No they do not. Just a few years ago oil bottomed out at 7 dollars a barrel. Gold was about 275 dollars an ounce. Oil responds to free market forces of supply and demand and to a certain extent fear. Golds price is controlled mostly by fear. Commodities will rise as a group. Gold will also rise as a commodity but will also have wild swings in value based on fear in the market. When people are afraid, as now, it is a good investment.
The barrel of oil to ounce of gold ratio fluctuates from roughly 10 to roughly 30. The ratio helps normalize out the changing value of the dollar relative to other currencies. "Fear" is not a rational basis for making decisions concerning large investment positions.