Why do banks sometimes take on so much risk? Risks like giving massive loans to borrowers without verifying income, or sometimes without even requiring any payments for up to two years

Sometimes the reason is as simple as dollars and cents. If a bank can't turn a profit due to bloated expenses and an inefficient operations, many times they'll turn to risk taking to make up the difference

As bank investors, we can use that knowledge to avoid the duds and find the banks that are maximizing profits without excessive risk taking -- even if those banks keep a low profile in the newspapers and on CNBC. To find them, we turn to the efficiency ratio.

Some quick and easy math before we get to the bank stocks
A bank's efficiency ratio is the ratio of the its non-interest expenses to its net revenue. This ratio provides an easy-to-understand metric to gauge how much cost is required to generate a dollar of revenue; therefore, a lower ratio is better, while a higher ratio indicates an inefficient bank.

The efficiency ratio doesn't tell the full story of a bank's investment prospects, but it is an absolutely great place to start. To kick start your search for an under-the-radar bank stock with a great efficiency ratio, here are five of the most efficient banks in the nation.

5. Toronto-Dominion Bank (NYSE:TD)
Kicking off the list is Toronto-Dominion Bank. More commonly known as TD Bank, this company reports an efficiency ratio of 52.3%, meaning that it costs the bank $0.52 in expenses to produce $1 in revenue. 

The key to TD Bank's efficiency is the bank's ability to produce lots of revenue outside the traditional lending business, without adding the same level of incremental expenses. In the second quarter, 41% of TD Bank's revenues were from non-interest sources, the second highest level on this list. TD Bank also holds the honor of being the largest bank included in this list, with $833 billion in total assets.

4. Cathay General Bancorp (NASDAQ:CATY)
Cathay General Bancorp is the smallest institution on the list, with $11.5 billion in total assets. The bank is a Chinese-American institution, serving that community in major metros across the United States. The bank sports an impressive 44.9% efficiency ratio.

Source: Company website.

In the second quarter, Cathay General reported a respectable 9.3% return on equity, which falls more or less in line with the industry average.

Cathay General does have the highest percentage of non-performing assets relative to its total assets of any of the banks on this list at 0.98%. Non-performing assets are loans that management thinks may not pay back all the principal or interest due, plus foreclosures.

Cathay General management appears to be on top of this weakness, though, as the bank's assets-to-equity ratio is a conservative 7.5. For comparison, TD Bank has a much riskier and more leveraged assets-to-equity ratio of 16.8.

Source: Company website

3. Prosperity Bancshares (NYSE:PB)
The second smallest bank on the list, Prosperity Bancshares, had an efficiency ratio of 42.9% in the second quarter. This $21 billion bank has just 0.18% non-performing assets and returned 10.1% on equity. 

Prosperity, headquartered in Houston, has benefited tremendously over the past several years from the robust economy in Texas. The bank has leveraged its strong local economy into such great metrics while still keeping leverage to a minimum. Prosperity has the lowest leverage of any of the banks here, with just a 6.81 assets-to-equity ratio.

Source: Company website.

2. The Bank of New York Mellon Corporation (NYSE:BK)
Bank of New York Mellon is a bit different from the other banks on this list. It's a custodial bank, meaning that its primary business is not the traditional gathering of deposit and extension of loans. Instead, Bank of New York Mellon relies on transactional, trust, and treasury services it offers to its deposit holders around the world.

As such, it is not an apples-to-apples comparison with the rest of the list, though I would argue that the bank's inclusion is justified. BNY Mellon's return on equity is lagging at 6.1%, but it is only moderately leveraged and has next to zero nonperforming assets, and the bank trades at just 1.21 times its book value.

The bank's efficiency ratio was 38%, meaning that it only took $0.38 to generate a dollar of revenue.

Souce: Company website.

1. Signature Bank (NASDAQ:SBNY)
Sitting at the top of the mountain is Signature Bank, the $24.5 billion bank headquartered in New York.

Don't let its Fifth Avenue HQ fool you, though: This is an old-fashioned community bank that serves the greater New York City market. Signature Bank reported an impressive 35.4% efficiency ratio in the second quarter. 

That efficiency trickled through to generate a solid 13.8% return-on-equity number. The bank is not overly leveraged, with 10.7 times assets to equity. It has just 0.14% nonperforming assets to total assets, and it operates within an old-fashioned, simple, and effective community bank business model. Its lending business makes up 94% of the its revenue, far and away the highest of any bank on this list.

This article represents the opinion of the writer, who may disagree with the “official” recommendation position of a Motley Fool premium advisory service. We’re motley! Questioning an investing thesis -- even one of our own -- helps us all think critically about investing and make decisions that help us become smarter, happier, and richer.