The pairing trick that rescues a hopeless comparison

You run two forecasting signals on the same 250 days and the same universe, so each day produces a return for signal A and a return for signal B side by side. Both signals swing around wildly day to day (standard deviation near 40bp each) because they ride the same market. But their daily difference $d = r_A - r_B$ has mean 2bp with a standard deviation of only 12bp, because the shared market move cancels out.

Test whether A truly beats B using the paired structure, and explain why this design is so much more powerful than comparing the two return series separately.