Citadel LLC, a hedge-fund giant still clawing its way back from losses during the 2008-09 financial crisis, pushed E-Trade Financial Corp. to explore a possible sale of the company.

In a letter addressed to E-Trade's chief executive that was filed with regulators, Citadel said that managers of the online brokerage had "squandered" a "phenomenal franchise" and that the board had "continually failed to act in the best interest" of E-Trade shareholders.

Since late 2007, Citadel has been the biggest of those shareholders. Citadel holds 9.8% of the company's common stock, which was worth about $400 million Wednesday after the shares jumped nearly 14% on the news of the filing.

E-Trade CEO and Interim Chairman Steven Freiberg said the online brokerage is "carefully considering" the letter. During a conference call with analysts, Mr. Freiberg said E-Trade was "surprised and disappointed by the letter" but added that "maximizing value for shareholders has been and will always be our primary focus."

Citadel's harsh letter represents a stark reversal from late 2007, when the Chicago hedge fund, in a closely watched move, stepped in to rescue the then-troubled brokerage firm, betting that the economic downturn then unfolding would be short-lived. Citadel plowed $2.55 billion into the firm, including buying a portfolio of souring home mortgages and other loans.

Citadel expected its investment to help shore up the company and stop a wave of withdrawals by E-Trade's customers of billions of dollars of cash and other assets from the company's bank and brokerage business.

The downturn proved much more severe than Citadel anticipated, with global markets almost collapsing the next year. And according to its letter filed with the Securities and Exchange Commission, E-Trade's board failed to address the company's "still weak capital position."

Citadel's aggressive tack with E-Trade's management follows tough times the hedge fund itself has faced the past several years.

It managed nearly $20 billion before the 2008-09 financial crisis, but losses from a range of investments helped shrink assets by $8 billion. Citadel lost money as holdings such as high-yield debt and convertible bonds tumbled in value and became hard to sell into dysfunctional markets.

The firm's performance has rebounded in recent years, and its main funds are up about 10.5% this year, better than most peers, and are close to earning back investors' losses from the crisis, investors said. The firm now manages about $11 billion.

In 2007, the E-Trade investment was the highest-profile move in Citadel's then 17-year history, representing about 2.5% of its overall investment portfolio. Besides the stock it acquired, it injected $1.75 billion into E-Trade, in exchange for 10-year E-Trade notes.

Despite a drop of more than 70% in E-Trade's stock price since Nov. 29, 2007, when the deal was announced, Citadel made money on its investment in the company, says a person familiar with the matter. Citadel exchanged the bonds it bought for convertible bonds, which were later converted to common stock at a favorable rate.

As Citadel incurred other losses in its portfolio, the E-Trade stake accounted for a greater proportion of its assets, while it faced limits on what it could do with the position. The position itself also was volatile.

In the fall of 2009, Citadel CEO Kenneth Griffin told investors the hedge fund was dialing back risk, and they shouldn't expect more big bets like the E-Trade one. Mr. Griffin joined E-Trade's board in 2009 and remains on it. This April, Citadel sold half of its stake in E-Trade, following an earlier share sale.

In its letter to E-Trade, Citadel's Chief Legal Officer Adam Cooper wrote that the online brokerage has consistently received "high marks for its trading platform, customer service and usability, and has benefited from strong customer loyalty. Yet, despite a powerful brand and excellent products, under the stewardship of E-Trade's board, the company has lost money every year since 2006."

He noted that the steep stock decline in recent years has destroyed billions of dollars in shareholder value.

Separately Wednesday, E-Trade posted weaker second-quarter trading volume as its daily average revenue trades — a measure of trading activity — fell 13% from a year ago. Rivals also have been posting weaker volume. E-Trade's profit rose 34% as the company set aside less money to cover bad loans.

Analysts have cited TD Ameritrade Holding Corp. as the most likely suitor for E-Trade. A TD Ameritrade spokeswoman said the company wouldn't comment on rumors or speculation.

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