President Barack Obama is warning of stepped-up economic punishments against Russia for its military incursions inside Ukraine. But U.S. sanctions have so far avoided the $10 billion Russian Direct Investment Fund.

The fund has partnered with brand-name American companies, and its advisers include top U.S. and European private equity executives. It's unaffected by sanctions despite ties to Russian state businesses and officials who are sanctioned.

The situation illustrates the Obama administration's struggle to punish Russian President Vladimir Putin's circle without damaging American companies doing business there.

The fund's international advisory board includes private equity executives Stephen Schwarzman of The Blackstone Group, Leon Black of Apollo Global Management and David Bonderman of TPG Capital. Businesses that have previously worked with the fund include General Electric and a JPMorgan Chase affiliate.