Clearly, private equity firms understand the public markets. Financial sponsors have been successfully bringing their portfolio companies to the public markets for years, as a way to both exit their investments and to bolster the value of the stock they hold.

But when private equity firms themselves have sought to go public, the response has been tepid at best. Distressed investor Oaktree Capital Management LP priced its initial public offering at $43 a share on April 12, at the low end of its range, and has closed below $40 nearly every day since. Apollo Global Management LLC, which went public in March 2011 at $19 per share, hit a low of around $10 a share late last year and is now trading at about $13 per share.

Those performances likely weighed heavily on the minds of managers at Carlyle Group in the run up to that firm's IPO on May 3, when it became the sixth sponsor to take itself public. Part of the problem is that the short-term trading strategies used by many stock investors don't work well for investments in private equity firms, which require more patience to secure solid returns, says Jason Stewart, an analyst with Compass Point Research & Trading LLC in Washington. Investors have treated private equity stocks like traditional shares, unfairly affecting their performance, he adds. But Stewart predicts that investors will eventually value these stocks more accurately as the investments grow older. Public trading in private equity has been around for only five years, he points out, dating back to Fortress Investment Group LLC's IPO in 2007.

In any case, there is an appetite for private equity in the public markets, and it remains strong. When the firms go public, they provide stock investors access to a previously inaccessible investment that has provided some of the financial industry's best returns, Stewart says.

When buying shares in a private equity firm's IPO, investors should pay attention to who is selling. If it is the founders and top management, investors may do well to be wary. Those principals have insight into how well their portfolio companies are performing, as well as broad economic cycles. If they're exiting a private equity firm in an IPO, it may be a sign of bearishness

Oaktree co-founders Howard Marks and Bruce Karsh each earned nearly $80 million by selling shares in their firm's IPO. Carlyle's founders, including David Rubenstein, didn't sell any shares in their firm's IPO, which priced at $22 a share, below its expected range of $23 to $25. The firm plans to use most of the $671 million in proceeds to pay down some $618 million in outstanding debt.