With a fortune estimated to be as large as a quarter of a billion dollars, Mitt Romney is among the wealthiest men ever to run for president.

But attacks from Democrats and Republicans over his career in the leveraged buyout business and his reluctance to release his tax returns have underscored another central fact about Mr. Romney: The wealth that has helped underwrite his career in politics remains shrouded in considerable secrecy, which now poses a major political risk on the campaign trail.