How Many Systems are Enough?

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svquant
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How Many Systems are Enough?

Post by svquant » Tue Mar 27, 2007 12:28 am

Attached to this posting is a PDF of an extended abstract I wrote ~8 years ago for a finance conference. This paper did not get in but the area is an interesting one. The paper deals with diversification especially when having a shortfall is a big concern. This is true in institutional portfolios where asset liability management (think pension funds) is a big deal.

I hint at a use for trading systems in the paper and it follows the same line of thinking as individual CTAs explored in the abstract. In managing money or an account with a collection trading systems one wants to minimize the potential of a shortfall or target, say returning 20% per year, at any given point in time. Therefore one should use as many systems, even of the same style, as possible to achieve this. Note in trading system assemblage we have the added advantage of netting out all the various trades in each system into one order so cost of implementation can be low compared to managing a pool or FoF with individual managers, fees, and hurdles.

Keep in mind that this does not state to increase the % allocation to CTAs or system based trading just discusses the minimization of "risk" for that allocation.

Enjoy,
Marc
Attachments
TWSD for TBB Extended Abstract.pdf
Paper on CTAs, diversification, and terminal wealth standard deviation. Applicable to trading systems too.
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AFJ Garner
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Post by AFJ Garner » Tue Mar 27, 2007 3:19 am

Interesting paper, thank you for posting.

As you might gather from other threads, I am looking at using a trend following strategy for investing in stock markets - perhaps in cash markets in general. I have been asking myself whether such a system will achieve much in terms of diversification from my LT futures system. After all, I trade a number of index futures, so do I really want to invest in the cash markets as well?

I had not focussed to date on end wealth value, although of course that has always been at the back of my mind.

I had been discussing things in general terms with a friend with long experience of stock markets and absolutely none in analysis or back testing. His career was as a salesman in a major brokerage.

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svquant
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Post by svquant » Tue Mar 27, 2007 11:30 am

Thanks for the thoughts. Just some further comments on this. You mention the correlation of equity curves as a focal point and that is correct. Many people perhaps use the following logic: instrument X and Y are highly correlated. Two long term trend following systems, A & B, are highly correlated. Therefore there is no advantage to trade X & Y with both A & B. Well as long as X & Y are not perfectly correlated and A & B are not perfectly correlated there is risk reduction in both time-series risk and terminal-wealth risk. The risk reduction in terminal-wealth keeps on going after the time-series has stopped showing incremental improvements.

On diversification of trading systems on a given instrument and reduction risk there has been a PhD thesis published in the early 1990s which shows using stochastic calculus what diversification and risk reduction one gets using different moving average or momentum based trading rules. Yes, a paper stating that the reduction of risk between trading MA(30) vs a combination of MA(10), MA(20), & MA(30). In fact given some time series property assumptions there is a way to pick the MA-lengths so as to maximize the benefit of multiple time frame single system diversification per instrument. See not all academic research is useless :wink: A link to a book that has some of this info: Advanced Trading Rules

As you explore this area you might want to also understand how the rebalancing mentioned in the abstract contributes to the results, eg volatility pumping on a manager basis. Keep in mind overall we are based on the assumption that managers or trading systems we are using have an edge or positive expectation. Finally, just want to re-inforce this is in no means advocating allocating more or less capital to a certain trading style just how to maximize that allocation. If you are 100% long term trend/momentum following then yes cash stock index momentum and TF-futures will work well together and give a "benefit". If you are allocating 50% of your capital to trend trading this is to help allocate that 50% not advocating moving 50% to 100% just because there are now "two systems".

Hope this helps rather than confuses.

Marc

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Post by nickmar » Tue Mar 27, 2007 12:45 pm

AFJ - assuming that you have an exposure cap by sector or sub-sector (e.g. max x% to equity index futures or max y% cap to European equity index futures), it probably makes sense to allocate to as many markets as possible within each sector/sub-sector subject to account size constraints (i.e. an investor would obviously not be able to trade 20 equity index futures in a $500K account).

I ran a test using a simple dual moving average system (150/300) on a portfolio of 51 global index futures markets (both active and inactive markets were included - see list below).

Other key points:
- Position-sizes were volatility-adjusted
- Slippage of 15% and roll slippage of 10%
- Test ran from 1980-03-31 to 2006-10-31

Chart interpretation:
1 - The lower chart represents total equity (log)
2 - The second chart from the bottom represents the total number of available equity index future markets (i.e. active markets)
3 - The second chart from the top represents the net position of all active equity index future markets (e.g. if 10 markets were long and 5 markets were short, the net position would be 5)
4 - The top chart (and most interesting) represents the percentage of Equity Index Markets positioned in the same direction (e.g. if the total number of available equity index future markets was 10, 3 of these markets were long and 4 were short, the percentage would be ABS[3-4]/10 or 10%)

As can be seen, with a basic stop-and-reverse long-term trend-following system there appears to be a fair amount of diversity even in the most correlated of sectors. I imagine that the amount of diversity would be even greater if individual equities are used instead of (or along with) equity index futures due to the introduction of nonsystematic risk.
[EDIT: it is probably best to focus on the >=1991 period since prior to 1991, fewer than 10 equity index futures markets were available]

Svquant - have you come across many papers that describe volatility pumping from a practical perspective? I have heard rumors that Renaissance may use this reallocation method.
Attachments
ScreenHunter_001.jpg
Index futures markets included in portfolio
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svquant
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Post by svquant » Tue Mar 27, 2007 1:30 pm

Nickmar - nice work. I fully agree that with individual equities will get more diversification. One caveat to watch for in going down this road is too large a sector bet depending on account equity. You don't want to have all oil stocks in the portfolio based on momentum. Using indexes forces this not to occur based on the index make up. It is even better when we look at this world wide like you did since different indexes have different sector weights, i.e. US S&P vs Aussie S&P.

You are correct that many (all?) of the papers on volatility pumping are academic in nature vs practical. Some are much more reasonable in terms of estimating the rebalancing costs etc but still a little short on real implementation. On the other hand many of the published academics in this area are consulting to or part of hedgefunds so perhaps there is a practical aspect that remains unpublished.

As for RenTec - my info tells me they do not use vol-pump especially as commonly described in academic papers. Of course this could have changed over time since I do not have first hand knowledge of their methods.

Regards,
Marc

AFJ Garner
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Post by AFJ Garner » Tue Mar 27, 2007 3:12 pm

Nickmar, I am a great admirer of your excellent charts and am in agreement with your thoughts. I do indeed intend to take on more individual contracts within all sectors in due course, subject to overall limits per sector. And it will certainly include such exotica as rubber, maize, palm oil, exotic currency pairs and so forth.

My thinking on cash equities is along the same lines. Were I working with others, I would undoubtedly use individual equities. I had long and useful chats with an eccentric Wizard whose thinking is much the same.

However, it is going to be much easier to work with the now very large number of country and sector specific ETFs. Including Reits and Bonds. And even some of the more exotic passive index based products (after very careful reading of the relevant prospectus, monitoring performance and tracking error, expense ratios and so forth).

The advantage of working with ETFs, in building a diverse international portfolio, is the avoidance of having to deal with the myriad of dividend receipts, capital distributions/changes and so forth which using individual equities would involve. Not to mention the placing and monitoring of a multitude of trades across a plethora of currencies.

Once again it occurs to me what a very useful (and indeed unique) resource this forum is for a frank and hopefully mutually useful sharing of ideas.

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