Best Buy: National Bank of Greece, Synovus Financial, or Allied Irish Banks?

In this Motley Fool series, we rank three related stocks on five criteria to determine the best buy.

Today's matchup features a multicultural selection of three beaten-down banks: National Bank of Greece (NYSE: NBG  ) , Synovus Financial (NYSE: SNV  ) , and Allied Irish Banks (NYSE: AIB  ) .

The problems in Greece are well-documented. The Greek debt crisis and concurrent debt crises in many of its eurozone brethren have rocked the euro and European stock prices. Now National Bank of Greece and Allied Irish Banks are two of the 91 large banks that are awaiting the results of the EU-wide bank stress tests.

Synovus Financial is located in the southeastern U.S., with some exposure to the Gulf Coast and a still-outstanding TARP loan. Like fellow regional banks SunTrust (NYSE: STI  ) and Regions Financial (NYSE: RF  ) , Synovus has heavy exposure to commercial loans and is the subject of persistent merger speculation.

All three have significant problems, but all three are trading way off their all-time highs. Using five short-of-scientific-but-carefully chosen criteria, let's determine which of these plays is the best buy.

Round 1: Leverage
For a bank, the balance sheet is paramount. Let's start by seeing which of these banks is the least leveraged using the assets-to-equity ratio. The lower the better from a risk standpoint. Synovus employs the lowest leverage at about 12.5, while AIB is above 16. Rank: (1) Synovus, (2) National Bank of Greece, (3) Allied Irish Banks.

Round 2: Allowance for credit losses/non-performing loans
Next, let's look at how conservatively the banks have reserved for loan losses. Ideally, you'd want this metric above 100%, meaning all foreseen non-performing loans are covered by an allowance. When the metric is under 100%, future income statement hits are likely. All three are well under 100% for the latest period they have information available. AIB is a lowly 17%. Rank: (1) Synovus, (2) National Bank of Greece, (3) Allied Irish Banks.

Round 3: Price/tangible book value
On the high end, Bank of Greece has a price/tangible book value ratio of 1.3. For a high-quality bank, that's pretty cheap. For a bank facing the uncertainties of Bank of Greece, not so much. For comparison, Allied Irish Banks is selling at a yowza-inducing 0.1. Rank: (1) Allied Irish Banks, (2) Synovus, (3) National Bank of Greece.

Round 4: Operations
Are the banks making money? In the case of National Bank of Greece, yes. Both in its latest quarter and on a trailing-12-months basis, it's profitable. The other two are swamped by write-offs. Rank: (1) National Bank of Greece, (2) Synovus, (3) Allied Irish Banks.

Round 5: CAPS rating
Our CAPS community looks favorably on both National Bank of Greece and AIB, giving them four stars (out of five). Synovus gets a more moderate three stars. Rank: (Tie) (1) National Bank of Greece and AIB (3) Synovus.

The summary rankings

Category	National Bank of Greece	Synovus	Allied Irish Banks
Leverage	2	1	3
Allowance/non-performing loans	2	1	3
Price/tangible book value	3	2	1
Operations	1	2	3
CAPS rating	1	3	1
Average finish	1.8	1.8	2.2

There you have it. By the numbers, National Bank of Greece and Synovus tie for best buy honors. I'm not particularly excited about any of these banks, though.

Of the larger U.S. banks, the three that are interesting to me at a price-to-tangible book value under 1.5 are US Bancorp (NYSE: USB  ) , BB&T (NYSE: BBT  ) , and Wells Fargo. They all have fairly conservative reputations and, as big banks go, have balance sheets that are understandable. At ratios of 3.0, 1.9, and 1.9, respectively, they're all on the pricey side, but keep them on your radar.

But what do you think? Declare your winner in the poll below and then share your thoughts in the comments section below the poll.