JPMorgan Chase (JPM) is the largest U.S. bank by assets, with $2.39 trillion at the end of the first quarter. Its most recent quarterly noninterest expense to average assets ratio was 2.67%, according to SNL Financial LC. Overhead to average assets was 2.84% in the first quarter of 1995, when JPMorgan's predecessor, Chemical Banking Corp., had $185 billion in assets. Since then, assets have increased by 1,190% but OH/AA fell only 6%.

With few exceptions, that's the story for large banks. Assets balloon and the overhead ratio falls either slightly or not at all. Sometimes it rises.

Of the 25 U.S. depository institutions with more than $25 billion of assets, the last four quarters' median OH/AA ranges from 0.81% at Hudson City Bancorp (HCBK) – a thrift; several of the large thrifts run leaner than the largest banks – to 4.27% at First Horizon (FHN). Line these institutions up in size order and you'll see that despite the huge difference in assets between the top four and everyone else, there's no OH/AA advantage to being big. The $65-billion asset Comerica (CMA) has essentially the same OH/AA ratio (2.66%) as JPMorgan Chase (2.65%).

So where are the promised cost economies of scale?

It's an important question, because belief in them is a key motivator for serial acquirers. It's hard for bank stock investors to be overjoyed about the 6% to 7% organic asset growth (best case) that banks deliver over the long run, because that translates into only 6% to 7% long-run earnings growth, excluding improvement in returns on equity, sensible acquisitions or stock buybacks. But if a bank could lower its OH/AA ratio even by 5% every time it doubled its asset size (say from 3% to 2.95%, and on from there), a doubling of assets would translate into 118% earnings growth. And that would be a powerful motivator to get big, fast.

But the savings just aren't there.

It's difficult to figure out precisely why, because large banks have unique business mixes and geographic footprints, complicating comparisons of a specific cost item such as how much it costs to build, staff and maintain a branch. It seems logical to assume technology costs would provide scale economies. Other costs, like advertising, might suffer diseconomies. Citigroup (NYSE: C) will spend $41 million over five years to be the lead sponsor of the "Citi Bike" rental bike program in New York City. It will spend $400 million over 20 years to have its logo on the New York Mets' Citi Field. The largest banks may very well be engaged in an arms race with respect to branches. I live in Manhattan, and I continue to be perplexed by the locations of bank branches. On Broadway between 57th and 58th Street, a short block, there are HSBC (HBC), Bank of America (BAC) and Chase branches. Citibank, TD Bank (TD) and Wells Fargo (WFC) branches are one block away. What other businesses in New York City are clustered like that, aside from Starbucks?

Smaller banks' management teams seem irritated by the large commitment of time and money to comply with Dodd-Frank and other regulations. But their OH/AA ratios haven't yet shown a material increase. Maybe they will. Hoping that this increase will motivate small banks to sell seems like wishful thinking. There are still about 7,000 banks and thrifts in the U.S., most of them tiny. You have to wonder why the large banks haven't simply driven the small ones out of business. Amazon has wreaked havoc on the book retailing business, has played a role in the destruction of the music retailing business, and has turned its sights to other businesses, all because of its ability to exploit scale and efficiency as competitive advantages.

I suspect that if an Amazon, an Apple or a Walmart were to enter the banking business, they'd be game changers, even though they'd be starting from scratch. Irrespective of what the management teams of large banks may think, I don't think retail consumers of banking services perceive one large bank as being meaningfully better than another. There's no Coke vs. Pepsi or iPhone vs. Android battle from the banking consumer's standpoint. Maybe banks realize this, and that leads them to focus on getting bigger, with the hope that this will somehow make them better.

So if a bank can't lower its overhead ratio in the long run, then it can't improve its return on assets either. Meaningful revenue economies of scale simply don't exist. So that means a bank can't improve return on equity either, unless it employs increasingly aggressive leverage. And low ROE constrains asset growth.

So, exactly what problem does acquisition-fueled growth solve?

Harvard Winters, a former investment banker, writes research on banks.