Private pages as featured content

I'd like to use the featured content feature but I'd like it to be visible only to users that have logged in. I've set all the pages that are restricted to logged in users to be private. I tried specifying one of these pages to be a featured context page, but the page appeared on my home page even when I wasn't logged in. Is there any way to have the items in featured context not be visible unless you're logged in? My website is https://wurmb.de. This site is still very much under development an the featured context is currently the sample items. Thanks for your help, Matthew