By Silvia Aloisi and Valentina Za

MILAN (Reuters) - With the ink barely dry on its bailout plan, Italian bank Monte dei Paschi di Siena <BMPS.MI> faces a Herculean task convincing investors to back a third recapitalization in as many years and avert a banking crisis that would send shockwaves across Europe.

To stave off the risk of being wound down, the world's oldest bank hastily unveiled the private sector-backed rescue blueprint late on Friday. It came just hours before the lender emerged as the worst performer in European stress tests that showed its capital would be entirely wiped out in a severe economic downturn.

The plan aims to clean up and bolster the bank's balance sheet once and for all, restoring to health a lender whose frailty threatens the wider Italian banking system, the savings of thousands of retail investors and the increasingly weak political standing of Prime Minister Matteo Renzi.

A financial crisis in the euro zone's third-biggest economy would also risk creating contagion across Europe, a region already reeling from Britain's decision to leave the EU.

The two-pronged rescue scheme hinges on Monte dei Paschi raising 5 billion euros ($5.6 billion) in a cash call to be completed by the end of the year - a tall order for a lender that is worth less than 1 billion on the market and has burned through 8 billion euros from share issues since 2014.

Global investment banks have made a preliminary agreement to underwrite the rights issue by Italy's third biggest bank.

But this is subject to conditions, including that the second prong of the bank's plan is successful: the sale of 9.2 billion euros of bad loans via a mammoth securitization, whose sheer size is unprecedented in Italy.

As the bank's shares - which have lost nearly 80 percent of their value this year - brace for Monday's market reaction to the bailout scheme, senior bankers and fund managers are already questioning the chances of the plan's success.

"Both legs of the plan are potentially fragile," said Filippo Alloatti, credit analyst at asset manager Hermes Investments.

"It will be difficult to complete such a big capital increase given their track record with past cash calls, and the securitization is a monster operation, a puzzle full of moving pieces that need to fall into place. The execution risk is significant."

CRISIS MODE

The global coordinators for the cash call, JPMorgan <JPM.N> and Italian investment bank Mediobanca <MDBI.MI>, have secured a pre-underwriting agreement from another six banks - Santander <SAN.MC>, Goldman Sachs <GS.N>, Citi <C.N>, Credit Suisse <CSGN.S>, Deutsche Bank <DBKGn.DE> and Bank of America <BAC.N>.

But at least three banks - Intesa Sanpaolo <ISP.MI>, UniCredit <CRDI.MI> and Morgan Stanley <MS.N> - opted out, highlighting doubts among investment bankers over whether Monte dei Paschi can muster enough investor support for its plan.

Also, the pre-underwriting is not a final commitment by the banks involved to mop up any unsold shares in the rights issue.

Monte dei Paschi has been in crisis mode for years due to a disastrous acquisition of a regional Italian lender on the eve of the financial crisis, accumulated losses and a fraud scandal.

Analysts at broker Equita said in a note it would be "almost impossible" for the lender to raise all the required cash in current choppy markets.

Italian bank shares have tanked this year as the industry is weighed down by 360 billion euros in problematic loans, more than a third of the euro zone's total. Italy's biggest bank by assets, UniCredit, is also expected to soon tap the market in a multi-billion euro rights issue that could lure investors away from Monte dei Paschi's own capital raising.

And market sentiment towards Italy could sour further if a constitutional referendum in the autumn, on which Renzi has wagered his job, does not go the prime minister's way.

Monte dei Paschi's management said on Friday it would also look at other capital-boosting measures, which bankers say could include the conversion of subordinated bonds into shares, to reduce the size of its cash call.

EXPOSURE

The banks' preliminary commitment to underwrite the capital increase is in any case subject to the Tuscan lender moving the worst of its bad loans off its balance sheet and into a special vehicle which will have to sell them.

The loans will be securitized, with a senior tranche of 6 billion euros benefiting from an Italian government guarantee, the 1.6 billion euro mezzanine tranche being bought by Atlante, a private-sector bank-rescue fund, and the riskiest or junior portion left with Monte dei Paschi shareholders.

But it is unclear how much of the senior tranche will fetch the investment grade required for the government guarantee to kick in. Sources close to the deal said the process could take a year as a due diligence of the underlying loans needs to be completed for rating agencies to gauge their worthiness against an uncertain economic backdrop for Europe post-Brexit.

JPMorgan has taken on additional exposure to the deal by committing to grant a syndicated bridge loan of around 6 billion euros to finance the special vehicle and give it breathing space to engineer the securitization of the loans.

JPMorgan did not immediately respond to requests for comment.

"It will be challenging to place the senior tranche as only part of it will potentially be eligible and assisted by GACSs (government guarantees). Part of the 6 billion will not be investment grade and it will be difficult to place," said LC Macro Chief Economist Lorenzo Codogno, a former chief economist at the Italian treasury.

Meanwhile, the Atlante fund is scrambling to beef up its coffers by around 2 billion euros with contributions from the post office, private pension funds and other institutions.

Despite the daunting obstacles, analysts say that if the rescue is successful, it could be replicated to help other Italian banks offload their bad loans and restore confidence in the sector.

"Italy is on a good course to solve its banking issues. However, leaving aside some near-term re-pricing of risk, this is not yet a turning point," said Codogno.

($1 = 0.8944 euros)

(Additional reporting by Pamela Barbaglia in London; Editing by Pravin Char)