Hopefully, the paradox of the paradox topic is over so I'm going to try getting the discussion back into topic... Managing a single system and multiple systems... 1. How are they similar and different? 2. How should a risk profile of a single system reflect towards a portfolio of systems? (OK... I'll reword it... You have a portfolio of systems, how do you decide whether the system should be added to the portfolio) 3. Position Sizing X Capital Allocation Models. You've got the basic % Allocations, (Anti-)Martingale and all the other crap about position sizing under a single system. On a portfolio, it's not that simple. What model do you use to manage the size of each position in a portfolio?
Let me try to tackle number 2 first. 2. How should a risk profile of a single system reflect towards a portfolio of systems? (OK... I'll reword it... You have a portfolio of systems, how do you decide whether the system should be added to the portfolio) Let's assume you have already combined three systems and that the new system has an edge of some sort. Putting systems with little or no edge together and hoping for a good outcome is not a good idea. Use the monte carlo method to select a first set of random trades from each system as your training set. The other trades are used for the validation set. This is important. You want the validation set to have very similar performance to the training set. An overtrained system will have stunning performance on the training set, and questionable or awful performance on the validation set. Combining several systems with no edge will typically exhibit this behavior... there are exceptions. Adjust the weight (% allocation) of each system so that the composite system is optimized in some way (maximum Sharpe for example). You can use a regression algorithm to do this. Is the new composite better than the old porfolio? Do we have a better edge, ie. better Sharpe, lower max drawdowns, steadier equity curve, etc. I also examine the statistical quality of the composite. What does the distribution of profits look like? Long negative tails? Negative skew? Preferably it will have a nice gaussian-like distribution with a positive mean. Does the validation set confirm an improvement? Without confirmation from the validation set, your composite has no prediction power. I run several monte carlos to look for weaknesses and see if I can fix them by adjusting the systems, or adding new systems that address the troubled areas. If the composite system has a better edge, you're on your way. More later.
The question I get is, if you optimize your performance of your portfolio using some fitness (like Sharpe) how will you readjust it? I agree that statistical tests to be the core function of the decision process. But we deal with multiple systems within different trading style. I can have a scalping model, swing model and a trend-following model. If I come up with a stat. arb model, it's likely that the market tendency which the model is exposing is unrelated to the other models. (Well, you run tests for these too... but anyways...) How will you decide if I added a counter trend model which exposes a tendency that utilizes both the tendency exposed by the swing and trend-following model? Will you reduce the swing and trend-following model's exposure? For the sake of the discussion, let's say that the new model has a correlation of 0.3 with both the trend and swing model. Also, assume that the system will fail if either system or swing tendency is demished in the market.
Why not use the Kelly framework? Maximize the median. Then the capital allocation between your systems is a simple math question. Trivial example â¦. Two independent systems with equal risk-reward , p1 probability of success for the first system (q1 = (1-p1) failure), p2 probability of success for the second system, f1 allocation to first system , f2 allocation to second system ⦠Choose f1,f2 to maximize g(f1, f2) = p1 p2*ln(1+f1+f2) + p1 q2*ln(1+f1-f2) + q1 p2*ln(1-f1+f2) + q1 q2*ln(1-f1-f2) In the general case where the outcomes of the systems are not independent you need to make some assumptions about the probability distribution of the outcomes for working with analytical formulas. Under some assumptions for example optimal allocation is F* = C^-1 * M C the variance â covariance matrix between available systems M the column-matrix containing the expectancy of each system The ratios of optimal allocation between systems f1/f2 etc. will be independent of the maximum risk one is comfortable taking.
TSGann.. I don't think the original point was about the paradox, but was used to illustrate the example of profiting from 2 "losing" strategies (however trivial an excercise). The example I used requires dependence, ("mean reverting" in my example) and volatility, which is not what the paradox assumed, and uses money allocation to profit off. Of course you could view the allocation of money as a whole new strategy, but that's not how combining multiple systems works. With regard to this topic, check out "Universal Portfolio". The discussed idea answers the question, "how do you compete with multiple portfolios that have different fixed percent allocations?" Its the same way you would compete with different stocks... you buy them all. So you're basically finding an average weighted percent allocation every day and then adjusting to the new average. This specific scheme is supposed to work for random stock prices. However, the question of transaction costs (rebalanced daily) and the time and volatility needed to see optimum results are the foreseeable costs of using this approach.
Ok. Let me give you an example. Mind you that this is a very sketchy, rough example. Suppose you have a channel with, let us say, 1252 price level as its upper level and with 1248 lower level. Imagine a pure mechanical system where if the price is below 1248 you would go short and if it is above 1252 you would go long. It is easy to show that this system has negative expectations as your losses crossing the channel will be on average grater than the gains you have on your holding position. Imagine then another game. This game requires you to sell 1 STD OTM naked strangle. We all know that this game is also a losing game on average as your losses of in-the-money options will be greater then the premiums you collected. But think what would happen if you combine these two games. Your losses on the first game will be greatly offset by the premiums of the second game and your options from the second game will be always covered (covered call or covered put) depending on the direction of the market using the underlying from the first game. The combination of these two games could be positive. Of course, there has to be a third game to make it all work, but I will not reveal it leaving you the pleasure to figure it out for yourself! Cheers, MAESTRO P.S. Keep smiling!
For starters: 1. Your stuff is dependent. 2. Signal hedge... There was a paper written by someone about 7+ years ago. I can't recall the details but it was written by an old school developer like Mark Johnson or Mark Brown... I know that it's by an OG poster from Trader's Club Forum or Omega-List era. Basically, it was about taking one tendency and using multiple signals to offset the underlying risk of each signal. I think it's very close to what you are doing.
It is not what I am doing. It was an illustration of the Parrondo's paradox applied to the markets. I think with a little bit more careful analysis you might find it deeper than you think by just glancing at the surface. I would never write about it if I did not find it potentially fruitful. As the matter of fact, a roughly similar model has been successful used by one of our funds for more than 3 years now. If I were you I would stop laughing and think it through more carefully. P.S. You disappointed me
You're still disappointing me. 1. "Deeper" meaning re-arranging the concept using it as an idea? 2. Roughly similar idea.... Potentially fruitful... Great. So it's roughly a potential idea that is fruitfully similar to what you used? Anyways, I think I've given it enough thought, maybe less compared to you. But I still don't find Parrondo's Paradox any useful than what's been around for quite sometime about inter-systematic coordination. As a base idea... sure... multiple system flipping is an interesting and significant research to be done. But taking Parrondo's Paradox (which is known (and I agree to it) to be worthless in real life situations) and trying to apply it with trading is just a waste of time. It's your time and resources, let me know when you've successfully applied Parrondo. I'll spread the word that you've found the Holy Grail in trading. I'll re-post the quote again: So... let me ask you how you overcame the problem. I would really love to know because it would revolutionize the theories of applied science from top-to-bottom. Do you understand what dependent variables and independent variables are? Seriously... didn't you just take an idea about inter-system coordination and re-interpret it based on your trading experience? Here: http://en.wikipedia.org/wiki/Dependent_variable
I got an E-mail from a buddy reading this thread, telling me I'm correct, along with a pdf file so I'll pass that along in ET. (It's not a big secret file, it's easy to find if you googled this... What they mention is nothing special too, just some rational thinking about probability theory) I kinda figured that rather than having my "shallow" brain explain why it's BS, I'll just post a PDF written by some other guy (who's prolly smarter than me) explain this stuff...