The point is to improve gain to pain ratios, like Sharpe ratio. Or net profit / max drawdown. Gain to pain ratios are improved by adding the losing anti-correlated strategy. A*2 has much larger drawdown of course. Same gain to pain as A alone.
Instead of saying "losing system", let's call it a random trading system ( losing could mean we could short the system and it's winning or it could be always losing if commissions kill a system with a small bank role). Pull out a spreadsheet and create random strategies and try to combine them. You can definitely create a winning portfolio if either there is enough volatility or if the mean return is nonzero. In black jack you can gain an edge if you either adjust your bet according to the card count or bet on all possible outcomes. There is tons of literature out there discussing this issue.
Gain to pain ratio is improved, but at what cost? The final gain is reduced to achieve this. Again, you can achieve this by just adjusting the position sizing of strategy A alone. Save yourself the cost of trading strategy B at all. While A*2 also have much higher overall gain as well.
This is a wrong statement. You don't understand the math. This is not a difficult concept to test and I suggest you take some time with excel and do a bit of experimenting before replying. Let us know when you see the flaw in your logic.
Do you want to learn? Are you willing to listen? Or you will continue pretending you know everything, when it is obvious to everyone here that you do not know anything about real trading and you're just a wannabe trader. Trading is all about assuming the lowest possible risk for the largest possible reward. Anything else is sub-optimal and even dangerous. Optimal f,, %kelly, people with a name made of two first names, anyone spewing the word optimal in general, have not traded real money in their life. I hope you and Rita will finally get to understand this: http://www.elitetrader.com/vb/showthread.php?s=&postid=3472387&highlight=Rita#post3472387
When you don't understand the topic of the thread and can only post platitudes and insults, then why do you post here at all? Not everyone knows portfolio theory or can understand mathematical concepts. That's ok. After all, trading is mostly a zero sum game, so we need guys like you to pay for the income of guys like me. I hope that you continue with that. But it's not necessary to expose yourself this way in a forum. Unless you have some even remotely rational argument to contribute - then just do it.
Assuming all are 100% systematic strategies/ mechanical systems. imo, theoretically one could combine (a first) two losing but (very much) uncorrelated strategies (A and B) into a compound strategy (C) for a better and profitable performance. He may even repeat the same process by finding another (highly) uncorrelated (losing) strategy (D) to improve the profitable performance of C strategy. However, there are two major problems. 1st, the final strategy (D) would be highly likely an over-optimised one, with an ununrealistic performance expectation. 2nd, most if not all the correlations would change their actual correlations from time to time that occasionally could cause serious drawdowns. Just 2 cents!
I don't think that over-fitting is a problem here, as it is not affected by portfolio composition. Overfitted strategies, traded in a portfolio, stay overfitted, but correctly optimized strategies are still correctly optimized. Of course, when the portfolio capital assignment factors are generated in an optimization process, they can also be overfitted. The 2nd issue is indeed a problem. Correlations tend to change. However I found that some strategies have quite stable negative correlations over 8 years, especially trend and mean reverse strategies.