Please read the thread title. That and the OP's first post clearly aim at the claim that a losing strategy can increase your total returns which is absolutely incorrect. I wrote several times that a losing strategy "may" add benefits in terms of risk reduction.
No, they are not. You probably mean the correlation between trade results, but this is normally not used in portfolio management. The algorithms normally use the correlation between equity curves. Anticorrelated equity curves do not "recognize the same events"; they are based on different events. A simple example of anticorrelated components are a trend trading strategy and a mean reverse strategy. Such strategies, even with the same asset, have often anticorrelated equity curves with correlation coefficients down to -0.3. All this is nothing new or exotic - it's very standard portfolio management knowledge.
...which you really do not seem to understand. I bet you take one of those econ or portfolio management courses and just covered portfolio standard deviation. I want to bet my farm I am right ;-) Still you must have missed the class when they talked about portfolio mean returns. But you have the opportunity to prove me wrong: Please show me a formula from your smart text book where mean portfolio returns are a function of correlation.
I don't think this would be consistent at all. I also don't think a bad strategy could be used to improve a good one, since all it would do is filter out a few of the good signals, reducing the number of trades.
The number of trades is not reduced by adding an unprofitable strategy. It does not "filter out" signals. The reason why a 'bad' strategy can improve a portfolio is the reduction of drawdown by anticorrelated strategies. You can see this already in the simple example posted. The lower drawdown allows increasing the trade volume, and thus improves the overall profit despite the losses through the 'bad' strategy. It's no filter trick or paradox, but simple math.
"Making money with a losing strategy"??? I think you're actually talking about "Making money when using a profitable strategy with the help of a losing strategy".
In the picture, Equity A is winning. Equity B is losing but anti-correlated. The drawdown of the combination A+B is so low that this portfolio can be traded with higher leverage, therefore has a higher return and at the same time, a lower drawdown than A alone. In practice, a losing counter trend system can often improve a winning trend following system. The correlations of the equity curves are pretty stable.
This doesn't make any sense to trade a negative expectancy strategy...for what??? To smooth out an equity curve??? It would be easier if you just reduced your size on Strategy A. It achieves the same effect of lowering your drawdown, but you save on the transactional cost with trading 2 strategy as well. If you have a successful strategy A and unsuccessful strategy B, you should only be trading A. You don't trade B, even if it means smoother equity curves. Instead you should focus on position sizing Strategy A.