I've liked Bermuda-based insurance and reinsurance company Arch Capital (NASDAQ:ACGL) for quite some time now, and with its second-quarter results on the books, I see no reason to change that opinion. From where this Fool sits, Arch Capital management seems to have an above-average ability not only to select and price risk, but also to maintain the discipline and flexibility to allocate its finite capital resources to the best opportunities.

Operating income grew more than 50% this quarter, and the company's quarterly results annualize to a very attractive return on equity in excess of 26%. Moreover, like many other good operators this quarter, Arch exceeded expectations when it came to writing more business. Taking advantage of a strong pricing environment in some lines, Arch Capital saw gross premiums up 21% and net written premiums up 10%. As might be expected, given what we've heard from the likes of RenaissanceRe (NYSE:RNR) and Everest Re (NYSE:RE) before them, premium growth was strongest in the reinsurance business.

Other performance metrics at Arch also looked rather good. The combined ratio improved for the company as a whole, with particular improvement in the reinsurance segment (the insurance business worsened a bit), and the overall loss ratio was down both before and after taking reserve developments into account. It's also worth noting that investment income was quite strong this period, but that's hardly exceptional for a reinsurance company right now.

As it sits now, Arch Capital looks expensive relative to many other players in the reinsurance sector, including RenRe and Endurance (NYSE:ENH). Of course, you can have a lively debate as to what sort of industry premium Arch Capital deserves -- RenRe has an excellent long-term record, but Arch has done even better lately. It's also probably true that any major storms or natural disasters will send its stock down with the rest of the group, until actual loss estimates come in and investors can discern who did better or worse than the rest of the industry.

This is one of the few sectors that has done pretty well this summer, at least on a relative basis, and I wouldn't be in a hurry to take profits. Arch Capital isn't as cheap as I might like, but you rarely find quality trading too far below its fair value.

For more Foolish thoughts on the insurance sector:

Endurance is a recommendation of Motley Fool Inside Value , where bargain hunters go to find the market's best undervalued stocks. Want in? You can try the newsletter service free for 30 days.

Fool contributor Stephen Simpson has no financial interest in any stocks mentioned (that means he's neither long nor short the shares).