If you're bullish on insurance giant AIG (NYSE:AIG), there's a good chance that your investment thesis goes something like this: AIG did some very stupid things in the past, but it's getting past those mistakes, and it's now a grossly undervalued company with quality insurance operations. 

That thesis, of course, hinges in a big way on that last part -- that AIG does, indeed, have insurance operations worth investing in.

For the third quarter, AIG's overall profit topped expectations, and results blew away what the company reported last year. But with so much messiness still showing up in AIG's results, it's hard to take away a whole lot that's meaningful from the overall bottom line.

Getting jiggy with P&C
Drilling down then to something that's more notable, AIG's property and casualty insurance operations managed to report a big bump, with profits climbing to $786 million from $492 million a year ago. The year-over-year gain was mostly attributable to investment performance as investment income, and capital gains were up a combined $300 million from 2011.

Underwriting, meanwhile, improved just slightly, with the quarter's underwriting loss improving from $532 million last year to $441 million this year. The combined ratio -- a measure of an insurer's underwriting profitability -- ticked down 105% from 105.9%. Better, but still not where I'd like to see it.

What's easy to like about these results is that they're much better than last year's. It never hurts to be able to say that profits improved 60% year over year. On the other hand, the "improvement" in underwriting isn't particularly encouraging. While the combined ratio moved in the right direction, it did so largely because of lower catastrophe losses, something that -- apart from business mix -- the company doesn't have much control over. The expense ratio, on the other hand, was up versus last year.

On the latter point, AIG chalked up the increase in spending to changes in business mix and investments in people and direct marketing. Presumably, these are things that will pay off over the longer term for the company in the form of better underwriting results, but we'll obviously have to wait to see if the improvements actually materialize.

The bottom line though, is that although profit line for AIG's P&C operations looks much improved this quarter, when it comes to proving that AIG has solid underlying insurance operations, this segment still has plenty of convincing to do.

Sandy cometh
Obviously as we look ahead, AIG's fourth-quarter results are going to look a lot different than the third-quarter numbers thanks to Hurricane Sandy. Though CEO Robert Benmosche has assured investors that Sandy won't be a huge issue for the company's financial strength, there's no doubt that the P&C unit will be absorbing considerable losses this quarter.

That said, AIG investors should be less focused on Sandy -- which is an industrywide, as opposed to an AIG-specific, issue -- and keep their eyes on the real prize in the company's P&C operations: long-term improvement of the overall underwriting results.

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.