At Wells Fargo's (WFC -0.02%) investor day on Thursday, the bank shared an interesting chart that clearly delineates between the nation's best-run banks and the rest.

The chart shows the relationship between bank profitability, measured by return on equity, and the volatility of a bank's earnings over the past five years. It looks specifically at Wells Fargo and five of its peers: U.S. Bancorp (USB 0.79%), JPMorgan Chase (JPM -0.10%), PNC Financial (PNC -0.32%), Citigroup (C 0.39%), and Bank of America (BAC -0.26%).

A chart comparing profitability to consistency of earnings among big banks.

Data source: Wells Fargo.

The chart reveals two interesting things. The first is that there's a cluster of banks that have both stable earnings and comparatively high returns on equity. U.S. Bancorp is at the top, followed by Wells Fargo, JPMorgan Chase, and PNC Financial.

All of these banks are considered among the best-run financial institutions in the country, though Wells Fargo has certainly lost much of its luster in the wake of its fake-account scandal.

These banks also tend to have the highest valued stocks, measured by the price-to-book value ratio. This makes sense given the logical correlation between the profitability and valuation of banks that I've discussed previously.

The second interesting thing, though it's a corollary of the first, is that the two banks on the chart that have the lowest returns on equity also have the most volatile earnings. These are Bank of America and Citigroup.

A Wells Fargo sign.

Image source: The Motley Fool.

It isn't a coincidence that these two banks were hit hardest by the financial crisis. Citigroup came within a hair's breadth of failure in 2008, and spent the next five-plus years retreating and retrenching from its former strategy of securitizing and selling derivatives and securities backed by toxic subprime mortgages.

And Bank of America was in a similar situation, though its troubles were largely inherited via its acquisition of Countrywide Financial. Since then, Bank of America has spent upwards of $200 billion on crisis-related costs, though the North Carolina-based bank has more recently turned the corner.

All of this matters because the size and consistency of a bank's earnings plays a role not only in the annual stress tests, which are administered each year by the Federal Reserve and dictate how much capital a bank can return to its shareholders, but also in a bank's credit rating. At Moody's, which is one of the three main ratings agencies, 15% of a bank's credit rating relates directly to profitability, as I dig into here.

In short, when it comes to picking bank stocks, it isn't only how much a bank earns that matters; it's also about the consistency of earnings.