Contrarian investors should utilize times like this to differentiate between stocks that are dropping for fundamentally sound reasons -- and those stocks that are simply being dragged down because of general market concerns. Sure, there's plenty to worry about -- gigantic federal deficits, sovereign debt problems in Europe, an economic slowdown in China. But let's not forget that in the midst of all of this volatility lies the prospect to grab some great companies at dirt-cheap prices.

Today I ran a screen strictly for bank stocks that have been beaten down in the past nine months and that are trading quite reasonably. In particular, I've sorted them by their attractive price-to-book valuations, and then added their rank status as proposed by our 165,000 strong CAPS investing community. Here are some of the most appealing stocks from that screen:

Company

Price-to-book Ratio

9-Month % Change

CAPS Rating (out of 5)

Allied Irish Banks (NYSE: AIB)

0.10

(52%)

*****

Bank of Ireland (NYSE: IRE)

0.12

(34%)

****

Barclay's (NYSE: BCS)

0.77

(4%)

***

National Bank of Greece (NYSE: NBG)

0.89

(56%)

****

Banco Santander (NYSE: STD)

1.31

(10%)

****

Sources: Capital IQ, a division of Standard & Poor's, and Motley Fool CAPS.

It shouldn't be much of a surprise to see that some of the cheapest stocks around are all European. After Greece's government announced their shockingly high federal deficit, a sovereign debt crisis exploded and rippled throughout the EU. As investors worried about which banks held the most sovereign liabilities on their books, financial institutions saw their share prices battered to a pulp.

However, the recently passed stress tests have calmed some nerves. Both Allied Irish Bank and the Bank of Ireland passed quite easily. It is worth noting, though, that Allied Irish still needs to raise about $9.8 billion in capital by the end of the year; if it can't, there's no doubt that the government will provide funding -- but who really wants to own a stock that may need a financial backstop in the near future?

Barclay's has gotten a double dose of good news as of late. Not only did it pass the stress test with flying colors, but it reportedly has a 13.7% Tier 1 capital ratio -- only a handful of banks could boast better than that. Compared with the ratios of other UK banks like Lloyds Banking Group (NYSE: LYG) and the Royal Bank of Scotland (NYSE: RBS), at 9.2% and 11.2%, respectively, Barclay's clearly reigns supreme. In addition, it just reported quarterly results announcing a 29% increase in profits and a decrease in loan loss provisions.

In the past month, National Bank of Greece has shot up by 33% as investors fears have been somewhat eased. Things have only improved since a month ago -- last Friday, the monitoring external agencies announced that Greece had met its austerity measures, providing it with a fresh round of IMF/EU funding. The days when this bank was a screaming "buy" may be coming to an end quite soon.

Banco Santander is currently my favorite bank, period. Besides their reasonable valuation, conservative nature, and great growth prospects, they pay a solid 4.1% dividend as a nice extra kicker. Check out my recent article on the reasons why I think you should own this bank today.

The foolish bottom line
The recent European stress tests certainly weren't the most stringent tests around -- yet they added some transparency to a murky situation, and, at the very least, separated the good from the terrible. The banks listed above are all trading at dirt-cheap prices, but I wouldn't expect those valuations to hang around forever, so if you've got an appetite for risk, they may be a great place to start.

Jordan DiPietro owns shares of National Bank of Greece. Try any of our Foolish newsletters today, free for 30 days. The Motley Fool has a disclosure policy.