LONDON—Scottish voters' decision to stick with the rest of the U.K. lifted stocks and reset market expectations for the path of the country's interest rates, but gave sterling only a brief boost as it left investors with gnawing doubts about the long-term political outlook.

Shares in Scottish lenders Royal Bank of Scotland Group PLC and Lloyds Banking Group PLC, which had both said they would move their headquarters to England if Scots backed a breakaway, soared.

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