The HDMI specification for version 1.4a indicates 120FPS maximum for 1080p.
At 1080p, it'll support upto 120 Hz. At 4K, it'll support upto 30 Hz.
HDMI 2.0, supports 4K at upto 60 Hz, and likely 1080p at upto 240 Hz.
Depends on your monitor. If you have a 60hz monitor, you'll max at 60 FPS. If you have a 120hz monitor AND it supports HDMI 1.4 @ 120Hz, you'll get 120 FPS.