Water level after an anchor goes overboard

A boat floats in a swimming pool with an anchor on board. The anchor is thrown over the side and sinks to the bottom. Does the water level in the pool rise, fall or stay the same?

It falls. While aboard, the anchor displaces water equal to its weight; on the bottom it displaces only its own volume. Since the anchor is denser than water, its weight-equivalent volume of water exceeds its own volume.