UPDATE 1-Italy's bank bailout fund set to own 90 pct of Pop Vicenza-sources

* Take-up in Pop Vicenza cash call around 10 pct -sources

* Fund rises 4.25 billion euros, at lower end of target (Recasts with sources on Pop Vicenza, data on bad loans)

MILAN, April 29 (Reuters) - Italy’s new bailout fund is set to own around 90 percent of Popolare di Vicenza after investors bought a fraction of the mid-tier bank’s 1.5 billion euro ($1.7 billion) cash call, three sources close to the matter said.

Popolare di Vicenza, which is due to announce the outcome of the public share offer later on Friday, declined to comment.

The Atlante fund - Atlas in English - was hastily set up this month by mostly private domestic financial institutions to bail out weaker Italian lenders and avert a wider crisis in the euro zone’s fourth-largest bank sector.

Earlier on Friday it said it had raised 4.25 billion euros, at the lower end of a 4-6 billion euro range it had initially targeted, from 67 mostly domestic financial institutions.

If the low take-up for the Popolare di Vicenza share sale is confirmed, the fund risks seeing nearly a third of its fire-power invested in a single bank.

Alessandro Penati, chairman of the Quaestio investment firm which manages the fund, said Atlante would aim to sell any stake it may get in Vicenza after 18 months.

It was not immediately clear whether Popolare di Vicenza, which must raise the cash to comply with capital requirements set by the European Central Bank (ECB), would have enough free float to list on the market next week as planned.

The minimum free float required to list is 25 percent of the share capital, but the Milan bourse can make exceptions.

Penati said the Atlas fund was set up as a backstop investor to avoid banks like Popolare di Vicenza being wound down and triggering a crisis for the whole industry.

The fund targets an annual return of around 6 percent and will spend 70 percent of its cash to invest in cash calls at ailing banks, he said.

He added that the rest would be used to buy junior tranches of bad debt from banks at a higher price than that offered by funds specialised in distressed securities, but not at book value - meaning banks would have to book further writedowns.

Traders said that contributed to pushing bank share prices down on Friday, with UniCredit dropping 5 percent.

Italian banks are saddled with 360 billion euros of gross problem loans but are reluctant to sell them at a discount because that would erode their capital.

Presentation slides for Atlante indicated a buying price at 33.8 percent of the loans’ gross value compared with around 21 percent usually offered by private equity funds. However, this partly depends on the success of planned government measures to shorten lengthy loan recovery procedures.

Analysts say Atlante should have enough money to buy between 20 billion and 35 billion euros of gross non-performing loans.

$1 = 0.8786 euros Additional reporting by Paola Arosio; Writing by Silvia Aloisi; Editing by Alexander Smith