Dave Carlson recently wanted to borrow about $1 million to fund operating expenses at Giga Watt, his cryptocurrency-mining operation based in East Wenatchee, Wash. The mining, which generates new units of cryptocurrency using specialized computers, requires vast amounts of electricity; Carlson said he spends about $250,000 a month on power. He could have exchanged some of his crypto for cash, but he didn’t want to miss out on future surges in value.

For Carlson and other cryptocurrency investors, this is the conundrum: They...