Editor's note: A previous version of this article erroneously referred to New York Community Bancorp as "New York Bancorp." The Motley Fool regrets the error.

Allow me to start by allaying your concerns: No, you're not crazy for thinking about investing in a bank.

You need a good head on your shoulders to be a good banker, but banking isn't rocket science. In fact, the more banking does look like rocket science, the more trouble a bank is likely to get into. Instead, good banking is borrowing at one rate, lending out at a higher rate, and making sure that your borrowers are likely enough to pay you back that you keep a profit in the middle.

Rinse, repeat, and you've got yourself a nice little banking business.

The banks that are constantly in the headlines -- JPMorgan Chase and its multibillion-dollar trading losses, or Bank of America (NYSE: BAC) and its seemingly unending legal woes -- live in a very different world than smaller regional banks, like New York Community Bancorp (NYSE: NYB). The banks like NYB are much closer to that picture of what good banking should be.

So why buy NYB in particular? Here are three top reasons.

1. That's a mighty fine dividend
Prior to the financial crisis, the banking sector was one of the go-to spots for dividend investors. In the wake of the disaster, it's a very different picture for many banks. Bank of America pays a meager 0.5%, Regions Financial's (NYSE: RF) yield is just 0.6%, and Citigroup's (NYSE: C) yield currently pays a laughable 0.1%. Some dividends have come back. For instance, JPMorgan pays a respectable 3.3%, and Wells Fargo (NYSE: WFC) yields 2.7%.

And New York Community Bancorp? How about 8.1%!

Typically, yields like that are reserved for companies that are on hard times and are widely expected to be unable to continue paying the dividend at the current level. However, NYB has paid out $1 in annual dividends per share since 2005. It maintained that payout through the recession. It even maintained that payout -- remember, we're talking per-share here -- after issuing 69 million new shares in 2009, following its Federal Deposit Insurance Corp (FDIC)-assisted takeover of AmTrust Bank.

There is a tradeoff here, though. A primary source of bank growth is retaining earnings, and adding that to its lending capacity. Because NYB pays out substantially all of its earnings through dividends, investors aren't going to see a whole lot of growth, unless the bank raises money through share sales -- which need to be well timed to avoid destroying shareholder value.

But if you like the idea of watching bank earnings go from the bottom line to your bank account, then NYB's dividend may look like a big target to you.

2. Hidden asset quality
I often use a powerful data tool -- S&P's Capital IQ -- for researching stocks. It's a great tool but, like any tool, it needs to be used carefully. NYB is a perfect case in point.

When I pull up balance sheet ratios for NYB on Capital IQ, it shows the bank with a recent nonperforming loans-to-total loans ratio of 2.1%. That's not terrible -- for comparison, PNC Financial was recently at 2%, while Regions Financial was up at 3.1%. But it's a misleading picture of NYB's balance sheet.

In the wake of the recession and financial crisis, NYB has made acquisitions with the backing of the FDIC -- notably, AmTrust, as mentioned above. In those arrangements, the FDIC absorbs 80% of the losses for covered loans to a certain point, and 95% of the losses beyond that point. That means that total nonperforming loans aren't a meaningful metric in terms of assessing potential loan losses that NYB will face.

When we actually dig into NYB's filings, the bank clearly separates its non-covered loans -- that is, the loans that it faces full losses on -- and covered loans. Considering just non-covered loans, NYB's NPL-to-total loans ratio is more than half, at 1.01%. It doesn't just stack up well versus competition, it clearly outperforms. In fact, in a recent presentation to investors, NYB illustrated that it's significantly outperformed the SNL U.S. Bank and Thrift Index in terms of credit quality in both this credit cycle (2008 to 2012), and the previous credit cycle (1989 to 1993).

This is a big potential boon to some savvy researchers, because many investors rely on an automated screening process to identify promising investments. For that latter group, a screen that looks for particularly high-quality balance sheets -- which would likely look at NPL ratios -- would likely skip over NYB. This is how opportunity is created.

3. Simple business model
Whereas it seems like understanding the balance sheet of one of the big banks, like B of A or JPMorgan, would take a PhD in financial engineering, NYB's business model is exceedingly simple.

The bulk of NYB's business is using deposits and wholesale borrowing to make loans on apartment buildings in New York City. The loans are on low-risk, below-market-rent properties, and are generally just 10-year loans. The bank also makes loans on income-producing commercial properties, like office buildings and retail centers -- also mostly in New York City.

For the most part, it's really that simple: classic banking done well.

Put all of this together, and I think there's a very compelling case for buying NYB's stock, and I've backed up my view by rating the stock an "outperform" in my CAPS portfolio.

More dividends
For obvious reasons, many investors will be attracted to NYB because of its fat dividend. And I'll give you a spoiler: NYB was chosen as one of nine stocks in The Motley Fool's special report, "Secure Your Future With 9 Rock-Solid Dividend Stocks." To get acquainted with the other eight, click here and download a free copy.