I would agree if the metric in question is not total profits but risk adjusted returns (e.g. measured by the Sharpe ratio). Adding an unprofitable system to a mix of systems can lower overall volatility and thus help increase risk adjusted returns.
Read about Parrondo's paradox in the link I provided ^^ above. There are some examples of the games that are individually losing but in combination they produce positive expectations. It took me a while to wrap my mind around it. I actually have built a system based on this paradox and tested it on ES markets. I got very surprising results! Totally counterintuitive.
Thanks Maestro, an interesting article. But it is only mathematic abstraction. From my point of view Automatic Trading Strategy ATS is some form of martingal with trend. We transform one martingal (stock of futures) into the other one, equity curve of ATS. If our ATS equity curve is not random then we can chose when to trade it or not. But that is a question of filters and finally your equity curve will be random. Then your ATS should be profitable in long time. Basically we need average return to be higher then buy&hold return and drawdown to be smaller then buy&hold. Original Markovitz theory was about mixing different stocks in one portfolio based on they return and risks. We can measure risks and returns the same way we do it for stocks. We can measure correlation coefficient between two strategies. So we can apply the Markovitz result but for our "artificial stocks" portfolio. Then it can be proven that when we combine such a portfolio we receive average return but diminish risks - exactly what we need. PS. Again each strategy should be profitable in the long run. In fact from Markovitz theory it can be useful to add stock with negative return but also negative risks (insurance). But my point is that for your portfolio to be profitable the average return should be > 0. For two ATS which return is < 0 the portfolio will be unprofitable.
That is what I thought initially. Apparently, it isn't so. I have 3 losing strategies for ES and their combination makes money! Not a lot and not very smooth, but nevertheless ....
I have been doing some research on Parrondo's systems for the past 2 - 3 years. I think that there is s hope. I cannot tell you that the results are awesome, but they are very interesting. I got 54% wins consistently so far.
Here is the Java applet that illustrates the paradox. http://www.cut-the-knot.org/Curriculum/Probability/Ratchet.shtml