In a related thread I caught myself making a statement to the effect of:
Less Things(i.e. timeseries,products,strats etc) allow for greater potential performance at the expense of stability, More Things allow for greater stability at the expense of greater mediocrity.
i.e the benefits and costs of diversification.
But then i thought that this could get shotdown by proponents of "Large Basket, Small Subset" (e.g. Sluggo) who could claim that by exposing themselves to a large number of products(beyond their means to finance perhaps), but then limiting actual trading to a Dynamic Subset Portfolio(DSP tm), they are able to materially improve potential performance through diversification, contrary to my assertion.
This got me thinking: is this DSP really "diversification" as I and perhaps others widely recognize the term, or is it something of a derivative, or perhaps altogether different phenomenon?
For example ,assuming for simplicity we have a single trade strategy and a Global Basket of 300 products, but at any one time was limited to 20 positions, then you could arbitrarily assign each current position to a "equity curve slot" within the DSP.
Whilst it is true that over time the constituent of each of these 20 Equity Curves will vary among products or cash as trades come and go, you still only have 20 equity curves at any one time, and therefore actual diversification of 20.
This is of course different from the Global population portfolio which would be all 300 product equity curves all of the time, and which would have diversification of 300. Being the population, this would represent average performance[lets ignore weightings issues for the time being please].
It is my conjecture that any outperformance achieved by the DSP is therefore the result of:
1) positive selection bias when new trades replace old trades on a first come first served basis(or any other basis for that matter).
2) Opportunity Benefit. More potential products within a population give rise to more frequent opportunities for positive selection bias to occur.
Note that expanding the global Basket population does not directly imply that potential outperformance will be increased(though it is likely, especially when starting out in expansion).
e.g. you could increase the global population from 300 to 400, but if the new products are all universally total dogs FOR YOUR GIVEN STRATEGY, then it is natural that they would crowd out some of your existing positive selection bias and reduce your outperformance.
To really blow your mind, imagine multiple, or godforbid, all possible trade strategies, applied to all possible products. you would then have the total universe population of individual equity curves. now pick 20 and rotate on a firstcome firstserved basis. I almost had to reboot my brain when i started thinking about how one would actually implement such a Demon!
Anyway. If we were to conclude that the DSP effects are not "Diversification" by the dictionary definition or whatever, what would we call it? am i missing something obvious?
Positive Selection Bias of a Dynamic Subset Portfolio through Opportunity Benefit Improvement
...is a bit of a mouthful!