Source: Frankieleon on Flickr

Banks come in a massively wide variety of shapes and sizes. There are the megabanks, led by JPMorgan Chase (NYSE:JPM), which reports $2.6 trillion in total assets. And there are tiny, local institutions with a single branch and hardly $25 million in assets. Comparing these institutions is clearly not apples to apples: JPMorgan is 100,000 times larger than the smallest banks!

It's not even always apples to apples on the big bank side. Consider Bank of America (NYSE:BAC). The Charlotte, N.C., megabank reported a $3.1 billion profit in the fourth quarter of 2014. That's a ridiculous amount of money by almost any standard -- except in comparison with other megabanks.

JPMorgan, for example, reported $4.9 billion in profits. That's 58% more than B of A. By comparison, that $3.1 billion looks a little lacking. But it gets worse.

Wells Fargo (NYSE:WFC) reported an incomprehensible $5.7 billion. Wells had $1.7 billion in total assets, compared with Bank of America's $2.1 billion, which means Wells earned 84% more profit with 19% fewer assets.

Suddenly, Bank of America's profits don't look all that great at all, even at $3.1 billion!

Leveling the playing field
Thee are over 6,000 banks in the U.S., many of which are publicly traded. With so many options, it's crucial for investors to have some comparable metrics to work with.

The two most common ratios for doing so are return on assets and return on equity, or ROA and ROE. To me, ROA is the more critical of the two.

Saving the best for last, let's start with ROE, which is a measure of the bank's profits relative to shareholder equity. This ratio is important because it represents the theoretical growth rate of the bank's equity. Investors don't just buy shares as charity -- they expect returns. ROE is the de facto measure of how effectively the bank is generating those equity returns. 

The downside of ROE is that it's easy to game using potentially risky accounting moves. A bank could, in theory, increase its earning assets using leverage. Equity would stay the same, earnings would increase with the new assets, and ROE artificially would increase. The problem, of course, is overleverage; the bank could very easily get itself into serious trouble if even a small portion of those earning assets go bad.

ROA eliminates this problem and gives investors a much crisper view of the real earnings engine driving the bank. By using the asset side of the balance sheet instead of the liability side, ROA ignores leverage and tells investors how much profit a bank is squeezing out of its assets. Expense management, efficiency, and the business model itself drive ROA, not financial trickery.

Using these ratios, we can confirm that Bank of America's $3.1 billion in profits aren't as great as they may first seem. 

JPM Return on Assets (Annual) Chart

JPM Return on Assets (Annual) data by YCharts

A more complex (and robust) approach
Value investor Joel Greenblatt uses a ratio called "earnings yield" to measure the relative strength of profits. The ratio is calculated by dividing a company's operating income into its enterprise value. The beauty of this approach is that it incorporates an element of market value in the ratio.

ROA and ROE are both measured using figures directly from the bank's financial statements. Neither addresses the price you must pay to buy a share.

For example, a bank with an ROA of 2% is by all standards doing a great job and producing very strong relative profits. But if the market price of that bank stock is two-and-a-half or three times book value, the profit relative to your dollar invested isn't quite a strong.

Using Greenblatt's formula, here's a look at the earnings yield for each bank:

 BankEarnings Yield (Greenblatt) As of December 2014
Wells Fargo 6.33%
Bank of America 2.15%
JPMorgan Chase 25.24%

Wells Fargo currently trades at 1.64 times book value. Bank of America, on the other hand, trades at just 0.72 times book value. JPMorgan splits the difference at 0.98 times book value.

By bringing earnings yield into the analysis, we can see that even though Wells Fargo has the best profits in terms of raw dollars, ROA, and ROE, its current valuation dilutes the value of those results relative to the cost of buying a share. On the other hand, JPMorgan's valuation comes into view as being a huge bargain relative to the bank's profits. Bank of America, once again, brings up the rear.

Foolish takeaway
Given the incredibly diverse bank stock options available to investors today, it's critical to analyze profits on a relative basis. Just because a small bank's profits top out at $10 million a year -- a figure that pales in comparison with the billions in profits that the megabanks report every quarter -- that doesn't mean the bank isn't a good investment.

Investors should go beyond the headlines and review bank profits using traditional metrics such as ROA and ROE. Then investors should consider those ratios in relation to the bank's valuation. Greenblatt's earnings yield ratio is my preferred method for doing just that.