The initial public offering of private equity firm The Carlyle Group LP (Nasdaq: CG) opened slightly below the IPO price of $22 on Thursday before climbing as high as $22.39. Shortly before the closing bell, shares were trading at $22.02. 

The valuation of the stock price for the Washington-based buyout shop means that many investors who had previously bought private stakes are automatic losers. A $22 IPO share price values Carlyle at $6.7 billion, less than the expected valuation of $7 billion to $7.6 billion.

The firm had previously been valued as high as $18 billion when Abu Dhabi's Mubadala sovereign investment vehicle bought a 7.5 percent stake in the company.

Besides the fact that the firm lowered its expected IPO price prior to the offering, the lack of a substantial first-day trading pop is surprising in view of the 21 underwriters hired by Carlyle to work on its relatively modest offering. Most public offerings, including large ones, have no more than a dozen bankers working on the deal.

Carlyle is one of the world's largest private-equity firms, with $147 billion under management. It is not the first private-equity firm to do badly in terms of valuation after going public.

Rivals such as The Blackstone Group L.P. (NYSE: BX), Oaktree Capital Group LLC (NYSE: OAK) and Fortress Investment Group LLC (NYSE: FIG) have all seen share prices disappoint after going public.