Here's a toy example of a simple trading strategy that I just read about (from a book called "Trading Alphas"):
Let's say that we expect a stock that's been going up over the past week to now go down, since traders are expected to book profits and the price will accordingly decrease. Our trading universe has only 2 stocks - Google and Apple. We could have a trading strategy in which our position in a stock is given by
position $ = - ($past week return$)$.
Using the above, we get positions in Google and Apple as $+2.5$ and $+7.5$ respectively. So far so good. Now, suppose we're expecting some bad event for the technology sector. A long position in these stocks could result in heavy losses. The book prescribes that one way to avoid such losses is to develop a sector-neutral strategy - the sum of positions of individual stocks in that sector would be $0$, i.e., take a long position in either Google or Apple and an equal short position in the other.
"This would change the old values of $+2.5$ and $+7.5$ to $-5.0$ and $+5.0$ for Google and Apple, respectively."
I can understand that we go long in Apple since our previous strategy prescribed a higher positive position in it ($+7.5$ as against only $+2.5$ for Google). But we could just as easily have had a different prior strategy that similarly assigned a more positive position to Apple. So the end result would've been similar - a sector neutral strategy that assigns $+x$ to Apple and $-x$ to Google.
In that sense, doesn't the sector-neutral strategy make our previous trading strategy completely irrelevant (apart from the magnitude of $x$)?