I recently purchased a 4K monitor and found out that my 13" MacBook Pro Late 2013 does not support 4K@60Hz even with the Mini-DisplayPort to DisplayPort adapter. It only supports 4K@30Hz.
According to Apple's support document, 4K@60Hz with a multi-stream transport (MST) display is only supported by 15" model of the same age:
These Mac computers support MST displays at 60Hz:
- MacBook Pro (Retina, 15-inch, Late 2013) and later MacBook Pro
- MacBook Pro (Retina, 13-inch, Early 2015) and later
Source: Using 4K displays, 5K displays, and Ultra HD TVs with your Mac