Is it okay to record a game from a 1080p source at 720p?

I've always wondered this. I'm starting a Let's Play on Tomb Raider (on Xbox One). If I have my Xbox One display set to 1080p, but set my recording software to only record in 720p, will that affect the final quality of a video? Additionally, what if I export the final video in 720p as well?

Will it affect the sharpness or overall quality of a video (since you're technically taking a larger resolution video, and resizing it)?

Submitted by RememberNobleGaming Xbox 720 Release Date 2015