If so, there is little to stop someone from walking up to your PC and using it. So that's one issue. If the browser is current then most attacks rely on the user to install something or to send them the needed information to complete the phish or attack.
So just an open web page is usually not extraordinarily risky beyond the obvious issue.
if i keep my google calendar open on my desktop all the time will i be subjecting my computer to any kind of attacks or "fisching" (not sure of spelling). i am sure this is very elementary to most, but i am just getting into this.