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BOSTON (Reuters) - Fortress Investment Group said it incurred a $3.7 million (2.2 million pounds) paper loss last year on an investment it made in the virtual currency bitcoin.

In a regulatory filing, the company said it invested $20 million in bitcoin in 2013, and that the stake was worth $16.3 million by the end of the year.

"Fortress recorded $3.7 million in unrealized losses on digital currency during 2013, which was included in gains (losses) in the Consolidated Statements of Operations," the company said in its 10-K filing.

Fortress, one of a handful of publicly traded hedge fund companies, is one of the first big-name investors to publicly say it has suffered a loss on its bitcoin investment.

On Friday, Tokyo-based Mt. Gox, once the world's biggest bitcoin exchange, filed for bankruptcy protection.

(Reporting by Svea Herbst-Bayliss; Editing by Bernadette Baum)