If two assets are correlated and one of them moves up but not the other, you expect the return of both over a longer time period to converge, you can make a statistical arbitrage by selling the one that moved up and buying the other c.f. https://en.wikipedia.org/wiki/Pairs_trade
If you are looking into diversification. You probably don't want to buy 2 1/1 correlated stocks or assets, since basically buying one of them will do the thing.
> If I put 2 buys either I will have double profit or double loss. If I put 1 buy 1 sell I get zero.
Yea, so it pays to know if something is correlated to avoid this. It also pays to know if something is correlated and their spread gets out of whack short term allowing you to profit from the expectation they'll return to being correlated.
