Shares of Bank of America (BAC) were up close to 3 percent on Tuesday, marking continued progress in the Bank’s major bull run dating back to mid-December. Now, the bank, which was flirting with the dangerously volatile share price of $5 a share late last year is now close to touching $10 a share. On the whole, the stock has gained over 96 percent since December 20th and given naysayers reason for real pause.

The jump in shares is likely more welcome news for one individual more than others. Berkshire Hathaway’s (BRK.A) Warren Buffett made a very public investment of $5 billion in the bank’s stock while it was floundering last year, an investment that has clearly more than paid off at this point. But is Bank of America really back? Has the company finally shed the restraints of the financial crisis and returned to business as usual? Or is it unreasonable to be this optimistic about a bank many saw as a toxic stock just months earlier?

Bank of America is Back

The rise of Bank of America could be viewed as a part of an overall rally for the financial sector as a whole. Most of the major financial firms and banks took serious hits after the financial crisis and almost all are still down significantly from levels five years earlier. Of the five major banks, Goldman Sachs (GS), Morgan Stanley (MS), JP Morgan (JPM), Citigroup (C), and Bank of America, only JP Morgan is even close to recovering the levels it reached in 2007 while all the others are off at least 40 percent. Last year proved to add gasoline to that fire, with the debt crisis in Europe reeking further havoc on balance sheets. Throw in a major flap over proposed fees for debit cards, and 2011 had many analysts questioning what the future of the sector really was.

Now, though, the entire financial sector appears to be in recovery. The situation in Europe is far from entirely resolved, but the deal of Greek debt reaches earlier this year appears to have bolstered investor confidence at least in the short term. Many other analysts have long been insisting that major banks remain seriously undervalued and, in time, will recover enough of their pre-financial crisis value to make them a solid investment (a strategy that Warren Buffett appears to at least partially endorse). And Bank of America, which fell the furthest, appears poised to recover the most. With European debt no longer appearing as toxic as it once was, Bank of America could be poised to make a solid recovery. What’s more, passing the most recent round of stress tests from the fed is no minor win for Bank of America. Long viewed as a prime candidate for another embarrassing exposure of a shaky balance sheet, Bank of America passed the stress tests and silenced many critics.

Is Bank of America Still in Trouble?

Of course, there’s still ample reason to believe that the recent bull run by Bank of America doesn’t represent the sort of recovery it’s being billed as by some. Bank of America was an extremely troubled stock six months ago, and it’s hard to see how all of those problems have simply disappeared. It would be easy to see much of the current bull run as an overreaction to a lack of bad news. Bank of America didn’t fail its stress test, Greece (and the Euro) didn’t collapse, the American economy didn’t stall early in 2012.

There’s also still concerns about how long these trends will continue. While Europe appears to have at least delayed any disaster, concerns about the long term stability of nation’s like Spain and Italy have to be lingering. If the continent undergoes a widespread recession like many are anticipating, there’s always a chance that even the aggressive austerity measures already implemented won’t be enough. If European debt starts to become troubled once again, it could negatively impact Bank of America, which has exposure to several European countries.

Bank of America’s balance sheet also might be an issue again in the future. There are plenty of examples of critics of the Fed’s stress tests who believe that they failed to adequately test the banks. Bank of America, which didn’t submit plans to raise its $0.01 per share dividend, passed, but many think that’s not a clear sign that its troubles are over. There’s also the issue of the American economy. Bank of America would most likely benefit greatly from continued recovery, and the stock market also seems to be in the same boat, but with rising gas prices and continued questions about the strength of the recovery, the continued bounce back seems anything but certain.

Only time will tell if Bank of America has really done enough to address the issues that dogged it throughout 2011, but investors should take a careful look at this stock and weigh both options.