Conceptually, we’ll explore why oil prices might correlate with oil stock prices, and then explore which case is correct.
There may be a positive correlation between returns to oil prices and returns to economic activity (stock prices) because a stock simply represents the current and future earnings of a company, and thus higher oil prices means higher earnings, and thus a higher stock.
This is not a hard rule but is reflected in general investing methodology whereas low P/E companies (or just those with low and stable raw revenue/profit multiples) are considered more valuable, all other factors held at a constant, than a polar partner.
There may be a negative correlation between returns to oil prices and returns to economic activity (stock prices) because fundamental investing in stocks, apart from speculative (technical, hype, e.g.) investing, infers that oil stocks should not move in alignment with short-run crude price changes, since these alterations do not change their fundamental value nor true price.
Furthermore, short-run oil price increases could be caused by supply or demand shocks, which can negatively impact stock prices.
Thus, the correlation between oil prices and oil stocks can change depending upon the nature of the price change, forecasted sentiment in addition to future sentiment, and the nature of the people trading the stock.