John Paulson and Sallie Krawcheck are staking a lot on the revival of Bank of America's fortunes. The hedge fund supremo is now the beleaguered institution's fourth-largest shareholder after buying 168 million shares last quarter, according to a regulatory filing. Meanwhile Citigroup's former wealth management and finance chief has been brought in to run asset management and B of A's Merrill Lynch brokerage — and she snapped up $1 million-worth of shares.

These might seem like a gamble. After all, B of A is hardly out of the woods. Its core operations are likely to continue losing money for the rest of the year and the bank will probably need to add to loan loss reserves in 2010. Takeovers struck both at the height of bull market and in the depths of the crisis either used up precious capital or revealed poor risk management — or both — and left the bank in need of $45 billion of support from the U.S. taxpayer. And the shenanigans surrounding year-end losses and bonuses at Merrill cost chief Ken Lewis the chairman's role and his reputation.

But B of A has more going for it than Citi, the other government-bailout heavyweight. B of A, for example, never suffered from the sclerotic sprawl that afflicted Citi, leaving the New York megabank struggling to hit earnings estimates and often failing to eke out positive operating leverage even during the boom.

The question is, how much is B of A worth? Its stock has jumped almost seven-fold since its low in February. Paulson has already made at least a 22% return on his investment — and would have raked in 150% had he bought all the shares at the start of April. But shares currently trade at just 75% of book value. Assume, with more losses to come, that's where the book value will settle.

B of A probably doesn't deserve to trade at rival U.S. Bancorp's two times book value, especially since it now owns a large investment bank. And hitting the 1.85 multiple it enjoyed back in 2006 looks a stretch. But 1.5 times book sounds reasonable for a post-crisis B of A, meaning its stock could rise another 50%.

Of course, that requires that the U.S. economy recover in the next year and not slip into another recession, causing further losses. But Paulson's smarts may be enough for him to jump out in time. And any more pain for Lewis could be Krawcheck's gain. For both, it looks like a gamble worth taking.

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