NEW YORK (Bloomberg) - Microsoft Corp. co-founder Bill Gates's Cascade Investment LLC took a 3.56 million-share stake in Bermuda-based insurer Arch Capital Group Ltd.

The holding represents about 6 percent of the stock, according to a regulatory filing on Thursday.

The stake adds to Cascade's holdings in companies including Warren Buffett's Berkshire Hathaway Inc. and trash hauler Republic Services Inc. The investment is valued at about $256 million based on today's closing price of $71.89 a share and makes Gates's fund the third-largest investor in the insurer, according to Bloomberg data.

Attempts to reach Michael Larson, identified in the regulatory filing as business manager for Cascade, were not immediately successful.