“I’m not sure Bain Capital could have grown or turned around some of the companies we invested in had we faced today’s anti-business environment. Andy Puzder, the chief executive of CKE Restaurants Inc., which employs about 21,000 people at Carl’s Jr. and Hardee’s restaurants, has said that the “current unfriendly economic environment perhaps best explains why American companies are sitting on over $2 trillion which they could invest.”

To be sure, it is impossible to say with any certainty if 2012-era Bain Capital would be able to turn around a 1986-era maker of truck wheels. Any more than anyone knows how 2012 Albert Pujols would fare against 1965 Sandy Kofax.

But we do know two things that shed doubt on Romney’s broader, anti-Obama point:

1. Private equity firms are doing just fine. In fact, take a look at benchmark returns from Cambridge Associates:

In other words, private equity firms have significantly increased the value of their portfolio companies under Obama’s watch. It’s certainly worth cautioning that short-term private equity returns can be finicky — it’s a long-term asset class for a reason — but these are the only numbers we have. Plus, private equity fundraising is on a post-crisis upswing. Does Romney have something different he’d like to share? I assume it’s not recent Bain returns, since those are in a blind trust.

2. CKE Restaurants was acquired by private equity firm Apollo Global Management in 2010 for just over $1 billion (including assumed debt). Since then, CKE has turned unprofitable and was unable to price an IPO earlier this month (something Puzder blamed on droughts, lackluster McDonald’s sales and the Supreme Court’s Obamacare ruling). In other words, it seems to prove Romney’s point: CKE was better off before Obama.

But a few caveats: First, CKE revenue has been declining consistently since 2008. In other words, the downturn began under Bush (yes, I know that I sound like an Obama campaign parody). Second, year-over-year revenue and earnings has actually risen between 2011 and 2012 for the 16 months ending May 31 (which is the most recent data provided). Third, the primary driver of bottom-line trouble since Apollo took over was the massive amount of debt — and a dividend recap — related to Apollo’s acquisition. In fact, there’s a good case to be made that CKE might have been better off without Apollo, at least from a balance sheet perspective (I can’t speak to its strategic value). Not exactly a good case study for a private equity exec who wants to be president…

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