A great place to start your search for a bank stock investment is return on equity, or ROE. As investors, we want a stock that is optimized to yield high profits as efficiently as possible. No single metric captures this combination of characteristics better than ROE. 

But bank stocks are unique animals. It's not enough for a bank to post high returns on equity every quarter. Banking is a business of risk; therefore, a high ROE while taking on too much risk can be a disaster in the long term. We must consider a few other factors to qualify a bank's ROE, starting with the bank's efficiency and its leverage.

Efficient returns without excess leverage
The logic of using these three ratios in combination is pretty straightforward. First, a bank with excessively high leverage is at a greater risk of failing if the economy takes a turn for the worse. If a bank has an assets-to-equity ratio of 10-to-1, that means that just a 10% drop in the value of the bank's assets would wipe out all of its equity. Currently, the industry average assets-to-equity ratio is about 9.5, according to data from the FDIC.

Second is efficiency. Obviously, a more efficient bank is better for shareholders because a higher percentage of each dollar in revenue transfers to profits. That's the name of the game for all companies. Banks, though, are unique in that the products they sell must be paid back. Once you buy your new iPhone 6, Apple doesn't care what you do with it. For a bank, though, the most critical part of the business is collecting those payments of principal and interest. 

The efficiency ratio, therefore, takes on even greater importance. If a bank can't control its expenses, then one very easy way to boost profits is to make riskier loans that pay a higher interest rate. That strategy can work for a little while, but as soon as there is any hiccup in the economy, those loans will be the first to default.

Bringing it all together, an optimal bank stock will yield a strong return on equity through an efficient operation without using excess leverage. 

Five bank stocks with strong return on equity
With that established, let's look at these five bank stocks: 

Company NameReturn on Equity*Assets-to-Equity Ratio*Efficiency Ratio** 
Bank of Hawaii Corporation (NYSE:BOH)  16.0% 13.4 59%
The Toronto-Dominion Bank (NYSE:TD)  15.5% 17.1 70%
Union Bankshares (NASDAQ:UNB)  15.0% 12.8 67%
U.S. Bancorp (NYSE:USB)  14.0% 9.1 53%
Signature Bank (NASDAQ:SBNY)  13.8% 10.6 37%

Sources: * S&P Capital IQ, ** BankRegData.com.

These five bank stocks are an excellent case study in the interactions of returns, efficiency, and risk. On one hand, you have a bank like TD Bank where that impressive 15.5% ROE is a mechanism of leverage and risk instead of strong operational performance. 

Swinging in the other direction, you have the New York City-based community bank Signature Bank, which is able to produce peer-beating returns thanks to its incredibly strong efficiency ratio. That efficiency allows the bank to stay conservative in its use of leverage. U.S. Bancorp is a similar case but on a super regional scale. The bank is one of the nation's best because of its conservative, efficient operations. The numbers speak for themselves.

Foolish takeaway
Before you become enamored with a single outsized metric on a given stock's financial statement, make sure you understand the fundamentals of the business that make that number a reality. It doesn't matter if you're seeking a dividend, hidden value, or growth, the lesson is the same. 

Without the context of its leverage and (in)efficiency, an investor may see TD Bank's great ROE and consider buying the stock. But by going that extra step, by adding the context of the bank's excessive leverage and 70% efficiency ratio, that same investor may instead choose to buy shares in another bank with equally strong returns, but far less risk.

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.