Hey I bought this monitor but I have question concering "adapter latency"

Tek Syndicate "Influenced" me to the buy this monitor:

http://www.bestbuy.com/site/hp-27-ips-led-hd-monitor-black/7504039.p?id=1219679619216&skuId=7504039&ref=199&loc=qcLRzjFniJE&acampID=1&siteID=qcLRzjFniJE-G6_L8UFiV3l9mMfEe3hqNA

According to best buy the monitor only has 1 HDMI input however I already use HDMI for my right elbow monitor and my GPU only has one HDMI output. So bought a display port to HDMI adapter.

This:

I am going to replace my current crap middle monitor with this new one I bought. So what I want to know is by using the adapter is there a chance that I will experience a lowered response time when I am gaming?

I guess it depends on the adapter but then again I'm not even sure if adapter induced latency is even a thing?

If anyone can help thanks.