E*Trade Financial's ( ETFC) writedown woes that sent the stock spiraling Monday have renewed analyst speculation about the possibility the online broker could sell itself.

E*Trade shares were rebounding almost 14% on Tuesday, after dropping nearly 60% on a string of bad news Monday and late Friday, including a Citigroup downgrade and accompanying note that said the company's bank was in danger of failing and the company's warning that it expected writedowns to its $3 billion asset-backed securities portfolio.

While bargain hunters were returning to the stock Tuesday, analysts were focused on repercussions for the business -- including the possibility of a sale.

"We expect that the company is aggressively pursuing various alternatives to deal with the bank deterioration," Richard Repetto, an analyst at Sandler O'Neill & Partners, wrote in a note Monday. He downgraded the stock to hold from buy.

"CEO Mitch Caplan will pursue what's best for shareholders and would step aside/give up control of the company if an appropriate transaction was presented," Repetto added.

One possible buyer is rival TD Ameritrade ( AMTD); market chatter this spring indicated it was in discussions with E*Trade over a possible merger. TD Ameritrade has been pressured by two big activist hedge funds to merge with an industry peer -- namely E*Trade or Charles Schwab ( SCHW).

Even without a sale, TD Ameritrade, Schwab and Fidelity could benefit from E*Trade's troubles by picking up retail brokerage clients. A spokeswoman for TD Ameritrade did not return requests for comment.

E*Trade said in a statement responding to the Citi downgrade that it is "well capitalized" and "capable of adapting to shifting market trends."

A spokeswoman did not respond to requests seeking comment about the possibility of a sale or other strategic options.

David Trone, an analyst at Fox-Pitt Kelton, says despite E*Trade's problems, there would be buyers of the company and at a premium to its current price of around $4, "even assuming fire-sale impairment," he wrote in a note Monday, when E*Trade's stock plunged 59% to $3.55 as a result of the bad news.

But Citi analyst Prashant Bhatia, who set off the decline after suggesting in his note that E*Trade's bank could fail, says neither consolidation nor a cash infusion would create "any meaningful value" for the company's shareholders.

"In its current form, burdened with a significant and deteriorating $42 billion mortgage portfolio, this franchise is an extremely unattractive acquisition candidate," Bhatia wrote in the same note.

Banking issues aside, E*Trade does have good momentum in its retail brokerage operations. The company's daily average retail trades rose 23% in October from a month earlier to 227,344 trades. It had a total of $227 billion in retail client assets as of the end of October.

Still, analysts worry that the positive retail brokerage momentum may not be sustainable as E*Trade struggles with its mortgage and other asset-backed securities and other negative news flow coming from the company.

The online broker on late Friday disclosed it plans to take further writedowns on its $3 billion securities portfolio. It also said that Dennis Webb, E*Trade's president of its capital markets unit, was leaving the company.

E*Trade is also facing a Securities and Exchange Commission investigation into its loan and securities portfolios, according to its quarterly filing on Friday.

E*Trade has seen declines in the fair value of asset-backed collateralized debt obligations, or CDOs, and second-lien, or home equity-backed, securities as a result of recent rating agency downgrades of asset-backed securities, it said. The securities portfolio held approximately $450 million in asset-backed CDOs and second-lien securities as of the end of the third quarter.

The company, which provides online banking, brokerage and lending to retail and institutional customers, joined the likes of Countrywide Financial ( CFC), Washington Mutual ( WM) and other smaller lenders hit hard by the housing downturn and mortgage deterioration, particularly as the secondary market for mortgages ground to a halt. The stock is down more than 80% this year.

E*Trade said in September that it was restructuring the business to eliminate its wholesale mortgage operations and streamlining its direct mortgage lending business to focus on the retail franchise, among other things.

It also said at the time that it was shifting its balance sheet to focus on retail assets and liabilities.

Still, E*Trade reported a third-quarter loss of $58 million, or 14 cents a share, last month. It ended up setting aside an extra $187 million for loans gone bad and taking $197 million in securities writedowns. E*Trade said that it expected to take the writedowns both this year and next year.

Aside from a sale, other options for E*Trade include a sale of certain bank assets or some sort of financial investment or capital infusion, much like Bank of America's ( BAC) $2 billion investment into troubled mortgage lender Countrywide through the purchase of its preferred stock in August, analysts say.

Matt Snowling, an analyst at Friedman, Billings, Ramsey, speculates that the company is exploring the sale of its home equity or second lien portfolio in order to "remove the overhang" on the stock, he says. He also downgraded the stock to market perform from outperform in a note.

"There are two options," says Snowling. "One is always the obvious -- to sell. TD Ameritrade would have to be looking. The ability to pick up these accounts that are highly profitable at a fire sale -- they have to be looking."

But what is a more likely outcome is that the company will look to sell its home equity portfolio at a loss, which would require them "to raise a little bit of capital," according to Snowling.

He suggests that among other potential buyers, private equity firms could be interested in buying the distressed portfolio and acquiring a stake in the brokerage firm at the same time.

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