During his tenure as Giants general manager, Jerry Reese never has traded up in the first round of the NFL draft. The Giants own the No. 23 overall pick in this year’s draft and Reese is unlikely to pull the trigger on a move up. But you never know. “If we have an opportunity to trade in the first round, we’ll do that,” Reese said Thursday. “Right now, we’ll just kind of let the board fall like it does. If we feel like we want to move up and get somebody, we’ll move.” With that, Reese essentially explained why he has never made a first-round trade. “It costs to move up, though,” Reese added. “If you’re going to move up, you’re going to give away a lot of draft picks to move up, even if you just move up a couple of spots. We like taking our picks.”