Many people seem to think that – as a new BIS working paper concludes – banks benefit when monetary policy tightens and interest rates rise (especially from a low level). Do they? In some instances, perhaps, but as a general principle, surely not.

A casual glance at recent U.S. stock market behavior seems to support the idea that higher interest rates would be good for banks now. When the Federal Open Market Committee decided not to hike interest rates on September 17, the S&P500 dropped by 1.85% over two days, while the KBW index of bank stocks fell by 4.85%. A week later, when Fed Chair Yellen speaking about inflation dynamics expressed her continued expectations for a rate hike this year, the S&P500 edged lower, but the bank index rose by nearly 2%.

The simple interpretation of these events is that investors believe looser policy hurts banks and tighter policy helps them. But one alternative is that investors are responding to news about the economic outlook more generally. We know that banks and the economy do well and suffer together. When it chose not to hike rates on September 17, the FOMC emphasized that “recent global economic and financial developments may restrain economic activity” and promised to monitor “developments abroad.” Chair Yellen’s September 24 speech – her first since early July – instead emphasized the economy’s “solid prospects.”

So, without a careful analysis that distinguishes the range of factors affecting bank stocks, recent performance can’t resolve the question of whether policy tightening per se helps banks.

There are two ways to pose and address this question. The first is to ask how it is that policy changes influence earnings and profitability that banks themselves report in their published accounting statements. Our reading is that this is what the BIS paper studies. The second approach is to examine the impact of interest rates on the ability of banks to withstand negative shocks: that is, how monetary policy changes influence banks’ true net worth and, hence, financial stability more generally. Because of some important accounting conventions that we will describe, the answers to these two questions can be quite different.

Our objective, then, is to analyze how it is that interest rate changes influence bank performance by examining the impact of three possible changes in the yield curve: (1) a rise in short-term rates that leaves long-term rates unchanged (a yield curve flattening); (2) a rise in long-term rates that leaves short-term rates unchanged (a yield curve steepening); and (3) a parallel upward shift in short- and long-term interest rates (a yield curve slope that is unchanged).

To understand the impact of each of these, we can look at the three principal ways in which interest rate changes affect banks.

First, banking is a spread business. Banks profit from the gap between the interest rate they receive on their assets (mostly loans and securities) and the rate that they pay on liabilities (mostly deposits). Because banks engage in maturity transformation – with assets having a longer maturity than deposits – this lending spread will generally fall when the yield curve flattens.

Second, since banks hold fixed-income instruments (bonds and loans), higher interest rates across the yield curve reduce the present discounted value of their assets. And, the longer the duration of their assets (relative to their liabilities), the bigger those losses will be. Similarly, banks face greater risk when the volatility of their portfolios (and the correlations among their assets) rise.

Third, rising interest rates are often a signal of stronger economic growth. An improved growth outlook benefits banks in several ways. It reduces the risk that borrowers will default, increasing the value of bank assets. It increases credit demand at any given interest rate, potentially raising the volume of their lending business. And, it is associated with greater stability, which makes bank assets more liquid. (See here for evidence on the procyclicality of bank profits.)

Importantly, since higher policy interest rates are normally associated with a flattening of the yield curve (and, when introduced after a long period of low rates, a rise in financial volatility), the first two of these mechanisms work to harm banks, reducing both profitability and net worth. Only the third mechanism, which is not about interest rates at all, can help them.

So, why do people think that a Fed rate hike will help banks? One possible argument – supported by the BIS paper – is that at near-zero interest rates banks cannot mark down their deposit rates sufficiently to maintain their interest rate spread as lending rates fall. From this perspective, as policy rates start to rise, banks would not need to raise their deposit rates, so their interest margins and profitability would go up. This would be possible if deposits are sufficiently sticky, meaning that investors are not very active in looking for higher yields as market interest rates rise.

At first glance, this focus on the zero-lower bound for bank deposit rates seems consistent with the decline of U.S. banks’ net interest margin (the gap between the weighted-average yields on their fixed-income assets and liabilities) to record lows in recent years (see upper chart). However, aside from the financial crisis, the trend of net interest margin compression is now two decades old, having begun around the time that Congress eliminated constraints on interstate banking in 1994. It is far from clear that this trend will reverse as interest rates rise. Indeed, the yield curve today is already a bit steeper than the average over the past three decades (see the lower chart), so banks may be compelled to compete more aggressively than usual for depositors.

U.S. Banks: Net Interest Margin, 1984-2Q 2015