wikipedia, the free encyclopedia

Yes: this is the part where I get screwed.

Yes! Got it! I found the dictionary I was looking for:
List of mathematical symbols - Wikipedia, the free encyclopedia

Thanks, wikipedia.

Anyway, let's keep reading.



I have gotten this far:
Formula - Wikipedia, the free encyclopedia

Then I'll also have to read the "expression" wikipedia entry.

I can't stop. I need to study some more. Let's not forget I have to read the list of documents in my signature. That's only 20 pages, but filled up with formulas.

So let's read what comes next.

Ok, done. I understood enough of it. I only need to understand enough to proceed to the next step. Now I feel ok about moving on to Expression. Then will come List of Mathematical symbols, and then I will try to get back to Markowitz. And if I am still not ready, I'll practice by reading some more formulas. It has to be like when I was trying to learn English.

This could be good practice:
Statistics formulas

bionicturtledotcom's Channel - YouTube

This guy is pretty good explaining sortino and sharp ratio, covariance and correlation using excel.

How do you decide on correlation on a portfolio of stocks or systems? Some sort of scoring system? I think Covariance is meant to be a better indicator because it takes into account the volatility of the system as well.

 

[Yamato]

Thanks for the link. I will take that into account, even though i already have a large experience on sharpe ratio and have discarded sortino ratio for good.

Regarding covariance, i heard markowitz talk about it, so probably his recipe includes that concept. So far I got an idea that he is the best chef, and so i am investigating on his recipe for portfolio selection.

 

[meanreversion]

Travis, forgive me if someone has already mentioned this, but would it not make more sense to re-draw your equity line to reflect daily % changes, i.e. forget absolute amount. This would give a much better representation of the P/L.

 

[Yamato]

Thanks for the concise post and the respectful tone. I will reply as I read.

I will forgive you, because in fact this has been mentioned by bbmac, or at least it was a similar suggestion. And I've already replied to him, but I'll do it again and maybe I'll reply even more thoroughly and/or clearly this time.

He asked: given that your equity line is the product of 11 different combinations of systems and 4 different levels of capital invested (15k, 30k, 40k, 160k), shouldn't you draw it in a way to reflect all these changes?

As a consequence of his remark, after a few weeks, I added some information (capital invested) on my equity line:



So, by all means, yours and his are not irrelevant observations. But the problem is that in everything, you can see things from many perspectives, and none of them is perfect. No chart will ever represent every aspect of your situation. So you have to simplify.

That is unless you want me to go crazy and burn out by creating 7 workbooks and over 100 sheets like the investors did.

But then synthesis goes down the ****ing toilet.

Anyway, as far as using one chart (because we cannot afford more than one chart or I'll go crazy and/or burn out), the clearest and most coherent synthesis is absolute profit, with the addition of capital invested (mostly for the readers, because it was pretty clear in my own mind how much capital was being invested at any given time).

If someone asks me what that chart is, I will simply reply that it is "profit by my systems". And if they ask what those little dots are, then I'll reply "every dot is a trade".

If I get started changing things according to your or bbmac's suggestions, and someone asks me what my chart represents, then I'll have problems replying as concisely and clearly, because the chart will become a ****ing mess.

First of all, I don't know even know how we should go about representing properly the 11 different combinations of profit and 4 different amounts of capital invested. Second of all, if it ever becomes clear... it will still never be as clear and as representative as an equity line simply showing profit.

It's just like for moving averages. I could use exponential bull****, but I always use the simple moving averages.

Some brainstorming on the difficulties and problems of changing that equity line:

1) what do we do? we take weekly profit and divide it by margin used? That changed every single hour: impossible to do

2) if we change anything in that chart, we lose the information of the precise amount made and lost by each trade: very precious information indeed. Merely losing that kind of information makes the whole suggestion of yours not worth following.

3) do we divide profit made by capital available? But we didn't even use all of it. We should do margin, but then it changes all the time, so what the **** do we do? It doesn't make any sense.

4) many more problems.

5) more problems.

6) another problem here.

There's times when you need to get rid of all bull**** and be synthetic. And I am good at that. And when you interfere with that, things go wrong. They don't even go any further, because you die, suffocated by workbooks, and worksheets, and rows, and columns.

But keep on giving me advice, because sometimes I get some good ideas from the readers. The last one was by weighbridge, in October 2009. He helped me with the max drawdown formula on excel:
http://www.trade2win.com/boards/trading-journals/72598-my-journal-44.html#post953574

Just kidding, there's been some more after Weighbridge, but that was the first good idea I got from a reader and he remained in my heart. That son of a bitch. He's not even reading my journal anymore. Mother ****er. I think he may have gotten offended by the language I use. But this is my normal language, as I learned English from some young criminals in a boarding school, and "mother ****er" was like an affectionate term. "**** sucker" is similar to calling someone "honey" or "darling". Not really. It's rather a form of saying to a person that you respect him.

But some people don't understand such nuances, and they get offended. That doesn't make any sense.