Come Monday morning, Bill Gross’ business card will read Portfolio Manager, not Chairman, Chief Executive, President, or boss of anything. For one of the most powerful investors on the planet, the abrupt transformation might be a letdown, but it is in some ways a relief. More important, it could be an unusual opportunity.

Unless you’ve been living on a distant planet, you’ve heard by now that Gross, known on Wall Street as the Bond King, bolted on Sept. 26 from Pacific Investment...