Accepted Refereed Manuscript Of: McMillan D & McMillan
Accepted refereed manuscript of:McMillan D & McMillan F (2017) The interaction between risk, return-risktrade-off and complexity: Evidence and policy implications for US bankholding companies, Journal of International Financial Markets, Institutions andMoney, 47, pp. 103-113.DOI: 10.1016/j.intfin.2016.11.004 2017, Elsevier. Licensed under the Creative Commons AttributionNonCommercial-NoDerivatives 4.0 y-nc-nd/4.0/
The Interaction between Risk, Return-Risk Trade-off and Complexity:Evidence and Policy Implications for US Bank Holding CompaniesDavid G. McMillanAccounting and Finance DivisionStirling Management SchoolUniversity of StirlingFiona J. McMillanBusiness SchoolUniversity of DundeeApril 2015AbstractThis paper examines two aspects of bank risk with a particular emphasis onexamining the interaction between them. Moreover, throughout the analysiswe differentiate between non-complex and complex banks, the latter of whichcould be seen as holding a further level of risk. We wish to establish how theserisk behaviours interact with bank specific, market structure and economicfactors. Key results indicate that earnings volatility (business risk) increaseswith market power but decrease with size and output. While risk-taking(managerial risk) decreases with market power and increases with size andoutput. Furthermore, in examining return per unit of risk, results demonstratethat increase return and risk-taking is associated with bank specific factors andthe economic environment, whereas decreased risk taking is associated withmarket structure. This suggests a management of risk, which increases aroundfactors under bank control or improving external environment but decreaseswith the interaction of competitors. Overall, the results suggest that policyshould focus on liquidity and equity buffers that should operate countercyclicality but size and market structure per se are not determining factors forhigher risk. In terms of the recent financial crisis, it is likely that the greatmoderation that proceeded it lead to higher risk-taking due to higher economicgrowth but without the necessary buffers being built up.Keywords: Banks, Risk, Earnings, Volatility, Risk-Return,Complex, Prospect Theory, Market Structure, Sharpe RatioJEL: C23, G21Address for Correspondence: Professor David McMillan, Accounting and Finance Division,Stirling Management School, University of Stirling, FK9 4LA, Scotland, UKPhone: 44(0)1786-467309; Fax: 44(0)1786-467308E-mail: david.mcmillan@stir.ac.ukElectronic copy available at: https://ssrn.com/abstract 2874434
The Interaction between Risk, Return-Risk Trade-off and Complexity:Evidence and Policy Implications for US Bank Holding CompaniesApril 2015AbstractThis paper examines two aspects of bank risk with a particular emphasis onexamining the interaction between them. Moreover, throughout the analysiswe differentiate between non-complex and complex banks, the latter of whichcould be seen as holding a further level of risk. We wish to establish how theserisk behaviours interact with bank specific, market structure and economicfactors. Key results indicate that earnings volatility (business risk) increaseswith market power but decrease with size and output. While risk-taking(managerial risk) decreases with market power and increases with size andoutput. Furthermore, in examining return per unit of risk, results demonstratethat increase return and risk-taking is associated with bank specific factors andthe economic environment, whereas decreased risk taking is associated withmarket structure. This suggests a management of risk, which increases aroundfactors under bank control or improving external environment but decreaseswith the interaction of competitors. Overall, the results suggest that policyshould focus on liquidity and equity buffers that should operate countercyclicality but size and market structure per se are not determining factors forhigher risk. In terms of the recent financial crisis, it is likely that the greatmoderation that proceeded it lead to higher risk-taking due to higher economicgrowth but without the necessary buffers being built up.Keywords: Banks, Risk, Earnings, Volatility, Risk-Return,Complex, Prospect Theory, Market Structure, Sharpe RatioJEL: C23, G211Electronic copy available at: https://ssrn.com/abstract 2874434
1. Introduction.This paper seeks to examine two aspects of bank risk, with a particular emphasis on how theyinteract with each other and how this impacts across banks comprised of differing complexityand with the aim of revealing the attendant policy implications. Following the financial crisis,much policy discussion has surrounded bank size and market structure. However, a completeset of empirical evidence regarding bank risk is lacking in which to ensure such policy isinformed. The aim and contribution of this paper is to enhance our understanding of bank riskbut rather than examine elements of risk isolation, the objective here is to examine theinteraction between different components of risk, including business risk and managerial riskas well as bank organisational complexity. The results of this paper should improve theevidence-based environment in which policy is established.In examining bank risk, first, we model the determinants of earnings volatility withthe aim of uncovering the links between volatility and three sets of variables; bank specificfactors, market structure and economic activity. While, this approach, which capturesbusiness risk, has previously (though not extensively) been considered within the literature, itserves as a base for the remainder of the paper. Second, we examine the relationship betweenearnings and earnings volatility; that is, the return and risk trade-off. This, therefore, capturesmanagement risk and has not been widely considered previously. Again, we are interested inhow the three sets of variables (bank specific, market and economic) affect the return-risktrade-off. Having considered these two elements risk separately, we are particularly interestedin how they interact, specifically in terms of whether the variables that are associated with anincrease or decrease in volatility are the same variables that strengthen or weaken the tradeoff with returns. Moreover, each of these analyses are conducted within the context ofseparating banks that are considered as complex versus those that are considered as noncomplex with regard to their structure.2
The aim of this paper is to contribute to the debate regarding bank risk and to providepossible policy implications. In particular, volatility provides a proxy for risk, where suchrisk in turn has implications for economic stability. Thus, knowledge of how bank specificand market structure factors as well as economic performance impact on risk has obviouspolicy implications. Furthermore, the nature of the relationship between earnings andearnings volatility can lead to inferences about the risk preferences of bank management,which again can lead to policy implications in designing incentives for management. Anunderstanding and examination of such risk is important given the recent crisis period.Furthermore, we separate banks into two risk categories as defined by a complexity indictorassigned to bank holding companies by the Federal Reserve. Again, greater complexity canbe regarded as a risk factor. This is of interest as policy discussion usually surrounds onlywhether banks are large or not rather than more specific detail regarding whether theinstitutional is complex and the nature of that risk.While there has been a significant amount of research examining the determinants ofbank earnings themselves, there is a relative paucity of studies examining earnings volatilityand the relationship between the volatility and mean of earnings. In particular, highly volatileearnings will affect a bank’s capital base and could lead to instability in the banking sector(see, for example, Albertazzi and Gambacorta, 2009; Couto, 2002). In turn, a banking systemthat lacks sufficient stability could impact negatively upon economic growth (e.g., Loayzaand Rancière, 2006; Lin and Huang, 2012). While within this context we may be able to infermanager risk-taking behaviour through the relationship between the mean and volatility ofearnings. In this respect, therefore, understanding the factors that affect earnings volatilitywill also contribute to the policy debate following the crisis, for example, regarding bank sizeand bank market concentration. That is, whether large banks are better able to withstandsignificant volatility without impact upon their operations and are able to diversify in order to3
reduce volatility (Stever, 2007). Similarly, a concentrated banking system may be less proneto volatility and exhibit greater stability (e.g., Beck et al, 2006; Schaek et al, 2009). Although,an alternative view exists whereby more concentrated banking systems become more fragile(Boyd and De Nicolo, 2005). Further, understanding periods when banks appear to exhibithigher levels of risk, perhaps undertake more risk, when managers of banks are more prone toengage in risk-taking behaviour and whether this differs between banks of differingcomplexity can enhance the discussion surrounding regulation, governance and incentives forrisk (Gonzalez, 2005; Laeven and Levine, 2009).As noted above, there exists a range of studies that have examined the relationshipbetween various market and bank characteristics and bank earnings, however, there isrelatively few that have examined earnings volatility. With regard to the former, a smallselection includes Levonian (1993), Roland (1997) and Berger et al (2000) for the US,Goddard et al (2004, 2010) for Europe and Liu and Wilson (2013) for Japan, while, Goddardet al (2013) examine a range of markets. With regard to the literature more closely related tothis paper, Boyd and Runkle (1993) argue that there exists a negative relationship betweenearnings volatility and bank size for US bank holding companies, while Stiroh (2004) arguesthat no such relationship exists. Most recently, De Haan and Poghosyan (2012a,b) examinethe relationship between size and earnings volatility both for commercial banks and bankholding companies. De Haan and Poghosyan (2012a) examining commercial banks argue thatthere is a negative relationship between bank size and earnings volatility, although thenegative relationship is weakened with increased market concentration. This result was basedon examining US banks over the relatively short period of 2004-2009. De Haan andPoghosyan (2012b) examining bank holding companies over a period from the mid-1990salso argue that bank size is negatively related to volatility, however, that relationship reversesover a particular size threshold.4
In regards of the relationship between earnings volatility and earnings, this issue hashitherto been overlooked in banking research. From a standard finance perspective, we wouldexpect there to exist a positive relationship between return and volatility (risk). While this isgenerally accepted within the asset pricing literature, with respect to company behaviour anegative relationship has often been reported, in what has become known as Bowman’sparadox (Bowman, 1980). This negative relationship would imply that managers are willingto accept greater risk for a lower reward and has been widely reported (for a review seeNickel and Rodriguez, 2002). The positive relationship between return and volatility (risk)arises from the crucial assumption of risk aversion. That is, investors will only accept higherrisk if they are rewarded by a higher (expected) return. However, if we allow managers toexhibit risk-seeking behaviour then a negative relationship between earnings and earningsvolatility will exist. Such risk-seeking behaviour would be undesirable from an investorsperspective, however, may be desirable for managers depending on their contractualincentives.1 While we may not expect mangers to be consistently risk-seeking, it wouldperhaps be reasonable to assume that there may be periods of time where managers are riskaverse and other periods of time where managers are risk-seeking. Hence, there may existperiods of time where the relationship between return and risk switches between positive andnegative. In this vein, the negative relationship can be seen through the application ofprospect theory (Kahneman and Tversky, 1979), where managers become risk-seekingfollowing bad outcomes and risk-averse following good outcomes.2 From the perspective ofthe banking sector, an examination of the nature of the return-risk relationship will aid ourunderstanding of the dynamics of risk.1Discussions regarding managerial incentives and risk-taking has a long history (e.g., March and Shapira, 1987;Beatty and Zajac, 1994; Wiseman and Gomez-Mejia, 1998), while with reference to banks, see for example,Jeitschko and Jeung, 2005; Chesney et al, 2012).2Evidence of prospect theory has been reported by Fiegenbaum and Thomas (1988) and Johnson (1994).5
We begin by examining these two issues separately through standard panel regressionapproaches. First, modelling the determinants of US bank earnings volatility in a mannerbroadly similar to that of De Haan and Poghosyan (2012a,b). However, we extend thatanalysis in three directions. First, we consider a sample period of over twenty-five years asopposed to six (2012a paper) and fifteen (2012b paper). Enhancing the sample period willimprove the robustness of the results as it will cover numerous periods of high and lowvolatility. Second, we include two key additional variables, first, a measure of the marketpower held by an individual bank through the Lerner index, and second, the economicenvironment, through GDP growth. In contributing to the discussion regarding large banksand market concentration, both market power and the economic environment in which theyoperate must also play a role in determining their behaviour. Furthermore, the Lerner indexprovides a bank level measure and may indicate the degree of contestability within a marketthat a concentration ratio does not capture. Third, in addition to considering the usual bankspecific factors, such as size, we also consider bank type as identified by the complexityindicator. In particular, we are interested in whether risk, as proxied by volatility, exhibitsdiffering dynamics across banks identified as being of different complexity.Second, we consider the relationship between earning and earnings volatility, again,identifying different categories of bank and volatility measures. Of particular interest iswhether there exists a positive or negative relationship and how that relationship may interactwith bank, market and economic factors. Notably, we are interested in whether bank size ormarket structure alters a banks perception of risk or indeed whether it is related to movementsin the business cycle. Again, banks are considered according to their complexity indicator asthe management of a complex bank may exhibit different risk preferences from one of a lesscomplex bank. Finally, we consider whether there exists any consistency in the factors thataffect earnings volatility (bank risk) and risk-taking (managerial risk) and conduct a third6
regression approach based around a Sharpe ratio type measure (returns per unit of risk). Thus,providing a viewpoint of how banks behave with respect to risk and its relationship withreturns, including risk adjusted returns. It is hoped that the results here contribute to thepolicy debate and in particular, whether policy should be applied differently across identifiedbank types as well as market and economic conditions.2. Data and Empirical Methodology.We obtain annual data on US Bank Holding Companies from the website of the FederalReserve Bank of Chicago. The data is obtained over the period from 1986 to 2013. Our keymeasures of earnings and earnings volatility are based on bank return on assets and return onequity, with volatility determined by the standard deviation of each.3 We obtain the standarddeviation as a three-year rolling average (a five-year rolling average is also considered forrobustness but not reported) based on quarterly data. That is, the annual standard deviation isobtained using observations from the past twelve quarter’s.4To examine the determinants of bank earnings volatility and the interactions withearnings in the return-risk analysis, we consider a range of bank, market and economicfactors. Notably, we are interested in the effects of bank size, market structure and economicgrowth. To assess the impact of size on earnings volatility we use (the natural logarithm of)total assets. Market structure is captured in two ways. First, market concentration is capturedby the Herfindahl–Hirschman Index (HHI). The HHI measure is calculated as: 𝐻𝐻𝐼 2 𝑁𝑖 1 𝑠𝑖 , where 𝑠𝑖 is market share of bank i, and N is the total number of banks in theindustry. Second, market power is captured through the Lerner Index which is calculated asLernerit (PTAit – MCTait) / PTAit, where PTAit is the price of total assets, which is proxied bythe ratio of total revenues (interest and non-interest income) to total assets, for bank i at time34Results are also available for the variance and absolute deviation but are similar to those reported.de Haan and Poghosyan (2012b) report results based on four, eight and twelve quarters.7
t; and MCTAit is the marginal cost of total assets for bank i at time t.5 The annual change inGDP is used to capture the effects of economic conditions. As a series of further bankspecific characteristics we consider several ratios: market share; equity-to-assets as a measureof leverage; loans-to-assets as a measure of liquidity; non-interest income-to-total income asa measure of diversification; non-interest expenditure-to-total income as a measure of costs;non-performing loans-to-total loans as a measure of loan portfolio risk. Table 1 presents somesimple summary statistics.To model the relationship between earnings volatility and the above identified factors,we consider the following empirical fixed effects panel model specification:vi,t α γi β1 Si,t β2 Ht β3 Si,t x Ht β4 Lt β5 Si,t x Lt θ Δyt j 1J λj xjit εit(1)where v refers to the measure of volatility for bank i, S is the measure of size for bank i, H isthe HHI measure, L is the Lerner Index, Δy is output growth and x contains the bank specificfactors. In modelling this equation, it might be expected that larger, more liquid and morediversified banks will be able to absorb shocks better and have lower earnings volatility. Incontrast, more levered banks, with higher costs and higher loan risk would have highervolatility. Our expectation would also be that GDP growth would have a counter-cyclicaleffect on earnings volatility, with greater volatility during economic downturns whenmacroeconomic risk is also higher.5Marginal cost is calculated using the following translog cost function:𝛽ln Costit β0 β1lnQit 2 ln𝑄𝑖𝑡2 β3 lnW1 β4 lnW2 β5 lnW3 β6 lnQit lnW1 β7 lnQit lnW2 β8 lnQit lnW3 2β9 lnW1 lnW2 β10 lnW1 lnW3 β11 lnW2 lnW3 β12 Trend β13 Trend2 β14 lnQit Trend β15 lnW1 Trend β16lnW2 Trend β17 lnW3 Trend εitwhere Qit is a proxy for bank output (total assets) for bank i at time t and Wk,it represent the input prices oflabour (ratio of personnel expenses to total assets), funds (ratio of interest expense to total deposits) and fixedcapital (ratio of other operating and administrative expenses to total assets), the trend terms are included tocapture technical changes in the cost function over time.8
To examine the relationship between return and volatility (risk) we consider thefollowing basic equation:πi,t α γi β1 vi,t εit(2)where π measures earnings for bank i and again v refers to the measure of
McMillan D & McMillan F (2017) The interaction between risk, return-risk trade-off and complexity: Evidence and policy implications for US bank . management risk and has not been widely considered previously. Again, we are interested in how the three sets of variables (bank specific, mar
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