Say you’ve discovered a wad of cash in a secondhand coat or, more appropriately, a wad of virtual bitcoin on the hard drive of a used computer. With the virtual currency up nearly sevenfold against the dollar this year, do you sell or hold?

That is essentially the situation facing Japanese everywhere-and-everything conglomerate SoftBank. Led by singularity-obsessed founder Masayoshi Son, SoftBank Group Corp. struck a deal back in February to snap up asset manager Fortress Investment for $3.3 billion. Buried in the company’s...