AIG (NYSE:AIG) needs no introduction. It's the massive insurer that played with fire prior to the financial crisis and got burned so badly that Uncle Sam had to come to the rescue with a gargantuan bailout.

At this point, that's where it begins and ends for many people when it comes to AIG. But a lot has changed for the insurer over the past five years, and CEO Robert Benmosche has done a great job putting the company back on the right track. 

So with the stock trading at what appears to be a bargain valuation, should investors be jumping at AIG? 

Back on the right path
As of the end of 2008, AIG was exposed to $1.8 trillion in notional-value derivatives that were putting the giant in mortal danger and completely freaking out everyone around it. As of the middle of 2012, that exposure had been reduced more than 90%. What's left has been carefully managed to reduce or eliminate the potential for disastrous losses going forward.

The stake that Uncle Sam has in AIG is also fast disappearing. In the fall of 2012, AIG happily announced that after a 637 million share stock offering, the U.S. Treasury's stake in the company had been reduced to 16% from 53.4%. Further, the sale resulted in the Treasury and the Federal Reserve Bank of New York going into the black to the tune of $15 billion on their combined investment in AIG. And that tally does not include the remaining stake that the Treasury has in the company.

Meanwhile, the businesses that are at the core of AIG are powering ahead. Chartis (property & casualty insurance) and SunAmerica (life insurance) are both producing considerable profits. ILFC, the company's aircraft leasing arm that it's hoping to spin off, has faced challenges from the economy and has been forced to take writedowns on its fleet, but it remains a market leader. Likewise, the economy hasn't been kind to AIG's mortgage guarantee business, but even that appears to be limping back to life. All told, on an operating basis, AIG is back to being significantly profitable.

Put this all together, and what we're left with is a still much-hated company that has drastically moved away from what drew the ire in the first place. With AIG's stock trading at just 0.6 times its tangible book value, there could be the potential for significant gains ahead.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.