WASHINGTON -- An Internet bank that ran its initial public offering as an auction began trading Tuesday near its offer price and sold more shares than originally planned.

San Diego-based BofI Holding, Inc. (NASDAQ:BOFI), holding company for Bank of Internet USA, priced its stock Monday at $11.50, near the mid-point of its expected range of $9 to $13. It sold 3.52 million shares, up from the 2.59 million it had scheduled. In the stock's first day of trading, it behaved like a textbook auction IPO: It opened at $11.65, 1% above its offer, and then settled flat with its offer price.

Unlike traditional IPOs, where underwriters gauge demand from investors, set the price and hope for a first-day trading pop, auction IPOs aim at setting the price closest to market demand through a bidding process.

Auction IPOs aren't supposed to result in any wild swings during the first day of trading, although that wasn't the case with the most prominent auction to date, that of Google Inc. (GOOG) last year. Its debut was marked by the underwriters cutting the price after the auction closed, followed by an 18% rise on the first day of trading.

BofI Holding, Inc., which used underwriter W.R. Hambrecht's OpenIPO process, hewed more closely to the ideal of an auction IPO, warning investors that if they were seeking first-day gains, they shouldn't seek shares.

Auction IPOs are touted as a fairer way to distribute shares to a broader segment of the marketplace, and a way to place shares in the hands of longer-term investors. They are supposed to generate the maximum amount of capital for issuers while charging lower underwriting fees than traditional IPOs. But the auction market has been slow to take off, with some investors grumbling that Google's process was cumbersome and didn't accomplish broad distribution or maximum capital.

BofI Holding, Inc., launched in 2000, operates primarily through the Internet with one "bricks and mortar" location in San Diego. It focuses on retail banking and loans, and has 24 employees. It doubled its total assets over the last two years, and grew its total deposits by 76% during the same time. Net income in 2004 rose 18%.

The majority of the money raised by the bank is aimed at adding more capital to its coffers so it can continue to grow its business, including through more lending activities, according to documents it filed with the Securities and Exchange Commission.

The next major IPO auction is that of Morningstar Inc., the Chicago investment research firm, which is scheduled to go public some time this spring.

-By Lynn Cowan, Dow Jones Newswires; 202-862-3548; lynn.cowan@dowjones.com