"Aramco is unique. In terms of quality of assets, scale and profitability it dwarfs just about any company globally," BofA said in a note. "Yet, at current valuations, most of the outstanding fundamental factors are already priced in."

BofA, the rebranded Bank of America Merrill Lynch research unit, joins a growing list of major brokerages who have started rating Aramco in recent weeks after its record $29.4 billion stock market floatation last month.

JPMorgan also initiated its coverage on Wednesday with an "overweight" recommendation. It set a price target of 37 riyals ($9.86) per share, saying that it saw scope for an increase in the energy giant's proposed $75 billion base dividend.

Goldman Sachs on Tuesday said it rated the company "neutral" but with a higher price target of 41 riyals, while HSBC issued a "hold" rating and a target of 36.80 riyals.

(Reporting by Marc Jones, editing by Louise Heavens)