I think we have sorted this one out. All you have to remember is that the displacement of a floating objects is defined by its mass, whereas the displacement of an object which is completely submerged is governed by it's volume.
Ignore the mass of the boat, and think of just the anchor.
When in the boat it is effectively floating. Hence the displacement is the mass.
Now assuming it sinks (and it wouldn't be much use as an anchor if it didn't) then it has a density higher than that of water.
Thus when it is submerged it will displace a smaller volume of water. Hence the water level should fall, albeit by a small amount.
Simple when you know how!
