This note analyzes recent trends in net interest margins (NIMs) at domestic bank holding companies (hereafter, banks).² Understanding the empirical behavior of NIMs has important implications for assessing the monetary transmission mechanism, particularly during the upcoming period of monetary policy normalization. For instance, an important component of the monetary transmission mechanism is the timing and degree of the pass-through of changes in the federal funds rate to deposit rates paid by commercial banks, and this pass-through behavior may have changed in the wake of the financial crisis. In addition, NIMs may also be used to help monitor banks' "reach for yield" behavior, because one concern associated with keeping interest rates low for an extended period is the potential for an excessive increase in risk-taking by banks.

The extraordinarily low interest rate environment that has prevailed in the wake of the financial crisis has put downward pressure on the NIMs of all banks, but especially the largest ones.³ As shown in Figure 1, over roughly the past five years, NIMs of large banks have fallen 70 basis points, while NIMs of small banks have decreased approximately 20 basis points. The more pronounced decline in NIMs at large banks is driven by two main factors related to the low interest rate environment. The first factor arises from the liability side of banks' balance sheets, namely from a more pronounced decline in funding costs at small banks, and accounts for the majority of the difference in the behavior of NIMs between large and small banks. The second factor stems from the asset side of the balance sheet. Specifically, in recent years large banks have experienced a somewhat bigger decline in the interest income that they earn on "other" assets, which includes assets held for trading purposes.

These empirical findings have implications for monetary policy as interest rates begin to rise. During previous monetary policy tightening episodes, the rates banks pay on deposits have risen more slowly than market rates, allowing banks to increase their NIMs. In particular, during the next monetary policy tightening episode, large banks could try to boost their profitability in the short term even further by delaying an increase in their deposit rates relative to previous tightening cycles. If that happens, more deposits than usual could leave the banking system, putting some downward pressure on the level of short-term interest rates. However, with interest on excess reserves higher than many deposit rates, and with the currently high level of excess reserves helping banks meet their liquidity requirements, banks may instead act to preserve deposits as a funding source, accelerating the pass-through to market interest rates relative to previous tightening cycles. That said, this latter effect may be damped because many large banks face balance sheet constraints in light of the new regulatory environment. In particular, the Basel III leverage ratio, which requires the same amount of capital be held irrespective of the risk of the underlying asset, may reduce the incentives for banks to preserve this funding source.

Contributions to NIMs by Asset and Liability Type
The difference in NIMs between small and large banks has been widening for some time. As illustrated in Figure 1, the difference in NIMs between small and large banks increased from 50 basis points in the first quarter of 2010 to 100 basis points in the second quarter 2015. As noted above, over this period, NIMs at small banks decreased approximately 20 basis points while NIMs at large banks dropped roughly 70 basis points. To understand the key factors that explain the difference in the reductions in NIMs at large and small banks, we calculate the contributions of each major subcomponent of interest income and interest expense over the period of analysis. Namely, the contribution of asset type i to the NIM in period t is defined as

where Interest income_i,t and Interest earning assets_i,t are the interest income and the amount of asset type i in period t, respectively, Interest earning assets_t is the total amount of interest earning assets in period t, and i = {loans, securities, other assets}. Thus, the contribution of asset type i to the NIM in period t is the product of the average interest earned on asset type i and the share of these assets relative to the total interest earning assets in period t.

Similarly, the contribution of liability type j in period t to the NIM in period t is defined as

where Interest expense_j,t and Interest bearing liabilities_j,t are the interest expense and the amount of liability type j in period t, respectively, and j = {interest-bearing deposits, other interest-bearing liabilities}. Therefore, the contribution of liability type j to the NIM in period t is the product of the average interest paid on liability type j and the ratio between these liabilities and the total interest earning assets in period t. The changes in these contributions between period t and t-1 are defined as

for asset type i and liability type j, respectively. By construction, the change in the contribution of each type of asset and liability adds up to the total change in NIM.

Figure 2 indicates that low interest rates helped offset the compression in NIMs of both large and small banks by reducing banks' funding costs over the period between the first quarter of 2010 and the second quarter of 2015, although this effect was more pronounced for small banks. In particular, the decrease in the cost of total liabilities contributed to a rise of 110 basis points in the NIM of small banks over the period. This compares with an increase of 70 basis points in the NIM of large banks over the same period. The difference in the behavior of NIMs at the two bank groups was due to a sharper reduction in the cost of deposits at small banks. In particular, the cost of interest-bearing deposits fell roughly 60 basis points at small banks over this period while it decreased only about 20 basis points at large banks. In general, deposit rates tend to move with short-term interest rates and are typically lower at large banks. With the federal funds rate at the zero lower bound since late 2008, the ability of large banks to boost their profitability by reducing their deposit rates has been more limited relative to small banks. So far, at least, large banks have been reluctant to charge negative deposit rates and, therefore, have been unable to reap as much benefit from the low interest rate environment relative to small banks.

Figure 3 shows that a reduction in interest income on loans was another primary driver of the declines in NIMs of both large and small banks over the period considered, and this factor accounted for a total reduction of approximately 95 basis points for large banks and roughly 85 basis points for small banks. Interest income on securities and other assets fell about 45 basis points at large banks while it moved down roughly 40 basis points at small banks. Although interest income on securities contracted a bit more at small banks, the decline in interest income on securities and other assets taken together was slightly more pronounced at large banks. Thus, large banks have experienced a somewhat bigger decline in the interest income that they earn on other assets, which includes assets held for trading purposes. Small banks experienced a somewhat lower negative contribution from interest income on other assets to NIMs, in part because small banks generally have lower holdings of trading assets relative to large banks.

Contribution to NIMs from Changes in Yields and Portfolio Composition
The contribution to NIM from each interest earning asset or liability type can be caused by changes in the return or cost of each type--that is, changes in yields--or by changes in the share accounted for by each type--that is, changes in portfolio composition.⁴ In this section, the overall change in the NIM of each bank group is decomposed into that which is accounted for by changes in yields versus changes in the composition of assets and liabilities. Overall, changes in the composition of assets or liabilities account for a small portion of the difference in the behavior of NIMs across the two bank groups. That said, changes in the shares of other interest-bearing liabilities explains approximately one-third and one-fourth of the liabilities' contribution to changes in NIMs at large and small banks, respectively.

Figure 4 indicates that, on the liability side, decreases in funding costs as well as changes in the composition of banks' liabilities have provided a boost to the NIM of both bank groups. This should not be surprising given that the federal funds rate has been at the zero lower bound since the end of 2008. In addition, the financial crisis led many investors to move funds into safe deposits. Given the slow recovery, a large portion of these funds have stayed in the banking system. That said, as discussed above, the decline in the cost of deposits is considerably more pronounced at small banks. In particular, the effect of the decline in deposit rates at small banks has pushed up NIMs about 60 basis points, while the corresponding effect of declining rates at large banks has increased NIMs roughly 20 basis points. Since large banks were paying lower deposit rates in the period prior to the past financial crisis, the degree to which large banks have been able to boost their profitability by reducing their deposit rates has been more limited relative to small banks. In contrast, for other interest-bearing liabilities, the impact of lower interest rates has been approximately the same across the two bank groups. Finally, the change in the share of other interest-bearing liabilities at both large and small banks has also pushed up NIMs about 25 basis points.

Figure 5 shows that, on the asset side, the bulk of the decline in NIMs during the past five years has been driven by a decrease in the yields of the various types of assets, especially loans. In contrast, changes in balance sheet shares have had fairly minimal impact on NIMs at both large and small banks. Nonetheless, over the past two years the share of loans at small banks--primarily outside the real estate sector--has been rising somewhat, increasing NIMs roughly 15 basis points in 2013 and 2014 (not shown). However, NIMs remained about unchanged since the first quarter of 2010 due to changes in loan shares. Because the difference in the change in NIMs between the two bank groups is primarily driven by the liability side of banks' balance sheets, the low interest rate environment does not appear to have manifested in a substantial reach for yield by small banks.

Conclusion
Banks' net interest margins, or NIMs, have remained compressed over the past 5 years as a result of the low interest rate environment that has prevailed in the wake of the financial crisis, particularly the NIMs of large banks. Our results suggest that the difference in NIMs between small and large banks widened mainly because of a more marked decline in deposit costs at small banks. In contrast, the possibility that NIMs at small banks have remained closer to the upper end of its range of the past decade does not appear to be driven by reach-for-yield behavior. Looking ahead, as monetary policy normalizes and short-term interest rates increase, it will be interesting to continue to monitor the timing and degree of the pass-through of changes in the federal funds rate to banks' funding costs to help assess the monetary transmission mechanism.

Appendix: Formulas for Yield and Share NIM Contribution Calculations

This appendix details the decomposition of changes in NIMs into changes in the yield and the share of each asset and liability type. For asset type i in period t, ΔCNIM_i,t can be decomposed as follows:

where

is the portion of the change in the contribution of asset type i between periods t and t-1 explained by the change in the average interest earned in this asset type (holding the share of asset type i constant at its value in t-1), and

is the portion explained by the change in the share of this asset type (holding the average interest earned on asset type i constant at its value in t). A similar decomposition can be done for liabilities by replacing interest income and assets with interest expense and liabilities, respectively.

Item	Formula
Level
Interest-earning assets	sum(BHCK0395, BHCK0397, BHCK1754, BHCK1773, BHDMB987,BHCKB989, -BHCK3123, BHCK3545, BHCK2122, -BHCM3543)
Interest paid on deposits	sum(BHCKA517, BHCKA518, BHCK6761, BHCK4172)
Interest-bearing liabilities	sum(BHDM6636, BHFN6636, BHDMB993 +BHCKB995, BHCK3190, BHDM4062)
Yield
Interest-bearing deposits	4*interest paid on deposits/sum(BHDM6636, BHFN6636 )
Other interest-bearing liabilities	4*sum(BHCK4073, -interest paid on deposits)/ sum(interest-bearing liabilities, -BHDM6636, -BHFN6636 )
Loans	4*(BHCK4435 +BHCK4436 +BHCKF821)/sum(BHDM2122, -BHDM2165, -BHCK3123) + 4*BHCK4059/sum(BHCK2122, -BHDM2122, -BHCKF162)
Securities	4*(BHCKB488 +BHCKB489 +BHCK4060)/sum(BHCK1754, BHCK1773, -BHCM3543)
Other Assets	4*BHCK4065/sum(BHCKF162, BHCKF163) + 4*BHCK4115/sum(BHCK0395, BHCK0397) + 4*BHCK4069/BHCK3545 + 4*BHCK4020/sum(BHDMB987, BHCKB989)
Share
Interest-bearing deposits	sum(BHDM6636, BHFN6636 )/interest-earning assets*100
Other interest-bearing liabilities	sum(interest-bearing liabilities, -BHDM6636 , -BHFN6636 )/interest-earning assets*100
Loans	sum(BHDM2122, -BHDM2165, -BHCK3123)/interest-earning assets*100 +sum(BHCK2122, -BHDM2122, -BHCKF162) /interest-earning assets*100
Securities	sum(BHCK1754, BHCK1773,-BHCM3543)/interest-earning assets*100
Other Assets	(BHCKF162 + BHCKF163)/interest-earning assets*100 + sum(BHCK0395, BHCK0397)/interest-earning assets*100 + BHCK3545/interest-earning assets*100 + (BHDMB987 +BHCKB989)/interest-earning assets*100

Name	Schedule	Line Item	MDRM
Total loans in domestic offices	HC-C	12.B	BHDM2122
Lease financing receivables in domestic offices	HC-C	10.B	BHDM2165
LESS: Allowance for loan and lease losses	HC	04.c.	BHCK3123
Total loans in foreign offices	HC-C	12.A, 12.B	BHCK2122 -BHDM2122
Lease financing receivables (net of unearned income)	HC-C	10.a., 10.b.	BHCKF162 +BHCKF163 (Note: pre-2007 this was BHCK2182 +BHCK2183)
Total Securities	HC	2	BHCK1754 +BHCK1773
Derivatives with a positive fair value	HC-D	11.A	BHCM3543 (Note: pre-2008 this was BHCK3543 +BHFN3543)
Interest-bearing balances in foreign offices due from depository institutions	HC	01.b.(2)	BHCK0397
Held-to-maturity securities	HC	02.a.	BHCK1754
Available-for-sale securities	HC	02.b.	BHCK1773
Federal funds sold and securities purchased under agreements to resell	HC	03.a., 03.b.	BHDMB987 +BHCKB989 (Note: pre 2002 this was BHCK1350)
Trading assets	HC	5	BHCK3545 (Note: pre-1994 this was BHCK2146)
Total loans (domestic + foreign)	HC-C	12	BHCK2122
Interest-bearing deposits in domestic offices	HC	13.a.(2)	BHDM6636
Interest-bearing deposits in foreign office	HC	13.b.(2)	BHFN6636
Interest-bearing balances in U.S offices due from depository institutions	HC	01.b.(1)	BHCK0395
Federal funds purchased and securities sold under agreements to repurchase	HC	14	BHDMB993 +BHCKB995 (Note: pre-2002 this was BHCK2800)
Other Borrowed Money	HC	16	BHCK3190 (Note: pre-2001 this was BHCK2332 + BHCK2333)
Subordinated notes and debentures	HC	19.a.	BHDM4062
Total interest expense	HI	02.f.	BHCK4073
Interest and fee income on loans in domestic offices	HI	01.a.(1)	BHCK4435 +BHCK4436 +BHCKF821
Interest and fee income on loans in foreign offices	HI	01.a.(2)	BHCK4059
Interest and dividend income on securities	HI	01.d.	BHCKB488 +BHCKB489 +BHCK4060
Income from lease financing receivables	HI	01.b.	BHCK4065
Interest income on balances due from depository institutions	HI	01.c.	BHCK4115
Interest income from trading assets	HI	01.e.	BHCK4069
Interest income on federal funds sold and securities purchased under agreements to resell	HI	01.f.	BHCK4020
Interest Expense on Time deposits of $100,000 or more in domestic offices	HI	2.a.(1)(a)	BHCKA517
Interest Expense on Time deposits of less than $100,000 in domestic offices	HI	2.a.(1)(b)	BHCKA518
Interest Expense on other deposits in domestic offices	HI	2.a.(1)(c)	BHCK6761
Interest Expense on deposits in foreign offices, Edge and Agreement subsidiaries, and IBFs	HI	2.a.(2)	BHCK4172

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