WHEN he was a Yale Law School student, Reuben Grinberg wrote one of the first academic papers about Bitcoin, a novel virtual currency that uses sophisticated cryptography to validate and secure transactions that exist only online.

When Mr. Grinberg, now a lawyer in the financial institutions group of the Manhattan law firm Davis Polk & Wardwell, first learned about bitcoins, they were selling for 10 cents. Now, after the latest price surge that began in January, the cost of a bitcoin on an exchange that converts them to dollars is something like $140, and the collective value of all bitcoins has passed a billion dollars.

That is a lot of coin in any form, and the billion-dollar milestone has turned the once-obscure online currency into a media sensation. Had Mr. Grinberg invested just $100 back then, today his investment would be worth ...

Ah, but that way madness lies. “People are buying bitcoins because the price is going up,” he said in an interview. “That is the classic indicator of a bubble.”