I'm also experiencing a random playback stuttering from my iTunes purchased movies saved to my RAID box. In a discussion forum at
https://discussions.apple.com/thread/7314597?tstart=0 a few other Apple TV (4th gen) owners are also experiencing this issue. iTunes purchased movies streamed directly from Apple's servers buffer and play back fine, but locally stored Apple purchases have this random stuttering issue. One user speculates that the new Apple TV may not be buffering locally stored movies, which would be bad, if true.
Apple is shipping me a replacement, but if this is a software issue, that won't fix this problem. We've confirmed my local gigabit Ethernet is performing up to specs, and anyway these movies play back fine to my old Apple TV (3rd gen).