When you intend to create a silhouette against a bright backkground,you really don't have to use exposure compensation at all. All you have to do is take the picture as you normally do. The bright background causes the camera to underexpose the picture, thus the subject becomes black and the bright background turns out very close to what you want. Check the LCD monitor on the back of the camera to make sure you're getting what you want, but probably the exposure will be perfect without any adjustment.
The settings for this picture I took in Namibia were 1/100, f/16, and 1000 ISO. I used a small lens aperture in the hope I'd get the sky as sharp as the cheetah. I didn't, and I don't like that. Still, I like the image because it shows the classic way these cats hang their head as they walk.