Conceptual Framework

9. The theoretical and empirical literature has proposed several determinants of bank profitability, which can be grouped into three broad categories: (1) bank-specific, (2) cyclical, and (3) structural. Key determinants, the rationale for their inclusions, and previous empirical results on their relevance are summarized below. In many cases, the theoretical impact of these determinants on profitability remains inconclusive, which further motivates the empirical investigation.

Econometric Approach

14. To set the stage, and to facilitate comparability with other studies, the empirical approach begins with standard panel regression analysis. An abridged representation of the baseline specification is as follows:

where y_b,c,t denotes the headline profitability measures (ROA, ROE) and relevant income components (net interest income, non-interest income) for bank b, in country c, in year t; whereas X_b,c,t−1, Z_c,t, and W_c,t, encompass the bank-specific, cyclical, and structural determinants; Other_b,c,t includes (bank and time) fixed effects terms and a residual term, respectively. Building on this baseline specification, an array of robustness checks are conducted. More importantly, this specification forms the basis of the quantile regressions used to generate conditional profitability distributions.

Conditional Profitability Distributions

15. The most novel aspect of this chapter is the estimation of conditional bank profitability distributions. In particular, quantile regressions are used to generate profitability distributions conditional on the bank-specific, cyclical, and structural determinants reviewed above. Selected determinants can then be shocked to assess how the shape of the profitability distribution changes—an approach which clearly goes beyond standard comparative statics centered on averages. Importantly, this powerful method can be used to quantify how selected determinants influence the probability of banks’ profitability being above and below a certain threshold of interest.

16. The link between profitability and the underlying determinants can be made using quantile regressions. Consider the following simplified specification:

where $y_{b,c,t}^q,{\mathrm{\Xi }}_{b,c,t},{\epsilon }_t^q$, and q denote the measure of profitability, the set of (bank-specific, cyclical, and structural) determinants, a residual term (as well as bank and time fixed effects terms), and q denotes various percentiles of interest, for example, q = {0.05; 0.25; 0.50; 0.75; 0.95}, respectively.¹⁴ The estimated conditional quantile function (inverse cumulative distribution function) would in turn correspond to ${\hat{y}}_{b,c,t}^q(={\hat{\beta }}^q{\mathrm{\Xi }}_{b,c,t})$, which is used to generate the conditional profitability distributions.

17. The conditional distribution is estimated by fitting a flexible parametric distribution to the data. Given the noisiness of quantile functions estimates in practice, recovering the corresponding probability density function (PDF) will require smoothing of the quantile function. In line with the approach of Adrian, Boyarchenko, and Giannone (2017), this is accomplished via fitting a (parametric form) ‘skewed’ t-distribution:¹⁵

where $g\left(z\right)=\overline{g}(z;\nu )/s$, with $\overline{g}\left(\mathrm{.}\right)$ denoting the PDF of standard Student-t with ν degrees of freedom; z is given by ((y − μ)/s), with μ and s referring to location and scale parameters, respectively. Skewness is governed by shape parameter ξ. This functional form for the skewed t-distribution is based on that motivated by Fernandez and Steel (1998), further explored and refined in Giot and Laurent (2003) and Lambert and Laurent (2002); see also Boudt, Peterson and Croux (2009).¹⁶ For specified values for the conditioning variables, the four parameters {μ, s, ν, ξ} of the implied density are pinned down by minimizing the squared distance between the estimated quantile function, ${\hat{y}}^q$, and theoretical quantile function y^{q, f} (μ, s, ν, ξ) corresponding to the above skewed-t distribution. Specifically, the 5^th, 25^th, 50^th, 75^th and 95^th percentiles, for example, can be matched via distance minimization:

where μ ∈ ℝ, s > 0, ν ≥ 2 and ξ > 0. Notwithstanding the skewness property, the choice of a skewed-t functional form is advantageous from the perspective of flexibility. For example, as ν → ∞, f(y; μ, s, ν, ξ) is characterized by tail properties resembling a Gaussian; moreover, the density is symmetric when ξ = 1.

Data

18. Data on large euro area banks is collected from publicly available sources. Balance sheet and income statement information from the FitchConnect database over 2007–2016 are complemented with country-level macroeconomic data and various structural indicators. Following the approach adopted by the European Banking Authority and the ECB, bank statements at the highest level of consolidation were used. The 109 SSM-supervised banks amounted to about €23 trillion in total assets in 2015, the year with the largest number of banks in the sample (Table 1).¹⁷

19. It is important to recognize several features of the data which can affect the results. First, some indicators may change over time because of merger and acquisition activity. Second, banks that closed during the sample period were excluded bringing about survivorship bias. Third, some banks have sizeable international operation and are thus influenced by global macroeconomic conditions. Fourth, included in the list of significant institutions are those that are more like development banks and do not engage in traditional lending and trading activities.

20. Some of these potential concerns are addressed as follows: First, as discussed below, both bank and time fixed effects terms are included in the baseline regressions. The former accounts for time-invariant bank-specific features and the latter captures regional and global developments that may be important with banks with significant exposures beyond the euro area (and also captures turbulent market conditions). Second, as a robustness check, the regressions are re-estimated using a balanced sample of banks. Third, quantile regressions are considered which are less sensitive to outliers. The baseline specifications are also complemented by an array of robustness checks.

Key Trends and Stylized Facts

21. Average profitability has been on a downtrend since 2007, but there is wide variation among banks:

• To assess key trends more accurately, a balanced sample of 45 SSM-supervised significant institutions (SSM SIs), accounting for 56 percent of sample assets in 2016, is used. Figure 1 displays the median, 25^th and 75^th percentiles, as well as the weighted average for a few bank-specific variables in this sample over 2007–2016. The two headline measures of profitability, ROA and ROE, have been persistently low over the past decade, but with notable variation across banks. Moreover, banks’ average ROE continues to trail market estimates of the cost of equity, and analysts do not expect this situation to change quickly for many banks despite the ongoing recovery. It is also important to recognize recent progress: ROE in 2017Q4 was about 6 percent on average across all SIs.

• Table 2 summarizes some stylized facts that reinforce the concerns associated with euro area bank’s profitability. The ROA outturn for 2016, at 0.34 percent, is the same as the sample average and has a sizeable standard deviation. Despite a higher reading relative to the 2007–2016 period, average ROE stood at only 4.1 in 2016. The starker variation across banks partly reflects the fact that small difference in leverage (the inverse of Equity/Assets) could make a significant difference in ROE among banks.

22. Low profitability is pervasive across bank business models. A scatterplot of SSM banks against two indicators—loans-to-assets and deposits-to-assets—enables us to see the distribution of SSM assets by broad business models (Figure 1). Although this two-dimensional business model classification is simplistic and based on coarse proxies, it nevertheless highlights the diversity of the largest euro area banks. Banks in the northeast corner are designated as “traditional” banks with an above-median share of loans-to-assets and deposits-to-assets and comprise €4 trillion in assets. On the other extreme are the “nontraditional” banks that have a large share of trading assets and depend more on wholesale funding. This set of banks includes the euro area global systemically important banks (G-SIBs) and accounts for €14 trillion in assets. Many banks are scattered across these two polar cases. The red dots indicate banks with ROE less than 8 percent, the lower range of the minimum cost-of-equity desired by investors—the incident of low ROE is strewn across a wide variation in business models.

23. NPL and cost-to-income ratios also display significant dispersion across banks. A fallout of the crises in the euro area has been high nonperforming loans across banks (as a share of gross loans, that is, the NPLs ratio), which is coming down gradually, but progress remain uneven (Figure 1).¹⁸ The average NPL ratio remained elevated in 2016, albeit concentrated in some banks, as reflected in the large standard deviation (Table 2). Overhead (non-interest) costs, as a share of operating income, is higher in 2016 compared to the sample average, likely reflecting the inertia of expenses related to large branch networks and servicing of nonperforming loans for traditional banks, and fees and fines for others. Other key bank-specific characteristics vary notably across banks as well.

24. Average GDP growth, which included both the crisis and the recovery, is below to the current estimates of potential growth. Over the 2007–2016 sample that is considered in the analysis, average real GDP growth was 0.8 percent and with wide cross-country differences due to both the global financial crisis and the European debt crisis. In fact, the standard deviation of growth was 3.3 percent as shown in Table 2. In 2016, growth rose to 1.2 percent and its standard deviation declined. This observation is in line with the synchronized nature of the recovery of the euro area countries, with all countries growing, and the variation in growth among countries at the lowest since the advent of the euro. Nevertheless, the IMF World Economic Outlook projects real GDP growth in the euro area to hover about 1½ percent over the medium term, suggesting that the current spurt of growth is likely not permanent in nature.

25. Slicing through the distribution of ROE reveals that the NPL and cost-to-income ratios reveal clear patterns. Table 3 shows the main bank-specific characteristics across four ROE levels in 2016: below the 25^th percentile (<Q1), between 25^th and 50^th percentile (Q1–Q2), between 50^th and 75^th (Q2–Q3), and above 75^th percentile (>Q3). The skewed nature of the ROE distribution is noticeable: the ROE of banks in the left tail have an average of −16 percent. Banks in this end of the distribution have an ROA of −1 percent, an NPL ratio of 22 percent, and a cost-to-income ratio of 81 percent on average and seem to confront similar challenges, but to varying degrees, which tend to be distinct from the other SIs in the sample. Specifically, moving rightwards across the columns uncovers a monotonic decrease in both cost-to-income and NPL ratios.

Benchmark OLS Regression Analysis

26. The baseline results show that real GDP growth and the NPL ratio, besides total assets, are the most reliable determinants of bank return on assets. Table 4 shows the baseline ROA specification under the first column, as well as key ROA components as dependent variables the shed further light on the main channels driving the results. Other than size, real GDP growth and the NPL ratio appear to be the two statistically significant determinants of ROA. A 1 percentage point increase in growth would raise ROA by 27 basis points. Given that average ROA across banks over 2007-2016 was 34 basis points, this is a notable increase. At the same time, recall that growth over the sample period had an average of 0.8 percent—in other words, the increase in growth is large. The results also indicate that the marginal effect of a 1 percentage point lower NPL ratio is a rise in ROA by 5 basis points. On average, the link between ROA and cost-to-income, concentration, and business model indicators are estimated less precisely. Although differences in sample, specifications, and econometric methodology, render comparisons difficult, overall, these findings are broadly similar to those of the studies discussed above.

27. The components of ROA were then used as dependent variables to explore the channels at play. Higher growth results in a rise in noninterest revenue streams (Table 4) and a decline in loan-loss provisioning (column 4). Lower NPL ratios would reduce provisioning costs and, hence, increase ROA. Note also that 60 percent of the effect of lagged NPLs on ROA stem from the provisioning needs (based on column 1 and column 4).

Robustness Analysis

28. Growth and NPLs remain significant determinants of profitability even as other variables are included in the baseline specification (Table 5). Various additional variables are added to the baseline ROA to assess the robustness of the main results. Bank-, country-, and region-specific variables groups are considered. For the first group, bank-specific loan growth and the change in the NPL ratio are considered. The second group includes country-specific measures of the slope of the yield curve (the difference between the 5-year and 3-month government bond yields) and FCIs. The FCI measures the ease of obtaining financing relative to each country’s history, see Arregui and others (2018) for further details. The third group includes a single variable, namely the area-wide level of the short-term interest rate (the ECB estimate of the 3-month zero-coupon yield on AAA securities). The baseline specification is also re-estimated using a balance sample as well as with the general method of moments (GMM).

29. The change in the NPL ratio is a significant determinant but strongly correlated with GDP growth. When added, the change in the NPL ratio is statistically significant and has the expected sign. Therefore, both the stock and the flow of NPLs act as a drag on profitability owing to servicing costs and the reduced availability of funds to lend. Since the GDP growth term is included and attention focuses on medium-term effects, the term is not included in further analysis.

30. A steeper yield curve or higher short-term interest rates do not appear to help profitability of these banks on average. The slope of the yield curve is an indicator of the intermediation margin given by the spread between lending and funding rates. All else equal, a steeper yield curve would raise net interest income. However, higher long-term interest rates would reduce the valuations of longer-term securities (that are held in the available-for-sale portfolio for instance). Since the crisis, the maturity of such securities held by banks have gone up, and so the valuation effects are sizeable even as net interest income improves with higher long-term interest rates. Furthermore, higher interest rates could push highly indebted bank borrowers to default on their loan payments that would increase provisioning costs and decrease profitability. Likewise, bank profitability and short-term interest rates are positively correlated, but this correlation is not statistically significant.

31. Tighter financial conditions tend to adversely affect bank earnings. Recall that the FCI discussed above contains various spreads and can therefore affect bank profitability in at least two ways: First, a spike in spreads would result in valuations losses (on holdings of both corporate and government securities). Second, funding costs are likely to rise faster than lending rates, thereby compressing interest margins.

32. Including a lagged dependent variable or using a balanced sample highlight the robustness of the main findings. Following the ECB (2015) and Das and Xu (forthcoming), a lagged dependent variable is included in the baseline and the model is estimated using the GMM estimator developed by Arellano and Bond (1991). There are two main takeaways from these results: First, the lagged dependent variable is statistically insignificant (Table 5). It also has a negative coefficient, perhaps a reflection of large yearly fluctuations in profitability possibly owing to the crisis experiences. Second, the GMM results are consistent with the baseline specification. For example, both the “short-run” coefficients and their “long-run” counterparts are broadly in line with those in the other specifications. Note also that re-estimation using a balanced sample produces results very similar to the baseline specification.

33. Using ROE yields broadly similar findings. The regressions discussed above were estimated using ROE as the main profitability indicator and again indicate the growth and the NPL ratio are the robust determinants (Table 6). Although total assets cease to be a significant determinant, the change in the NPL ratio gains in significance. As will be discussed below, the OLS regressions may mask underlying non-linear relationships, which motivates the use of quantile regression analysis.

34. A final robustness check considered risk-adjusted profitability metrics. Following Demirguc-Kunt and Huizinga (2010), the z-score (also interpreted as a measure of bank risk) is considered. The z-score reflects the number of standard deviations that a bank’s rate of ROA must fall for the bank to become insolvent. It is constructed as the sum of the mean rates of ROA and the equity-to-assets ratio divided by the standard deviation of ROA (Roy, 1952). A higher z-score signals a lower probability of bank insolvency. In addition, risk-adjusted variants of ROA and ROE are considered whereby each profitability metric is scaled by its respective standard deviation (broadly analogous to a Sharpe ratio). The entire 2007–2016 sample was used to calculate the needed standard deviations as accurately as possible. This transforms the panel data set into a cross-section (thereby losing many degrees of freedom). Regressions using the full set of banks and the balanced set of banks are shown in Table 7. Note that the NPL ratio is highly statistically significant, whereas the correlation between growth and risk-adjusted profits is less precisely estimated in the cross-section.

Quantile Regression Analysis

35. Quantile regressions reveal that growth and the NPL ratio remain the most robust determinants of bank profitability. The results for three quantiles (25, 50, and 75) are reported for ROA and ROE in Table 8 and Table 9, respectively. To facilitate comparisons, the baseline OLS specification is shown in the first column in each table. For both profitability metrics, growth and the NPL ratio have the expected signs and are statistically significant across all quantiles. Notably, the (absolute value of the) coefficients on growth and NPLs decrease monotonically across the 25^th to the 75^th quantiles in both sets of regressions. For example, in the ROA regressions, the growth coefficient is 0.2 versus 0.09 in the 25^th and 75^th quantile regressions, respectively. A similar pattern holds in the case of the NPL ratio. These findings suggest that banks with the greater profitability challenges stand to benefit the most from an increase in GDP growth and from lower NPL ratios.

36. In contrast to the OLS regressions, the quantile regressions suggest that improved operational efficiency is important for bank profitability. The quantile regressions indicate that lower cost-to-income ratios are associated with higher ROA for banks outside of the weakest end of the profitability spectrum.¹⁹ Changes to business models hold promise as well. Evidence points to a positive correlation between ROA and a greater deposit-to-asset ratio.