Illustrator :: Object Scaling Doesn't Seem To Work Correctly With Objects Containing Bezier Curves

I created a closed object that had a Bezier curve as part of it's definition. I wanted to scale it by 110% and then use this second enlarged object to create a sort of a background underneath the first object to create a sort of a shadow effect. But rather than the second object being uniformly larger than the first it intersects the original object in ways that don't make sense to me.
 
Is there an easier/differnt way to create an effect like this? I can do it but have to manually adjust a lot of points in the new object so that they create a uniformly larger version of the original object but it's a lot of effort for something that works fine for normal polygons with straight lines (e.g. a star with 5 points).
 
i've attached an image of what I get with this technique of creating two examples of two objects one a 110% scale version of the other. The first star shows the effect I'm trying to get and the second shows the problem (the red border does not surround the black object uniformly around the perimeter)