Combining multiple systems

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Several threads have speculated about the topic of combining multiple systems to create a better system. The latest 'Acrary is a genius' thread was getting off topic with the martingale stuff, so I decided to start a thread to review the subject.

The fact of the matter is that combining multiple systems that have a certain degree of uncorrelated performance is not only a technically sound idea, but can be very profitable. As Acrary and others have shown, simple systems with nominal Sharpe ratios can be combined to form a composite system with a higher Sharpe ratio. Extending this to a high number of systems can produce quite remarkable results ... Sharpe ratios of 2, 3, 4, ... not only on back-tested data, but in real trading. This means that with the same amount invested on average, a better return with less risk can be attained.

My experience is not simply theoretical, but has been implemented, successfully paper traded using IB's API which accounts for commissions and slippage, and traded live with real money for several months ... and the live results work just as well.

This is not a holy-grail, care must be taken when combining systems and things like good monte carlo validation, avoiding the dreaded probability tails, etc, etc, need to be used so that the solution not only provides good historical back-testing performance, but has predictive power so that it will work on data sets that were not used in the optimization, and will work into the future.

If there is interest, we can discuss some of the issues. I'm not interested in arguing about whether or not combining systems produces better results, but I can help people with questions about how to. As expected, I won't discuss any systems, but for those who are developing their own stuff, just thought it would be nice for you to know that you can combine them for some real performance. :)
 
More than one theory has been put forward, seeking to explain why overall performance increases when you trade more and more (partially-) to (un-)correlated strategies.

Harry Markowitz believes this is essentially a diversification effect: more and more individual market-systems are being added to the trading ensemble, so the final equity curve is the average of the equity curves of the individual market-systems. Averaging a bunch of uncorrelated curves smooths out the hills and valleys of the individual market-systems, producing a very smooth (high Sharpe-ratio) final equity curve. For perfectly uncorrelated market-systems (ha!), the variance falls as (1/N) so the Sharpe Ratio rises as (sqrt(N)) where N is the number of perfectly uncorrelated market systems.

Ralph Vince, on the other hand, dismisses "diversification" as bunk. He thinks the reason more, more, more systems works better, better, better is simply this: more trades per unit time. If the systems are profitable, and if anti-martingale betsizing is used (which it is), profits are exponential in the number of trades. Raising the number of trades increases profits exponentially, while reducing the betsize by a factor of N (to keep drawdown manageable) decreases profits linearly. Bang! Exponential beats linear every time. So the net result is larger gain with the same pain, namely, higher Sharpe ratios.

It's worth mentioning that one of these theories was awarded a Nobel Prize in economics and the other one, wasn't.

(link 1) (link 2)
 
Quote from phattails:

If two systems are volatile enough, neither of them have to be profitable to get a profitable total system.
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I just don't see it. If two systems are losing individually, I don't see how they can win collectively unless you can time them properly. And if you can time them properly, then they can be profitable individually and, therefore, they are not losing systems.
 
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