Letterbox when converting 4k to 1080p
Because 4096 / 1920 = 2.13333 and 2160/1080 = 2.  They are different aspect ratios, so yes, they end up letter boxing when you convert between them.  That is the expected result.

The 4K format you are using is a multiple of 2K and is not the same widescreen aspect ratio as 1080p.  You can't translate between them without letterboxing, though there are several different competing "4k" resolutions, so it won't hold true for all "4k" formats, but it does for the one you are working with.