Risk Adjusted Efficiency and the Role of Risk in European Banking Mohamed Shaban Universy of Leicester School of Management A co-authored work-in-progress paper wh Mike Tsionas (Lancaster) and Meryem Duygun (Leicester)
Intuive introduction It is assumed that banks managers are risk averse. Consequently they manage the banks resources efficiently to obtain risk adjusted return. Tradional finance theory is based on the concept of the higher risk, the higher return. However, higher level of risk might in turn negatively affect banks efficiency that will have impact on profabily and risk. Hence distorting or disturbing the risk adjusted return. The banking sector is a very complicated organism studying from one angle might not provide all the answers. The complicated network and the sophisticated mathematically driven products further complicates the operation of banks and hence our understanding of this operations. Assessing banks from the point of view of risk and return could be an easy approach to understand the complexy of the industry. However, we should not isolate this approach from the pressure on banks manager to perform better in a competive market.
Motivation Few studies cover the relationship between risk and prof efficiency. Ignoring risk might provide misleading prof efficiency. The link between risk, financial stabily and profabily or performance. The need for indicators that can provide early warning on the industry augmented risk to policy makers. 3
Objectives Proposing a new modelling approach to measure the effects of financial instabily in the banking system. The model is organized around the prof function, building on the popular z-score. We perceive prof inefficiency as the unrealized prof potential and examine whether this systematically depends on the three concepts that make up the z-score: return, capalization and volatily of return. Volatily is measured endogenously using a panel stochastic volatily model. Using Simulated Maximum Likelihood (SML). We relate prof inefficiencies systematically to volatily, past profabily, capalization, conventional and unconventional z-scores. This allows us to investigate whether the tradional z-score plays an independent role given that we include s constuent into the model. We are also keen to understand whether the models wh or whout the z-score perform better relative to the new proposed models. 4
Overview production and risk Just and Pope (978) JE: Appropriate formulation for the production function under risk. Opposed the implic assumption that the marginal risk, defined as the partial derivative of the variance of output wh the respect to the k th inputs will be posive for all inputs. A change in variance for random components in production factors not necessarily imply a change in expected output when all production factors are held fixed [ E(y)/ E(e) = 0 possible. 5
Overview production and risk (cont d) Griffths and Anderson (98) JoASS: Provide empirical implementation of Just and Pope (978) model in the context of panel data. The disturbance term of the models includes both time specific and firm specific components. Perms the variance of output to increase or decrease as the kth input is increased. 6
Overview production and risk (cont d) Kumbhakar (993) EL: Measure production risk and technical efficiency using panel data. Flexible translog function where risk is incorporated into the model, and hence affects the estimates of technical efficiency (i.e. the standard stochastic frontier model becomes heteroskedastic). Similar to Just and Pope (987) and Griffhs and Anderson (98) a multi-step procedure is used. 7
z r c T i T r ri t Z-Score v, u, Total risk can be decomposed into two components there is a bankspecific and timevarying measure of insolvency According to Boyd & Graham (986) and Boyd et al. (993) =z can be observed as the upper bound of the probabily of insolvency (that is the probabily of negative capal asset ratio plus ROA) This implies that the z-score can be used in the wider context of insolvency, prudence and stabily of financial instutions. Z r c 8
The model w, q max : pq wx g( p, w, x) 0 M K p, x () where g( p, w, x) represents the pricing opportuny function, x,q represent inputs and p,w represent output and input prices. However since profs are often negative, the popular translog functional form cannot be used. For that reason we use the revenueto-cost function pq w, q max : g( p, w, x) 0 M K wx ' p, x 9
Revenue-to-cost function specification log f w, q ; W, β v u where f represents a functional form like the translog, is a vector of parameters, W is a vector of other variables, v is noise and u 0 represents prof inefficiency. for presentation simplicy, we assume that is actually the ratio of profs over assets and log w,log q x so that we can wre x β v u. () log 0
Autoregressive Dynamic Regression (ADR) L L l l i, t l x l i, t lβl i, t x i, t δ. (3) log log log v u lags of differences of dep. variables and regressors lagged levels of dep. variable and regressors Pesaran and Shin (998) v ~ N0, independently of, u ~ N 0, u here represents the volatily of the prof-assets ratio. We can use a panel stochastic volatily model: log log c log v v, (4) i, t i, t i, t i, t ~ 0, N where captures the effect of past returns and c is the capal-to assets ratio. The abnormal returns are included in the equation in the form of v, and v,
Prof efficiency, profabily, volatily, and capalisation log u log u log log c c og z Z o i, t 3 i, t 3 3 i, t 4 i, t 5 i, t 5 abnormal return effects persistent inefficiency return volatily capalization effects profabily zeffects vi, t vi, t 3 log ut 4 log t ~ N 0,, (5) n t i i, t u n u contagion/spillover effects average inefficiency in the sample u n t n i i, t log average volatily a proxy for contagion / spillover effects z c The above model represents a val question in this research. Whether prof inefficiency can be reduced based on past profabily, capalization and volatily of returns? Where: measures the inefficiency persistence effect, measures the effect of volatily, 3 provides the effect of capalization, and 4 measures the effect of profabily. 5 to test whether the z-ratio plays an independent role given that returns, capalization and return volatily have been controlled for in the prof loss equation (i.e. the equation for log u ).
Volatily of inefficiency, log log c log v v u u u, i, t u, i, t i, t i, t 3 i, t 4 i, t ~ 0, N, (6) We consider the volatily of inefficiency as the second source of risk in the model. In this specification, in addion to abnormal returns (v), we also include their technical inefficiency version (u) in the form of u, u. i, t i, t 3
Data The dataset includes commercial, cooperative, savings, investment and real-estate banks in Eurozone countries that are listed in the IBCA-Bankscope database over the period 00 0. After reviewing the data for reporting errors and other inconsistencies, we obtain an unbalanced panel dataset of 9,03 observations, which includes a total of 4,065 different banks. The Bankscope database reports published financial statements from banks worldwide, homogenized into a global format, which are comparable across countries and therefore suable for a cross-country study. Nevertheless, should be noted that all countries suffer from the same survival bias. 4
Data (cont d) The number of banks by year included in our sample is: 00:,4; 00:,08; 003:,909; 004:,994; 005: 3,053; 006: 3,075; 007: 3,04; 008:,990; 009:,95; 00:,949 and 0:,88. The addions to the sample are not necessarily new market entrants, but rather successful banks that are added to the database over time. Exs from the sample are due to eher bank failures or mergers wh other banks or due to changes in the coverage of the Bankscope database. Our sample covers the largest cred instutions in each country, as defined by their balance sheet aggregates. Due to the specific features of the German banking system (large number of relatively small banks), our sample is dominated by German banks. 5
Variables For the definion of bank inputs and outputs, we follow the vast majory of the lerature and employ the intermediation approach proposed by Sealey and Lindley (977), which assumes that the bank collects funds, using labor and physical capal, to transform them into loans and other earning assets. In particular, we specify three inputs, labor, physical capal and financial capal, and two outputs, loans and other earning assets (which include government securies, bonds, equy investments, CDs, T-bills, equy investment etc.). input prices: the price of financial capal is computed by dividing total interest expenses by total interest bearing borrowed funds. the price of labor is defined as the ratio of personnel expenses to total assets. the price of physical capal is defined as the ratio of other administrative expenses to fixed assets. output prices: the price of loans is defined as the ratio of interest income to total loans. the price of other earning assets is defined as total non-interest income to total other earning For a review of the various approaches that have been proposed in the lerature for the definion of bank inputs and outputs see Berger and Humphrey (99). 6
RESULTS 7
Estimated models SFM: Variances and are fixed and vary only over i. wh this u, model is possible only to compute technical (in)efficiency measures but not compute z-scores etc. Model I: Variance depends on the characteristics in (4) but variance is constant. Model II: Both variances and the characteristics. u, depend on 8
SFM MODEL I MODEL II log, 0.30 0.85 0.5 (.7) (.67) (.89) c -0. -0.350-0.78 (-4.33) (-5.7) (-6.700) log, 0.77 0.8 0.67 (3.4) (4.566) (8.9) v, 0.336 0.6 0.0 (.95) (3.78) (3.66) v, -0.07-0.0-0.07 (-6.7) (-4.78) (-5.55) log, logta 0.07 0.05 0.0 (0.9) (.85) (.35) c logta -0.035-0.0-0.0 (3.56) (5.66) (5.8) log, logta -0.07-0.05-0.09 (-4.588) (-7.0) (-6.5) v, logta 0.07 0.03 0.0 (6.779) (4.77) (3.660) v, logta -0.006-0.009-0.00 (-3.7) (-6.5) (-4.503) average log t 0.5 0.89 (.3) (.78) average log t 0.4 0.8 average volatily (.78) (4.89) average vt a proxy for 0.07 0.05 contagion / (8.) (3.89) average v -0.0035-0.00 t spillover effects (-4.89) (-5.80) average c -0.7-0. t (-.67) (-8.66) average log t logta -0.005-0.00 (6.80) (3.80) average log t logta 0.0034 0.005 (.78) (6.89) average v t logta 0.005 0.00 (3.7) (4.67) average v t logta -0.00-0.003 (.66) (4.70) average ct logta 0.07 0.03 (4.84) (3.7) u, 0.3 (6.78) average ut 0.055 (4.3) log,, 0. (4.90) average log, t 0.05 (3.7) u, logta 0.055 (.89) average u t logta 0.07 (5.85) log,, logta 0.7 (.78) average log, t logta 0.076 (3.98) z 0.067 0.033-0.006 t (0.78) (.5) (-.007) Empirical results for log (volatily of profabily -Risk) wh alternative specifications of regressors (t-statistics appear in parentheses) log log c log v v i, t i, t i, t i, t. Lagged profabily seems to increase risk (variabily of prof). Higher capal asset ratio c tend sto reduce risk (capal buffer). 3. Risk is persistent. 4. Higher abnormal returns is associated wh higher risk. 5. The larger the bank, the higher the effect of profabily to increase risk. 6. The larger the bank,the negative the effect of volatily on risk. 7. The larger the bank, the higher effect of capalisation on reducing risk. 8. Contagion risk (industry) tends to exacerbates bank risk. 9. Higher Prof efficiency at both bank and industry level is associated wh higher risk. 0. Higher variabily in prof efficiency tend sto exacerbate risk.. The larger the banks the larger the effect of profabily, risk, and efficiency risk on banks risk (i.e. increase risk). 9
Empirical results for log (volatily of profabily -Risk) wh alternative specifications of regressors (cont d) (t-statistics appear in parentheses) log log c log v v i, t i, t i, t i, t SFM MODEL I MODEL II Z zt z 0.033 t (.5) logta -0.055 Z, 0.57 (3.8), logta 0.003 (5.7) (-.) 0.7 (.7) -0.0045 (-.7) -0.006 (-.007) 0.008 (0.340) 0.00 (.78) 0.00 (-.07). Neher tradional Z-score nor the z-score from the model have significant effect on the volatily of prof. This something that we are investigating further.. In other words by including the components that comprise z-score in the model, neher the tradional Z-score nor the model generated z-score systematically affects banks total risk. 3. This suggests that we can use the model generated z-score as an indicator of insolvency and in s wider term as indicator for financial stabily. 0
SFM MODEL I MODEL II average 0.007 0.008 log t logta (4.50) (3.9) average log t logta 0.05 0.03 (3.67) (5.90) average v t logta 0.00 (3.89) (6.780) average v t logta 0.000 (4.9) (3.8) average ct logta -0.0037-0.005 (3.90) (.78) u, -0.78 (-5.89) average volatily average ut a proxy for -0.0 contagion / (-4.44) log u, i, t spillover effects 0.77 (7.9) average log ut, 0.06 (3.44) u, logta 0.048 (7.7) average u t logta (3.33) log,, logta 0.04 (3.70) average 0.033 log ut, logta (5.8) z t 0.6 0.06 (0.87) (0.90) zt logta -0.003-0.00 (0.85) (.7) Z, 0.05 0.07 0.07 (5.9) (4.49) (6.0) Z, logta -0.0-0.03-0.0078 (-3.38) (-6.00) (-4.30) Empirical results for log u (prof inefficiency) (tstatistics appear in parentheses). Inefficiency is persistent.. z-score generated from the model not significant. log u log u log log c c og z Z o i, t 3 i, t 3 3 i, t 4 i, t 5 i, t 5 persistent inefficiency return volatily capalization effects profabily zeffects v v log u log i, t i, t 3 t 4 t abnormal return effects contagion/spillover effects 3. Z-Score (tradional): Lower probabily of insolvency is associated wh higher (lower) inefficiency(efficiency). It has a systematic effect on prof inefficiency.
Empirical results for log u (prof inefficiency) (tstatistics appear in parentheses) SFM MODEL I MODELII log, -0.07-0.0-0.04 log log, log 3 log, 3 3, 4 og, 5, 5 (-3.67) (-5.7) (-.89) persistent inefficiency return volatily capalization effects profabily zeffects c -0.3-0.0-0.35 (-4.55) (-3.87) (-5.55) vi, t vi, t 3 log ut 4 log t log u, i, t 0.35 (4.77) 0.446 (8.) 0.7 (4.76) abnormal return effects contagion/spillover effects v, -0.6-0.8-0.0. Lagged profabily seems to decrease prof (-6.77) (-3.67) (-6.50) v inefficiency., 0.05 0.0 0.09 (4.89) (3.94) (4.5). Higher capal asset ratio c tend to reduces log, logta -0.005-0.000-0.003 (-6.7) (-9.8) (3.77) inefficiency. c logta -0.07-0.03-0.05 3. Higher risk is associated wh higher (-6.7) (-3.89) (-4.78) log inefficiency. u,, logta 0.05 0.07 0.06 (7.90) (3.5) (4.55) v 4. Higher abnormal returns is associated wh, logta -0.8-0.3 (-4.99) (-3.7) (-5.989) lower inefficiency. v, logta 0.000 0.005 (.85) (.7) (.056) 5. Contagion effect (industry effect) average log t -0.0056-0.000 6. Higher profabily at industry level reduces average volatily (-.89) (-4.78) average log t prof inefficiency. a proxy for -0. -0.74 contagion / (-4.90) (-3.0) 7. Higher variabily of industry s profs is average v spillover effects t -0.9-0.6 (-7.004) (-4.78) associated wh higher prof efficiency. average v t 0.003 0.007 8. Higher capalisation at industry level seem to (.87) (.78) average c 0.003 0.006 increase inefficiency. t (.78) (3.9) u u c c z Z o i t i t i t i t i t
SFM MODEL I MODEL II log, 0.007 0.00 0.003 (.78) (3.8) (6.00) c -0.45-0.6-0.78 (-3.) (-4.89) (-.6) log u, i, t 0.6 0.555 0.60 (8.76) (5.79) (7.9) v, 0.033 0.0 0.07 (4.4) (5.30) (3.44) v, -0.005-0.003-0.007 (-3.38) (-5.59) (-8.0) average log t 0.006 0.00 (3.0) (.89) average log t -0.07-0.056 (-5.89) (-4.30) average volatily average vt -0.555-0.5 a proxy for (-6.40) (-9.0) contagion / average v t 0.003 0.00 spillover effects (.4) (5.55) average c -0.04-0.09 t (-.35) (-4.0) u, -0.04 (-4.90) average ut -0.05 (-6.8) log, -0.07 (-6.7) average log t -0.0035 (-7.00) z t 0.78 0.344 0.57 (.) (0.97) (.0) Z, 0.030 0.045 0.09 (3.30) (4.78) (5.30) Empirical results for (volatily of prof log u, inefficiency) (t-statistics appear in parentheses) (summarised table). Higher profabily increases volatily of inefficiency.. Higher capal reduces volatily of inefficiency. 3. Higher abnormal returns increases volatily of inefficiency. 4. Higher prof volatily increase the volatily of prof inefficiency. 5. The higher Z-score the lower the probabily of insolvency reduces the 3
Prof efficiency All the models provide negatively skewed distribution for prof efficiency. SFM: (blue line) the average efficiency is located almost in the middle between the average efficiency from model and model. Model I: (green line) the lowest average efficiency and they highest variance, Model II: (red line) the highest average efficiency. Distribution of prof efficiency 4
Risk adjusted efficiency Crisis time Warning window 5
z-score Crisis time Warning window 6
z-score distribution over the period See 005 See 004 See 006 See 005 See 006 See 004 7
Efficiency distribution over the period See 004 See 006 See 005 See 005 See 006 See 004 8
CONCLUSION 9
What we achieved? One model two measures I. Risk adjusted efficiency II. z-score model generated (vary over time: Bank specific, country specific [average], for whole sample [average] and for sub-samples [average]) Profabily and risk Size and risk Capal and risk Efficiency and risk Performance risk and total risk Contagion effect 30
Conclusion Higher profabily is associated wh higher risk and higher risk is associated wh higher profabily. Banks capal acts as buffer and the higher the capals the lower the risk and the lower the banks prof inefficiency. Higher inefficiency augments risk and higher risk increases the level of banks inefficiency. Volatily in performance (inefficiency) augments inefficiency and risk. 3
Conclusion (cont d) Large banks are important drivers for the risk, return and efficiency in the banking industry. The complicated banking network motivates us to look at the performance, risk, and profabily of both large and small banks. The insolvency of large banks might not instantaneously be reflected on their own z-score. Howevers could have a leading effect on small banks z-score. 3
Conclusion (cont d) The volatily of performance overtime is an essential indicator for future financial disruption. It is important to incorporate risk into performance measures to be able to detect such volatily. Small banks tend to be affected more from the industry risk. They also tend to recover slowly compared to large banks. 33
Conclusion (cont d) A bank specific time variant insolvency risk is achievable measure. It can provide more insight compared to tradional Z-score measured. 34
THANK YOU 35