Variance reduction does not require negative correlation (although that can help). As long as correlation is less than 1 then you will get variance reduction in the portfolio of strategies/assets/whatever. Do a search for modern portfolio theory. Better yet play about with it in Excel, use 2 systems to simplify. Of course, correlation is a spurious measure to start with ...
I think I am going to have to side with maestro on this one (hopefully I am interpreting him correctly). If you take 2 structurally independent systems (defined here as different mean/variance characteristics in w/l profiles) and run a monte carlo over a large run of trials of the two systems, you can get a range of the correlations between the two systems, in order to observe how the total risk/reward of the combined system fared over that range of correlations. Note that the combined system avg reward/risk is simply the average of the two independent system reward/risk averages. The result of a small run of 200 total trials is shown. Note that the combined reward/risk ratio stays pretty much flat about the expected avg rwd/rsk of the combined systems (the variance about the average rwd/rsk is due to the joint variance of the independent system variances not due to a systematic improvement). There is no noticeable systematic improvement in the total avg. w/l of the combined systems over different correlations. You could increase the number of trials to get a larger range of correlations (-1 to +1), but I do not expect the results to deviate much from the conclusion demonstrated.
Not to get off topic but I never understood how Acrary said he trades all 'strategic' and not tactical. He went on to explain there is a finite # of behaviors present in the market and then he tried to estimate what behavior was present that day in the market and plug in the specific strategy designed for that behavior. I see infinite types of behaviors in the market. By that I mean if you were to plot 500 daily sp charts over each other you would end up with a block of ink. Tactical is the only way I see trading
great analysis there dt, unfortunately, maestro's whole argument is MOOT... and the reason is: THE OP REFERENCED ACRARY'S WORK WITH NON_CORRELATED SYSTEMS, WHICH HAD NOTHING TO DO WITH R:R, BUT RATHER SHARPE.. IE VOLATILITY OF RETURNS!!! so NOTHING is in contention here, except for the FANTASY that someone is arguing the other side of the R:R "arguments". the "argument" stemmed from the fact that man was confused (w/ maestro) because he actually understands acrary's work, while maestro was confused (w/ the entire topic) because he does not. hopefully the both of you (dt and maestro) will do a little reading up on that work, so that we can cut-out the off-topic banter on R:R. you're both obviously smart guys, so maybe stop using those smarts to assume you know what someone else's work is and use them to actually understand it.
dtrader i like when people quickly check stuff and come back. well done. but from my perspective the flaw starts earlier on, namely at the utility function. expectation, or what you call risk/reward, is simply the absolute wrong thing to look at. it does not tell you anything about the distribution of outcomes, since it just uses mean of wins and the mean of losses. the point is you can have two portfolios with the same value in this figure, but one would certainly make you a billionaire and the other one would certainly make you broke. think of counter trend scalping. tiny expectation (i hesitate to call it risk/reward, since that name is truly misguiding), but an equity curve as stable as a rock. take the same expectation at a trend follower on daily data and you get bust. huge difference. no way the figure tells. that means: that figure is the wrong starting point.
it is the absolute same thing with profit factor. completely useless on a standalone basis. these figures come out of trader thinking. absolute dollars. absolute amount won to absolute amount lost. but they need several other to derive a useful picture. on their own these figures are meaningless at best, misguiding at worst.
ok. Not knocking acrary's work, as I already mentioned I'd like to see more. Just wanted to try to put the rr argument to rest (and from my perspective there was plenty of contention over the basic concept maestro was arguing, which appeared crystal clear to me). Granted it's slightly off topic, as acrary had some subtle differences in the definitions (structural correlation may be different under his def, and rather than rr, he specifically mentioned re/max dd metric. Anyways, I'll be happy to refrain if this side menu pontificating is irrelevant. Look forward to hearing more intelligent discussion on acrary's ideas (particularly from the man himself), whereby maestro's ideas are always welcome.
the most important thing in system development these days is the use of human intelliegence in connection with a computer. by that i mean the early chocie of "what to seek" is utterly important. let me be more specific. if you run a random system on daily data you will find about 3% of such runs having a sharpe above 1. i do not know the figure from top of my head, but you will find some above 2 and some above 3. since today's computer power (i for example have 56processors combined for backtesting) enables you to run millions of tests you constantly find tons of flukes. big number of purely random systems with a sharpe above 3. so the problem is to first find a way how to distinguish "true" systems from "fluke". there are several ways we try to tackle this, one of them being the choice of what we look for. we want to understand the effect in the first place, using our human intelligence as a prefilter before we start a single code line. what i am saying is that the path you choose before you start testing is utterly important. alan chose statistical analysis of the whole time series, like the sp future, to derive trading ideas he would then follow. if your choice is to find negatively correlated stuff it is first of all important to completely understand the current stuff. when do you profit, but more importantly, when do you fail currently. could be low vola environment. then you need something that makes money in exactly that siutation. and you go deeper and deeper into that. what makes money in low vola, but does not get too heavily caught in high vola. and so forth. you see the point. this is probably the only way to get into negative corr systematically. we found that our intraday trading negatively corrs our intraday stuff. but that negative corr was not intended. just happened. nevertheless, it is probably smarter to add two uncorrelated systems than one with negativ corr. the development time for the two might actually be shorter ...
I'm lightly following this thread and I'm waiting for someone else to provide a substantial answer towards this topic but no one seems to so... I'll BITE. Dealing with correlated and non-correlated system is a portolio level issue. Theoretically speaking, having a non-correlated system IS far more advantage-ous, in terms of smoothing your equity curve. Though in real life trading, this isn't the case. You have margin/capital limitations and you need to have a sound portfolio level allocation towards which systems and markets you trade. Let's say you have two systems: Intraday scalping system where you are trading 5-10 times a day with a 2.5ish Sharpe and a R:R of 0.75. Long-"er" term system where you are trading 1-5 times a month with a 0.75 Sharpe and a R:R of 2.5. Now... both systems have a correlation of 0.33 on a monthly basis. Under a static size portfolio allocation, the intraday system will be holding a larger weight on the portfolio. Real trading does not work that way. Portfolio allocation is a lot more dynamic than what is discussed over this thread. Markets are always changing, and "generally speaking" shorter term models are more vulnerable towards change. You can't place most of your money on the short-term model considering how the future may change. You need to find the perfect balance between maximizing your performance, while REDUCING YOUR RISK. I'll declare one thing... Most of you who's posted in this thread are sucker system traders. You guys are too concentrated on Maximizing a certain aspect that you are blinded about thinking in terms of Minimizing the risk. To give a hint on what I mean... R:R is vulnerable towards the freqency of the reward. All measures have a flaw/vulnerability and always have a required counter-measureS that needs to sustain a certain level. Human aspect is a completely seperate issue towards what's discussed in this thread.