Does rooting a phone expose the phone to security risks?
Yes and no. 

If you carelessly install apps to your phone without reviewing permissions, then yes your system is more vulnerable to malware and such.

But if you "read the fine print" and are conscientious about what you install, then no your system should be just as safe as not rooted.

You can also control permissions with the native AppOps or you can use a third party app. A excellent example of that would be My Android Tools. You can enable/disable Activities, Broadcast Receivers, Content Providers, and Services. So even if an app has an undesirable permission you can still control what your apps, while rooted, are doing (even in the background). Not only can you change the settings for user apps, but also system apps. It even has an option to backup the settings before any changes are made, in case of any issues.

Once rooted the Android becomes very interesting. The sky's the limit.



If you don't have AppOps in Settings (because its a hidden setting) you can download a shortcut to it from the PlayStore. There are several apps to accomplish this, just pick one you like.