When you're in the exam room, you never want passing doctors to stop and blurt out, "Ooh, I gotta see this!"

Unfortunately, if doctors were stock analysts, the banking sector would have been the subject of a lot of medical rubbernecking over the past few years.

But this patient isn't terminal.

For good or ill, banking is the circulatory system of capitalism. From individuals using credit cards and financing houses to entrepreneurs getting start-up capital to municipalities funding infrastructure projects to Fortune 500 companies ensuring liquidity and easing international expansion, banks are everywhere.

The largest banks aren't just too big to fail. They're too essential to fail.

That's a major reason I think the beaten-down banking sector as a whole will outpace the Dow (INDEX: ^DJI) and S&P 500 over the next few years. Quite simply, we will continue to need their services and there isn't really a meaningful alternative. In fact, I see the distinct possibility of a double (or even a triple) for at least one big banking stock.

From the ashes...
If the banking sector as a whole has been treated like a leper colony, no big bank has been more maligned than Bank of America (NYSE: BAC). Part of that is deserved. There are reasons Bank of America is being priced by the market as the worst big bank in America. The biggest reason? The botched Frankenstein-ing it did during the financial crisis, adding both Countrywide and Merrill Lynch.

As the largest mortgage lender in the nation, Countrywide brought with it around $200 billion worth of especially toxic assets as well as a bevy of mortgage-related litigation that is still rocking B of A's financials more than four years after the purchase. 

In the fall of 2009, at a time when more savvy players like Wells Fargo (NYSE: WFC) (with Wachovia), JPMorgan Chase (NYSE: JPM) (with Washington Mutual), and Barclays (with Lehman Brothers) masterfully picked over carcasses, Bank of America wildly overpaid for Merrill Lynch. The $50 billion stock deal (at the time of the announcement) was a 70% premium to where Merrill shares were trading and represents about half of Bank of America's current market value.

...there could be a phoenix
There is a lot not to like about Bank of America, but part of its bad rep has been unfair. As the perceived weakest of the herd, B of A makes an easy target for Occupy Wall Streeters, folks angry about foreclosures or $5 debit card fee plans, and the salacious press. Because of the outsized focus on Bank of America leading to a beaten-down share price, I believe there's that much more upside if things go better for the housing market and economy in general and Bank of America's operations in particular.

I did a good job railing against Bank of America's terrible financial crisis acquisitions, but we can't blame current management for past management's mistakes. Similar to Vikram Pandit at Citigroup (NYSE: C), Bank of America CEO Brian Moynihan has been working to get smaller by jettisoning non-core assets. This also has the effect of shoring up capital. Moynihan's also working to meaningfully lower costs via Project New BAC, which will be ongoing till the end of 2014. Once we differentiate between the actions of Moynihan and the actions of his predecessor (Ken Lewis), I like what I'm seeing.

A double from here?
Many will look at Bank of America's stock price, which has nearly doubled from its lows in December, and say optimism is already priced in. I don't think that's true. It's been up on good economic news and on passing its recent stress test, but it's not hard to envision a double (or even a triple) from here.

This is how I'm thinking about it. A double would put B of A at a market capitalization of about $200 billion. Assuming the market isn't ready to pay up for a bank of B of A's ilk, that would mean $20 billion in earnings to justify a P/E ratio of 10.

B of A has fought to eke out a small profit over the past 12 months, but it's been dragged down by roughly $20 billion in losses from its mortgage operations. Think of this largely as the "sins-of-its-past" bucket, chock-full of foreclosure, litigation, and impairment expenses. Once Bank of America can get this area back to treading water, you've justified a double. And if you're looking for a catalyst beyond earnings, eventually raising dividends past its current penny a share per quarter is your huckleberry.

Taking a different angle, if Bank of America can get back to producing a slightly less than mediocre return on equity of 9%, it'll produce that $20 billion to justify a double. How reasonable is that? It beat 9% every year from 1992 to 2007.

And if we raise that P/E ratio from 10 to 15, that double becomes a triple.

Triple or nothing?
Bank of America has gotten a lot of headlines as it's flirted with $10 a share, but as I've explained, I don't think $20 or even $30 a share is out of the question as it turns around.

Just don't confuse Bank of America for a sure thing. Real risks remain in this turnaround. For a bank that's generating twice Bank of America's profits despite being more than 100 times smaller(!), check out the free report I wrote: "The Stocks Only the Smartest Investors Are Buying." Just click here to access it.