I don't write a headline like the one on this article lightly. Sure, a lot of stocks could double if you give them enough time -- a 100% gain over five years is 15% per year, while over 20 years it's just 3.5% per year. But some recent catalysts have given a handful of stocks the potential to double much quicker than that.

Before I name names, let me share two events this week that gave me the conviction that I have in these potential gains.

A fellow named Warren
Unless you're living under a rock, like the fellas in the GEICO commercial, you've likely already heard that Berkshire Hathaway (NYSE: BRK-A) (NYSE: BRK-B) announced that -- price permitting -- it will start buying back shares. Share buyback announcements happen all the time, but not at Berkshire. It's never bought back its own shares before.

The company's press release read:

Our Board of Directors has authorized Berkshire Hathaway to repurchase Class A and Class B shares of Berkshire at prices no higher than a 10% premium over the then-current book value of the shares. In the opinion of our Board and management, the underlying businesses of Berkshire are worth considerably more than this amount, though any such estimate is necessarily imprecise. If we are correct in our opinion, repurchases will enhance the per-share intrinsic value of Berkshire shares, benefiting shareholders who retain their interest.

That reads pretty clearly: Warren Buffett and the rest of the Berkshire board think that shares are cheap. What, then, would be full value for Berkshire shares? I don't know exactly, but I can tell you what Buffett doesn't think full value is -- 10% above book value.

Still with me? What I'm getting at is that Buffett isn't going to have Berkshire buy back shares unless the valuation is very attractive. Since he's willing to be a buyer at 1.1 times book value, we have to assume that full value is well above 1.1 times book value.

Something happened in Pennsylvania
The Berkshire buyback announcement was interesting, but if it hadn't been followed by another very significant event yesterday, I might have simply left it at "Berkshire stock is a really attractive value right now."

The event that I'm referring to is this: Pennsylvania property and casualty insurer Harleysville Group agreed to be bought out by privately held insurance giant Nationwide. The price? Nationwide is coughing up $60 per share, which was not only a 90% premium to Harleysville's previous closing price, but more than double the company's book value per share of $28.81.

I'm not going to presume that private companies don't do stupid things, but without the pressure of Wall Street, the growth imperative, and the quarterly earnings charade, I generally assume that private companies are better able to manage with the big picture in mind. And yet Nationwide thought it smart to pay more than two times book value for Harleysville.

Add it up
One week, two very significant events that suggest the market is not properly valuing property and casualty insurers (remember that Berkshire's primary business is insurance). Not only that, they're also signals that if the market doesn't start doing a better job, companies -- whether through share buybacks or acquisitions -- will take advantage of Mr. Market's short-sightedness.

You've read this far based on my headline promise to name five companies that could benefit from this dynamic and see their stocks double. I don't want to disappoint, so without further ado.

Company

Market Capitalization

Price-to-Book Value

W.R. Berkley (NYSE: WRB)

$4.1 billion

1.04

Markel (NYSE: MKL)

$3.5 billion

1.05

White Mountains Insurance (NYSE: WTM)

$3.2 billion

0.87

Alleghany (NYSE: Y)

$2.6 billion

0.83

OneBeacon (NYSE: OB)

$1.3 billion

1.06

Source: Capital IQ, a Standard & Poor's company.

Let me level with you. I'm no soothsayer. I don't know whether the market will take these cues and boost the stocks above. And while it's possible that there are takeover targets among these companies, at a price-to-book value of two, each of these companies would be a significantly larger buyout than Harleysville.

But this is more than a list of names that have price-to-book values around one or less. These also happen to be some of my favorite insurance companies (along with Berkshire, of course) that boast some of the best people the industry has to offer.

Earlier this year, fellow Fool Mike Olsen sunk The Motley Fool's very real cash into W.R. Berkley, and described founder and CEO Bill Berkley as an "inveterately individualistic" chap who "has built a culture that encourages non-consensus thinking. In common terms, that means they're willing to roll up their sleeves, and write insurance policies on seemingly weird, idiosyncratic risks, the type others shun."

If you're not familiar with Markel's investment ace, go ahead and type "Tom Gayner" into your favorite search engine.

What's next? Rather than throw this idea out there and never return to it again, I'm going to put my score on Motley Fool CAPS on the line and give a thumbs-up to all five of the stocks above. While it's not a lock that they're going to make a lickity-split double, I think all of them make fine investments at these valuation levels.

Want to start keeping an eye on this group yourself? Add them to your Foolish watchlist (or create a new watchlist for free).