Younger investors might not recognize the name Bill Miller, chief investment officer of Miller Value Partners, but he stands as one of the giants of mutual-fund history. Mr. Miller beat the S&P 500 index 15 years in a row from 1991 to 2005 when he was managing the Legg Mason Capital Management Value Trust fund. That streak—still a record—was built on big, value-oriented bets.

His fund cratered, though, during the 2008 financial crisis, as he invested heavily in financial companies such as Citigroup and American International...