## Abstract

Using unique data sets on German banks, we decompose their net interest margin and quantify the different components by estimating the costs of the various functions they perform. We investigate three major functions: liquidity and payment management for customers, bearing credit risk, and term transformation. For 2013, the costs of liquidity and payment management correspond, in the median, to 47% of the net interest margin, with bearing of credit risk and earnings from term transformation accounting for 12 and 37%, respectively.

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## Notes

- 1.
Bolt et al. (2012) also model banks’ net interest margin as a function of the past and current interest rates and expected loss rates. However, their data set is much less granular (no maturity breakdown and no industry breakdown), so that they have to rely heavily on simplifying assumptions. Even in our data set, we have no information about borrowers’ creditworthiness or about soft information, which is fundamental to the German “Hausbank” relationships (see Elsas and Krahnen 1998).

- 2.
If we interpret the risk premium as a contribution to the unexpected loss in the Basel formula, the relationship between the probability of default (a measure for the expected losses) and the unexpected losses is not linear, but strictly monotonic increasing. In this context, Eq. (2) can be seen as an approximation. We refrain from a more sophisticated functional form so as to have a parsimonious model.

- 3.
- 4.
Our sample mostly consists of small and medium-sized banks that engage in little trading activity. For large banks, a significant part of the bond portfolio may belong to the trading book so that these bonds do not contribute to the interest income.

- 5.
We prefer fixed effects to random effects, since the Hausman test has shown systematic differences between coefficients, indicating inconsistency of the coefficients in the random effects specification.

- 6.
- 7.
- 8.
Some banks, most of them regional banks, did not report the number of ATMs, cards, and transactions; we treat these as missing values.

- 9.
Large banks comprise “Landesbanken”, “big banks,” and central cooperative institutions. We chose this grouping because individual groups differ in their income ratios due to differences in business models.

- 10.
For ease of readability, henceforth we use “industries” instead of “industries/sectors”.

- 11.
We rely on specification II-b to calculate the operating expenses for the provision of liquidity and payment management, as time trend and interaction term do not play a significant role, but the differentiation between PAYMENTS-IN and PAYMENTS-OUT does provide further information.

- 12.
This could be due to a short time horizon. Even in specification I, some banks face short time series as we control for mergers.

- 13.
The shares of the variances that are due to the cross-sectional variation are 98.3% for the net interest margin, 97.6% for the loans’ credit risk, 96.9% for the bonds’ credit risk, 94.1% for the earnings from term transformation, 99.0% for the cost of payment and liquidity management, and 95.9% for the variable “Other.”

- 14.
Correlations between variables and their squared terms in specification I and specification II are about 90%.

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## Additional information

The views expressed in this paper are those of the authors and do not necessarily reflect the opinions of the Deutsche Bundesbank. The authors thank Puriya Abbassi, Helmut Elsinger, Rodrigo Guimaraes, Peter Raupach, Benedikt Ruprecht, Alexander Schmidt, and the anonymous referee, as well as the participants of the Bundesbank seminar, the 17th SGF conference (2014, Zurich) and the conference “Achieving Sustainable Financial Stability” (2014, Berlin) for their helpful comments.

## Appendix

### Appendix

In this appendix, the weighting function \(h(\cdot )\) is derived, i.e., the function that shows how the past and current expected credit loss rates for an industry are to be weighted for the contribution to the net interest margin that covers the expected losses in a bank’s credit portfolios (see Eq. (1)). The expected loss rates \(\mu \left( {t_m ,j,m} \right) \) in \(t_m \) in industry*j* for newly granted loans with maturity *m* are relevant for today, i.e., at time *t*, for loans that were granted at time \(t_m \) and have not matured yet, i.e., \(m>v:=t-t_m \). We make two assumptions. First, the expected loss rate at time \(t_m \) is the same for all the loans in the initial maturity bracket under consideration, i.e., \(\mu \left( {t_m ,j,m} \right) =\mu _{t_m ,j,k} \). Second, the loan volume for a certain initial maturity *m* is spread equally across the maturity bracket *k*, i.e., \(g(m,a_k ,b_k )=1/(b_k -a_k )\), where \(g(\cdot )\) is the density, and \(a_k \) and \(b_k \) are the lower and upper bounds of the maturity bracket *k*, respectively. In a given time span \(\Delta t\), the fraction \(1/m\cdot \Delta t\) of loans with initial maturity *m* must be renewed to have a constant balance sheet. For \(1\le a_k <b_k \) and \(0\le v:=t-t_m <a_k \), the expression for the weighting function \(h(\cdot )\) is therefore

where \(v:=t-t_m \) is the time difference between today *t* and the point in time \(t_m \) in the past.

In the event that \(a_k \le v<b_k \), we can express \(h(\cdot )\) as

As we have only yearly data for the expected credit loss rates, we calculate the yearly average of the weighting function, i.e.,

For \(l\le a_k -1\), we obtain

and for \(a_k -1<l\le b_k -1\), the corresponding expression is

This can be seen using the formula \(\int {\ln (x)\mathrm{d}x=x\cdot \ln (x)-x+C} \). For the first maturity bracket, i.e., \(a_1 =0\) and \(b_1 =1\), the function \(h(\cdot )\) and its average \(h_{0,1} \) are set to 1. The values of the weighting function \(h_{l,k} \) are shown in Table 1.

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Busch, R., Memmel, C. Quantifying the components of the banks’ net interest margin.
*Financ Mark Portf Manag* **30, **371–396 (2016). https://doi.org/10.1007/s11408-016-0279-3

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### Keywords

- Net interest margin
- Credit risk
- Term transformation
- Liquidity and payment management

### JEL Classification

- G 21