There are certainly some bargains to be had in the banking sector, with many companies trading at historically low valuations and growing their operations very rapidly. However, some stocks might appear to be better investments than they actually are.

We asked three of our top financial sector analysts about the bank stocks they would avoid right now. Here is what they had to say.

Jordan Wathen: New York Community Bancorp (NYCB -3.48%) is an excellent bank that is, unfortunately, completely uninvestable due to its capital allocation practices.

The company recently reported a return on average tangible equity of about 15%, well within the range of its historical returns. In banking, especially in a low interest rate environment, such a return is very good.

But despite this compelling return from its core business of deposit gathering and lending, New York Community Bancorp continues to pay out substantially all of its earnings in the form of a dividend. Little to nothing is retained. As such, this bank's capacity to compound your wealth is essentially limited to its current dividend yield of 6.5% per year.

If it instead retained its earnings, the bank could compound shareholder wealth at a clip that more closely resembles its 15% return on tangible equity. That would make it a no-brainer, in my view.

In due time, the dividend might come down and retained earnings could enable this compounding machine to work its magic. The bank is pondering an acquisition that would put it above the $50 billion threshold at which the Federal Reserve begins to scrutinize capital returns to shareholders. But until it crosses that threshold, and proves that it can grow by way of retained earnings, I think it's a bank to pass on.

Jay Jenkins: Over the last year or so, hedge fund megainvestor John Paulson has made huge investments in Puerto Rico. Despite the island's struggling economy, major unemployment, and declining population, Paulson has purchased a hotel and $100 million of municipal debt, and he pledged to invest $1 billion over the next few years. Paulson is a smart guy and a savvy investor -- is this a signal that Puerto Rico really is on the rebound and a worthy turnaround story for investors?

I don't know the answer to that question, but I feel confident that Puerto Rican-based regional bank First BanCorp (FBP -2.38%) is not the answer either way. In fact, of all the banks in the U.S. financial system, this is the one I would avoid at all costs.

In the last decade, First BanCorp's stock has fallen 98.7%. Year to date in 2014, the stock is down more than 20%. It's an ugly story, and based on the company's current fundamentals I don't see a turnaround in sight. Why? Because a ridiculously high level of loans on the bank's books are not being repaid.

As of the end of the second quarter, First BanCorp reported that 6.4% of its total assets were either severely past due or in foreclosure (known as nonperforming assets in industry parlance). Management reported that 6.38% of the bank's loans are unlikely to repay either principal or interest in full, and an additional 2.83% are between 30 and 89 days past due (meaning there is a pipeline of loans heading from bad to worse). For context, Bank of America's nonperforming assets represent just 0.73% of total assets. The key to being a successful lender is collecting your loans, and on that most fundamental objective First BanCorp is failing.

Puerto Rico might end up being a great turnaround story, but I will avoid First BanCorp.

Matt Frankel: I would avoid any bank with significant exposure to Europe or Brazil, especially Banco Santander(SAN -1.85%). The bank has operations in the U.S. and U.K., but conducts most of its business in Spain and Brazil.

On the surface, the bank looks rather cheap, trading for little more than the value of its assets and paying a 9% dividend.

However, this is one case of a stock being cheap for a reason. The weakness in the eurozone (particularly Spain) doesn't look likely to be relieved anytime soon, and Brazil isn't doing any better. Brazil's debt was recently downgraded by Moody's, which lowered its outlook for Brazil's banks to "negative."

The company has sustained its high dividends since most shareholders take their payments in stock rather than cash. However, Banco Santander's earnings haven't covered the dividend amount, and aren't expected to in 2014 or 2015. So every time the company pays a dividend it is effectively diluting the shares.

There absolutely could be some long-term value in Santander if the troubles in Europe and Brazil go away, but who knows when that might happen? While Banco Santander could be a decent value, other banks are just as cheap and have more growth opportunity with less risk.