With a 1920x1080 source in 4:2:0 format.

Method used:

For h264: ffmpeg -y -i $SOURCE -codec:v h264 -preset slow -vf format=pix_fmts=yuv420p -pixel_format yuv420p -qp $QUAL -an out.h264

For h265/hevc: ffmpeg -y -i $SOURCE -codec:v libx265 -preset slow -vf format=pix_fmts=yuv420p -pixel_format yuv420p -x265-params crf=$QUAL -an out.h265

For jpeg2000: ffmpeg -y -i $SOURCE -codec:v jpeg2000 -vf format=pix_fmts=yuv420p -pixel_format yuv420p -q:v $QUAL -an out.j2k

For mpeg4: ffmpeg -y -i $SOURCE -codec:v mpeg4 -preset slow -vf format=pix_fmts=yuv420p -pixel_format yuv420p -qmin $QUAL -qmax $QUAL -an out.mp4

Using ffmpeg version 3.0 Copyright (c) 2000-2016 the FFmpeg developers
built with Apple LLVM version 6.1.0 (clang-602.0.53) (based on LLVM 3.6.0svn)
configuration: --enable-gpl --enable-version3 --enable-nonfree --as=yasm --disable-shared --enable-static --enable-libfaac --enable-libmp3lame --enable-libx264 --enable-libx265 --enable-libbluray --enable-libopenjpeg --enable-libtheora --enable-libvorbis --enable-libtwolame --enable-libvpx --enable-libxvid --enable-libssh --enable-libfdk-aac --enable-libopus --enable-libschroedinger --enable-librtmp --enable-libfdk-aac
libavutil 55. 17.103 / 55. 17.103
libavcodec 57. 24.102 / 57. 24.102
libavformat 57. 25.100 / 57. 25.100
libavdevice 57. 0.101 / 57. 0.101
libavfilter 6. 31.100 / 6. 31.100
libswscale 4. 0.100 / 4. 0.100
libswresample 2. 0.101 / 2. 0.101
libpostproc 54. 0.100 / 54. 0.100