Why does an arrow go deeper in water than a bullet?

The tip of an arrow is pointed and so it exerts very little pressure on the water surface. Also the shape of the arrow is streamlined so that it has as little Resistance as possible. However, the tip of the regular bullet is blunt and so it exerts more force than the arrow when it comes in contact with the water surface. And the deflection of the bullet in the water will be more than that of the arrow away from the normal due to reflective index.