Twoblink's 2013 Journal

Yes, not 2013 yet but that is life.

Despite basically not posting for a few eons, I get PM'ed all the time to post something and so I will try to as much as possible. I do find that posting does help me remember things; and there is a lot to remember. But I want to send out a fair warning early:

THIS IS MY JOURNAL, IF YOU DON'T LIKE WHAT I SAY, THAT IS FINE, START ANOTHER JOURNAL TO REBUT ME, BUT PLEASE KEEP THE POSTS POLITE OR ELSE I WILL SHUT THIS DOWN.


With the shouts out of the way...

I begin usually by observation, and then making a grandiose assumption; formulating a theorem from it, and then setting about proving it or disproving it. So first, a quick update on theorems that I have proven and not proven or proven false.


I had initially said that averaging up was correct; I now would like to retract that. Not a full retraction, because compared to averaging down, averaging up is much better, but it's not mathematically optimized.

Given position A in the market: Averaging down is defined as entering more positions into a market when the market has turned against you (negative open profits).

Given position A in the market: Averaging up is defined as entering more positions into a market when the market has gone your way (open profits).

I now have the research and the math to back up both:

Given position A in the market; averaging down will asymptotically approach ZERO in expectancy as frequency or lot size increases.

Given position A in the market; averaging up will asymptotically approach ONE in expectancy as frequency or lot size increases.

So there, I have now made peace with the world as far as averaging up is concerned. It will NEVER push your expectancy over 1.0, it can't mathematically, but it at least will not pull you into the grave like averaging down will.


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The Trend Paradox: The more data points there are, the more a trend is confirmed. But as the number of data points to confirm a trend increase; the likelihood of a trend ending increases exponentially.

Corollary: The Turkey Fallacy (a la Nassim Taleb): Everyday the turkey is not killed is a reaffirmation that it will not be killed; consequently, the confidence level of a turkey with respect to the trend of not being killed is highest the day before Thanksgiving.


To all those that have PM'ed me asking me what I have been working on in terms of trading of FX; this is basically it. The Trend Paradox. I had conjectured that there is a method in which to defeat the trend paradox; but I had been working on it for quite a few years. So the problem in layman's trading terms looks like this:

If I enter too early without enough datapoints to establish a solid trend; then I have very low probability that it is a trend.

If I enter later; after enough datapoints establish a trend, the likelihood of that trend ending just after entering increases exponentially with increases in data points.

So kind of you are screwed if you enter early, and you are screwed if you enter late. The goal of course is not to get screwed.

My partner and I (yes, I do have a partner, brilliant one at that) have come up with a solution to the Trend Paradox. It is a mathematically defeatable problem. So there is hope!

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Mini-Max: I had conjectured and then mathematically that there exists a point in which risk can be minimized and potential reward maximized for all entry exit set [E1,E2].

That was what.. 3 years ago?? 4 years ago? Don't remember now, will have to check my own old journal. But since then, a few people have PM'ed me with independent confirmations; and so all it takes a bit of hard work and some knowledge of calculus. I think like the 4 minute mile, once you know someone (and now, a few someones) have done it, it's doable.

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The Cocaine Distribution Model: This is the crux of my trading system; and to this end; I have not been able to prove it true; but I have also not been able to prove it false; and it seems to hold up quite well. I think however my proof of averaging up might apply equally to this; but I am finding that my math skills are a bit lacking in the proof department; wish I paid more attention in college. Oh well. But the cocaine distribution model is still the most optimized model for distribution of anything; INCLUDING entry points and exit points. So far, I have not found a math system that is as optimized.


Those who have asked; my current system is in alpha stage; and is called "The Tardis" (named after the model of travel for us timelords). An upgrade from "The Fist". The Tardis uses the Cocaine Distribution Model, does not average up or down, defeats the trend paradox. I have not yet been able to come up with an optimized method for adjusting for bid/ask and slippage theft. But I believe there is an optimized equation for it as well.

I initially conjectured about optimizations of lot sizes using a Pascal's Triangle, and I was correct; since it inherently contains the golden ratio.

I now conjecture that interval optimization can be done by optimized Golomb Ruler. But I have yet to prove so.



Moving onto "e". My current conjecture proof that I'm working on is my conjecture of optimized profit curve growth based on "e". For every expectancy; there is an expected profit growth curve; but the question is; for every bankroll+position+open profit; is there an optimized trajectory? I believe that there is, and I believe that it can be found in "e" or more specifically in the "natural log".

Given a log system, log base 10, we can generalize it to a log system of log based x. Given that to be true; there must exist a number in which given a derivative of the curve (and thus an integral of the curve as well) there exists a number x in which the curve derived or integrated, is the curve itself. Mathematically, that is true and we know that number to be "e". And so log base e, allows for an easy proof and derivation and manipulation of numbers since the derivative of itself is itself. I am not sure because my math is just not that good; if that then qualifies as a "fractal" but it has fractal like qualities and is always guaranteed to be optimized. And so my conjecture of curve optimization says that we know that given a trajectory of profit for the bankroll + positions +open profits, there exists an optimized trajectory in which can be proven to be optimized because the derivation of itself is itself. Confusing I know; but the reason why I think this is important is because if this is true; then we know that the trend is thus sustainable. If you extract too much profit too quickly, it tells me that risk/reward was skewed and you got lucky; if you extract too little too slowly, bid/ask and slippage will eat you alive. Like a space shuttle on reentry, I maintain that there is exactly ONE trajectory for the given bankroll+positions+open profits. This then basically if proven to be true and equation controlled, becomes to automatic portfolio management mechanism.

Hi

I would love to see your conjectures be put to action in terms of trades statistics. Is it possible for you to link this journal to a trade explorer? I find it easier to follow a system that way. just a thought.

good luck.

https://en.wikipedia.org/wiki/Golomb_ruler

Given a Golomb style ruler; if the lot sizes were "golomb-ized" then you basically have the most options for creating the most options with the least amount of lot sizes. So it's my continued theory then that all lot size manipulation should be golomb-ized for maximization of options.

Why I am all over this like white on rice; I know the optimized re-entry point that would produce maximum potential profit for minimum risk (original mini-max theory) but I was never able to prove that there is such a thing as optimized initial size of entry; there is one with respect to your bankroll size; and if you believe the turtles, there is one based on N or Average True Range; but is there an intrinsic one? I believe that with the Golomb Rulers, I can say yes... So on with the tests...

Sabermetrics:

Long before Brad Pitt was Billy Beane, I had started applying the equivalent of Sabermetrics (Forexmetrics) to Forex. I apply mostly non-obvious stats to the underlining price structure like Bill James does. I have yielded good results from it. Systems as simple as "buying the 3rd Monday and sell the 3rd Friday of the month" works because generally the options expire on the 3rd Friday of the month; increasing volume and volatility. So some systems are fairly basic, but if you have good Forexmetrics behind it; they work well.

My goal is to optimize everything into a fire and forget system; every facet of trading I have been tackling and conjecture that there is an optimal method to either increase gains or decrease risk. So far, have not been wrong. I hope to be the Bill James of FX...

I'm sure it's possible to Luke to a trade explorer, but I'm not seeing the benefit of it for me..?

Colorful language as always:

The long term optimal bet (position) sizing algorithm has already been created, and a proof has been conveniently made available.

Kelly Criterion



Kelly only has about 50 years on your efforts, but who's counting?


Yes it is confusing, and terribly optimistic. If only. However the reality is that you are dealing with a variable mean and variance when considering price or specifically price trends, and the underlying data is stochastic trend, not deterministic trend as your statement above implicitly assumes. This means that you cannot with any degree of reliability build a model of future price movement, nor must price arrive at your predefined coordinates, no matter how intricate the proof. Now if you're looking to optimize a portfolio according to some predefined fitness score, to achieve a desired level of utility, this is an achievable outcome. However the usual caveats apply.

Long Term optimal bet size of Kelly works if you know what your Expectancy is and if your expectancy is not fluctuating. I am very familiar with Kelly, and he has 50 years on me in terms of age; and I build off of his work, but I am not talking about the same thing.

First, to define what you are talking about, there are 3 types of bankroll we can Kelly off of:

1) We look only at the bankroll, and disregard open profits in the equation.
2) Bankroll + pending open profits
3) Setting a Stoploss first; assuming you will take that loss, and calculating your bankroll based bankroll - SL's.

So when you talk "Kelly" optimization, I assume you mean #1 or #3, as #2 is the goal I am after, of which Kelly is not optimized for;

The other thing you will notice with Kelly is that the truly mathematically optimized Kelly is an insane amount; most of us aren't Larry Williams and so most will probably never ever Kelly; and will more than likely do a Kelly/2 or Kelly/3. This of course is based on the assumption that you have a fixed expectancy; of which I don't know how you would; again if you have open profits and take them into account.

Instantaneous optimized angle of trajectory at point in time of query is what I am after; as a method of portfolio control and management. If you read any of my old posts, I talk about Kelly quite a bit. If it were as easy as taking a derivative and setting it to zero and solving for your Kelly; everybody would be rich.

"Terribly Optimistic" is my dayjob. I am not seeing how "Terribly Pessimistic" which I assume is your suggestion for me, assists me with profit raking.

would be beneficial for us readers. Since you did mention in the beginning 'so many people PM you to post something", i'm sure they're asking that to learn and see your trading results.

but i'm all ears here to learn.

I am not sure I would be able to put my trading results and my graphs up here without violating my confidentiality agreements.. Sorry!

You are right about fractional Kelly being more common in practice. Full Kelly is rarely used for another reason. If you over-estimate your expectancy and end up sizing positions too large based on Kelly, the downside is much greater than the downside of sizing at say half of Kelly.

But initiating new trades based on the size of open profits brings conditional probability into play. The expectancy of those newly added trades is totally separate from the expectancy of the original entries. It is as if you have two (or more) systems going on at the same time with independent probabilities. And as a result the sizing of the positions should be based off from the "expected winnings" divided by the "net winnings if you win" calculated from the position of the new trades. So the historical win % and wins must be computed according to the Kelly criterion at each point along the line you wish to estimate.
Conditional Probability
Conditional Probability in Practice - Chapter 3 page 15

Now we are getting into a good discussion..

But I think it is insane to discuss Kelly without discussing its kissing cousin, RoR. I think without accounting for RoR, Kelly is scary, not just scary but down-right dangerous. Kelly requires you state "how much I win when I win" but that is not realistic when you have open profits. This isn't like blackjack or something where the odds and probability and thus your expectancy is easily calculated. The other problem is RoR, which I NEVER hear a discussion about; so either most don't know about it, most don't care, or it's not part of their trading regimen.

If you have an open profit; tick up vs tick down will effect your kelly number; so it's a moving target to optimize for; I am thinking more of overall portfolio management; exposure, risk, etc.. If trade pair A is increasing, I can take it one of a few ways:

I can say, great open profits, I will use them like realized profits, and buy some more (and thus be averaging up)
I can say, great, open profits, I will be using them to enter positions in another pair and thus double my risk (since they are unrealized but I am kellying off of them and opening myself to more risk by enter another position somewhere else, and thus [ironically] reducing my kellying number since my open risk is higher
I can say, great, open profits, we will just babysit it and see if we can't maximize it and have it converted to realized profits once the trend ends or whatever method signals me to exit.

In all cases, Kelly becomes a moving target, and not so realistic unless I'm doing 1 lot at a time, 1 at a time. If it were as easy as take a derivative and set it to zero; then we'd all be filthy rich from reading just a wiki page. It is TOUGH.

But early in my research; I began with Kelly, and met up with RoR at Starbucks and found it quite interesting that nobody pairs the two together; when the two should be inseparable.

Hi Twoblink, why you don't post any more?

?? Aren't I posting now?

You mean aside from having 2 kids and running 14 businesses?

I've been digging more into Kelly and can share a couple of thoughts that are related to our discussion. First, most gamblers and traders use discrete Kelly. Discrete Kelly is not appropriate for trading, and so continuous Kelly should be used. Continuous Kelly boils down to (assuming zero percent riskfree rate):


Unlike what I posted previously regarding conditional probability, continuous Kelly does not require anything other than returns and your account balance to make the calculation. Since this can be done continuously, there is no problem from a measurement standpoint as alluded to in your previous post:


If you use a sufficiently large number of samples of your returns, the numbers should not shift that much during an open trade. However, even if they do, this is no problem.

Read the attached paper and maybe the concept will make more sense than my description. Note how it is possible to apply continuous Kelly to the purchase of a single stock (GS), assuming a long-only strategy, and to thereby outperform the buy and hold.

With regards to the point about how to keep Kelly leverage in control, there is a very interesting post that covers the topic. You essentially create a fictional sub account for Kelly as a fraction of your account equal to your desired maximum drawdown. If you select 20% max drawdown on your account, you use the 20% of the account balance as your Kelly balance, and multiply your Kelly ratio (leverage) times the Kelly balance to determine your trade size. Upon new equity highs, you adjust your total balance and re-apportion 20% of your total stake to the Kelly balance. In this way the maximum you can lose is 20%. So there you have it, bounded risk and the potential for geometric equity growth! Pretty cool eh?

How Much Leverage Should You Use?

I think CVK (Continuously Variable Kelly) probably is necessary if you are trading $10M and up, but I think if your account is like $10K, I don't find it to be necessary and probably way too much waste of resource. The problem is that scaling goes both ways; and when you have a small account, you probably have difficulty scaling downwards; if you are only buying and selling 1 lot; then you would need to move to mini or micro to do any subdivision.

Continuous Kelly is applicable to trading applications because unlike a typical wager where there is a discrete risk and reward (such as betting on 3:1 odds at a horse race) for each bet, in trading the risk and return are fluid and continuous. If a trader were to implement a system that had a hard stop and take profit and only execute based on these two cases then I think it could be argued that discrete Kelly would be appropriate. But for all other strategies where there are more than two outcomes possible, continuous Kelly is appropriate whether the account size is $10 or $10M.

However, minimum bet size enforced by a broker does have a direct impact on the ability to implement any sort of dynamic sizing so you make a valid point. This point is equally harmful to continuous Kelly as to the desire to build, "Instantaneous optimized angle of trajectory at point in time of query" or any other strategy that deals with continuous, dynamic or instantaneous measurements used for altering position size.

To the point regarding minimum trade size, many broker offer mini lots consisting of 10,000 size with fractional lots down to 100 units or 0.01 lot. Oanda offers trade units down to 1 unit and so if someone were interested in implementing any form of dynamic position sizing based on a formula such as Kelly, they would do well to use the intermediary that gives them the biggest advantage in this area.

Hi twoblink, A very low brow question harking back to an earlier time... 2006!, and your OCC thread! Every time I read over the thread(many times over), the same question arises... After a trade has run its course, and without MAs having changed orientation, how would reentries be managed? Big fan of OCC, and The Hat... Thanks for both...

Recently I have been bombarded with questions; and so I figure writing on the public forum instead of sending the same thing to a dozen emails is the easier way.

My group and I have managed as I predicted; to set up a system that is Delta Neutral and Gamma Neutral; with corrections. I didn't think it possible to do with just FX; since in the options world (Thank you for the intro George Fontanills) you have a fixed item like a stock that has a delta of 100; and something variable like an option; and how you can muck with both to get a delta neutral with corrections; as delta varies with price movement (yes; for you calculus options traders; I did say delta varies, I know it redundant, deal with it.) So reading my old journals, and posts; as I predicted; I would eventually move to a delta neutral trading system.

With Delta Trading, the interval at which you check becomes the optimizer; check too often and you get bad SnR; check not often enough and the market might flip on you. This has been the bane of my system; and one that I could not solve. But having been a cryptographer most of my life; I looked to the crypto world; filled with people much smarter than I; to hopefully solve this problem.. And I read about a system that suffered roughly the same problem and he came up with an elegant solution.

So I was not going to share; but I thought; I should since I'm sick and tired of someone taking my ideas and claiming it as their own; since these posts are time and date stamped..

Given an increase in volatility; signal to noise increases.. as noise is in dB; and thus logarithmic, so it is for FX. There might be times that the market is very very quiet and flat; and there might be times when it is volatile; I needed a system in which reactions were near instantaneous; and would be auto correcting; auto leveling; and auto compensating bi-directionally. My brilliant solution was someone else's solution, namely Kimoto's Gravity Well from megacoin.

http://bitcoin.stackexchange.com/que...ate-difficulty


This is the exact profile that I was looking for in a compensation algorithm. Given cryptocoin mining and FX; almost all the variables match one to one; and situationally it's a mirror as well.

So hope that answers most questions; My group is doing delta/gamma neutral trading with adjustments using Kimoto Gravity Well for interval as well as lot size management.