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The next time you’re grinding your teeth while filling up at the gas station, you may wonder if buying oil stocks is a good way to offset all that money pouring out of your wallet and into your gas tank. It’s a tempting proposition—but a complicated one.

Higher gas prices don’t necessarily translate into more revenue for oil companies. For one, higher prices tend to lower demand and lead to less driving. Cumulative miles traveled in the U.S. fell 1.2 percent in 2011. There’s also not a perfect correlation between oil prices and oil company stock prices. In the first two months of this year, the prices of gas and crude oil have both risen by more...