* Sets IPO price at 3.7 euros per share
* Pricing range had been 3.7-4.0 euros - sources
* Sale to raise up to 774 mln euros for UniCredit (Recasts lead, adds detail, background)
MILAN, June 27 (Reuters) - Fineco, the online broker of Italian bank UniCredit, has priced its initial public offering at the bottom end of a revised price range in what is Italy's second-biggest market listing so far this year.
A raft of Italian companies, including state-owned shipmaker Fincantieri and the Italian post office, are looking to list on the market to take advantage of growing investor confidence in Europe's economic recovery.
But some bankers have warned the rush of companies tapping investors could clog up the market at a time when some banks are also seeking funds to boost their balance sheets.
Fineco and Fincantieri come to the market as troubled bank Monte dei Paschi di Siena's 5-billion-euro rights issue draws to an end.
In a statement on Friday Fineco said it had priced its offer at 3.7 euros per share. Earlier this week sources said it had set a price range of 3.7-4.0 euros per share, revised from a previous 3.5-4.4 euros.
The final price was set at the bottom end of the revised range "probably to avoid a flop in the first day of trading," a asset manager said.
Information solution group Cerved fell 1.5 percent on its market debut on Tuesday.
Fineco, which expects to debut on the stock market on July 2, said its initial market capitalisation would be equal to 2.243 billion euros ($3 billion).
The broker plans to list around 30 percent of its shares in the offer but that could rise to 34.5 percent if an over-allotment option is exercised.
The sale will raise between 673 million and 774 million euros for selling shareholder UniCredit, depending on whether the greenshoe option is exercised, for a capital gain of up to 410 million euros.
Asset manager Anima raised around 690 million euros in April when it listed around 55 percent of its share capital.
The IPO will boost UniCredit's Common Equity Tier 1, the measure of a bank's financial strength, by up to 16 basis points, the bank said.
Joint Global Coordinators in the IPO are UBS and UniCredit which also acted as Joint Bookrunners with Mediobanca.