The horsepower behind long-term bank profits is the bank's core earnings. That's most easily represented by a bank's net interest margin -- the spread between the interest it makes on loans, and the interest it pays out to depositors.

Let's take a moment to compare and contrast this figure for three regional banks in the U.S.: First Republic Bank (NYSE: FRC), Hudson City Bancorp (NASDAQ: HCBK), and People's United Financial, (NASDAQ: PBCT). These three insitutions are comparably sized between $30 and $45 billion in total assets, and each generates at least 75%-80+% of revenue from interest on loans.

We'll use the most current filings from each bank's regulatory call reports so we can break down the numbers into plenty of detail. We'll use the FDIC's definition of net interest margin, as well, which is the bank's total interest income less total interest expense (annualized) as a percentage of average earning assets for the given period.

First Republic Bank
First Republic reported net interest margins of 3.19% for the first quarter. The loan portfolio produced a yield of 3.56%, and the bank's cost of funding was 0.36%. 

First Republic's net interest margin trend. Source:

First Republic has four main portfolios that drive core earnings, with heavy reliance on residential and commercial real estate. Yields for each of those portfolios are broken down in the table below.

Note: "Commercial & Industrial" refers to non-real estate business loans. "All Other Securities" are all securities excluding U.S. government treasuries and mortgage-backed securities.

Loan Category % of Total Interest Income Yield
1-4 Family Residential 49.6% 3.24%
All Other Real Estate 25.6% 4.46%
Commercial & Industrial 6.3% 3.99%
All Other Securities 10.5% 3.69%

Non-significant portfolios omitted. Percents do not add up to 100%.

Hudson City Bancorp
Hudson City produced a very tight 1.39% net interest margin for the quarter. Hudson City's margin was driven primarily by a very high costs of funds at 1.96%. The loan portfolio yielded 3.35%.

Hudson City Bancorp's net interest margin over time. Source:

Hudson City's loan portfolio is exceptionally reliant on mortgage lending. The one-to-four Family Residential and Mortgage-Backed Securities portfolios accounted for a combined 97.1% of total interest income. They yielded 4.25% and 2.27%, respectively.

Of much great concern is the bank's cost of funding. The bank relies heavily on borrowed funds, which come with a significantly higher interest rate than more typical deposit accounts. A total of 77.8% of the bank's interest expense comes from purchased Federal Funds, or borrowed cash from the Federal Home Loan Bank of New York.

This presents a very significant risk to the bank. First, Hudson City is primarily a mortgage lender and, in today's low-rate environment, most homeowners seek a fixed-rate mortgage. For Hudson, that means the bank could end up with a large portion of fixed-rate loans that wouldn't rise with an increase in rates across the economy. If that were to occur, the bank's already tight margins would shrink even further, and it would happen fast.

In 2011, the bank's regulator issued an order requiring the bank to "reduce its level of interest rate risk and funding concentration." That was three years ago. The bank has improved -- interest expense is down $34 million on a quarterly basis since March 31, 2012, but the problem persists in a very significant way.

People's United Financial
People's United reported a solid net interest margin of 3.27% as of Q1. The yield on the bank's loan portfolio was 3.60%, subtracting yield on the bank's funding of 0.33%.

People's United's net interest margin over time. Source:

People's United's portfolio breaks down similarly to First Republic's, with the primary difference being a greater emphasis on business lending and an inverse concentration between one-to-four Family and Other Real Estate lending. 

Loan Category % of Total Interest Income Yield
1-4 Family Residential 24.1% 3.75%
Mortgage Backed Securities 7.2% 1.92%
All Other Real Estate 49.2% 4.56%
Commercial & Industrial 12.4% 2.44%

Non-significant portfolios omitted. Percents do not add up to 100%.

Foolish takeaway

Here's how the comparison breaks down, side by side:

So, which bank is best positioned for the next five years? 

We can immediately eliminate Hudson City. The bank-funding model is simply too flawed, and will likely remain so for some time. When rates rise, Hudson City may be one of the few banks that sees margins actually shrink, instead of grow.

The decision, then, between First Republic and People's United boils down to personal opinion. Both have similar yields, similar funding costs, and similar portfolios. First Republic caters to higher-end mortgages for the affluent, while People's United focuses on a broader client base. 

When rates rise in the next few years, I think that both First Republic and People's United will do just fine. They both have finely tuned earnings engines.