Digital Foundry has completed their analysis of the performance of the PS4 version of Call of Duty: Black Ops III and have some rather startling revelations. Despite some optimizations and the use of dynamic resolution scaling, the framerate still only barely reaches 60FPS and only in some rare cases.
What's surprising, perhaps, is that despite Black Ops 3 having PS4 exclusive windows for DLC and maps, and also being the new platform that'll be used to compete in professional eSports, it still fails to maintain even the framerate target set by Treyarch.
Perhaps the problem in this case is the base resolution that's being targeted at 1080P and the use of filmic SMAA, which is effective and generally considered great looking but it also has a larger effect on performance than normal non-filmic SMAA.