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NEW YORK—Wall Street reversed early losses to close higher Tuesday, as investors monitored the movements of record high oil prices but still laid bets that the economy and companies are in recovery mode.

Crude oil climbed to a record near $123 a barrel on the New York Mercantile Exchange as traders, who have nearly doubled the price of oil over the past year, reacted to the weakening U.S. dollar, supply threats, and a note from Goldman Sachs & Co. predicting that oil could reach $200 a barrel. High oil prices threaten to crimp consumers’ discretionary spending.

But oil ...