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A New Approach to the Valuation of Banks

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  A new approach to the valuation of banks Michael Adams ∗ , Markus Rudolf  ∗ This version: November 24, 2006 Abstract Despite the discussion surrounding the disintermediation of the financialsector, banks still play a prominent and special role in the allocation of capitalin the economic system. We argue that the business model of the bank ex-hibits such peculiarities that it deserves a special treatment in the approachto its valuation as well. In particular, the exposure to interest rate risk isa major characteristic of its business, not only in the process of maturitytransformation but also as a major determinant of price margin and businessvolume. Although these traits have been noted before in the literature, toour knowledge, there exists no common framework to value a bank which ad-equately accounts for these features. We propose a valuation model for banksbased on Merton’s (1974) structural model of the firm, which we adapt tothe banking firm by the help of term structure models of the interest rates.In this setting, we interpret banks as a particular portfolio of long and shortpositions in interest-rate sensitive assets with special characteristics, and thusbenefit from the rich toolbox of continuous-time finance to derive its value. Indoing so, we are able to show another peculiarity of bank valuation, i.e. thatthe exercise price of a call option on the firm value, representing the bank’sequity, is not the face value of bank liabilities but their economic value. JEL classification: C22, G12, G13, G21. ∗ WHU, Dresdner Bank Chair of Finance, Burgplatz 2, 56179 Vallendar, Germany. Contacte-mail:  michael.adams@whu.edu . We are grateful to Stewart C. Myers, Matthias Muck, andparticipants of the 2005 Burgenland doctoral seminar for helpful comments and the WHU USAfoundation for its financial support. Any remaining errors are our own. 1  1 Introduction The principal function of financial markets is the efficient and intertemporal alloca-tion of capital, but, if let alone, financial markets tend to imperfections and exhibitfrictions in performing this function. Financial intermediaries in general, and banksin particular, owe their existence to these inefficiencies in the distribution of capitalfrom those with a surplus to those with a need, i.e. reducing transaction costs, andat the same time efficiently selecting among those with capital needs according totheir respective risks, thereby solving problems of asymmetric information. Most of the reasons literature has brought forward for the existence of banks can and havebeen subsumed under these two broad categories. 1 The importance of these serviceshas been underpinned in several studies showing that the level of development andsophistication of financial intermediaries, among which banks certainly belong tothe most important, can have a significant impact on economic growth. 2 When we define a bank’s business as accepting (shorter-term) deposits and issu-ing (longer-term) loans in our framework, this is congruent to common definitionsin the literature. 3 As such, the bank is one of the oldest institutions of financialintermediation and still plays a prominent role in the economy for the allocation of capital—this also in spite of the discussion surrounding the disintermediation of thefinancial sector. 4 Nonetheless, technological advances have had a profound effect onbanking and have lead to a worldwide consolidation in the sector. 5 In Germany,consolidation is also underway but still lagging behind. Germany’s comparably stillvery fragmented banking market is often attributed to the institutionalized segre-gation in three pillars. 6 However, the strict segregation of this three-pillared systemis currently up for discussion, possibly opening the gates for further consolidationin the largest European banking market.Given these considerations, the value of banks is clearly a question of interest,be it for shareholder value-oriented management or in the course of a merger oracquisition. Although firm valuation is one of the core problems of corporate fi-nance and has attracted extensive coverage in the literature, we argue that a bank’s 1 See e.g. Santomero (1984) or Bhattacharya and Thakor (1993) for surveys and Freixas andRochet (1997) as a more comprehensive textbook. 2 For a review of this issue, see e.g. Levine (1997). 3 See e.g. Freixas and Rochet (1997). In a classification of banks, this refers mainly to com-mercial banks, but not exclusively. For example, in the regulatory framework of many countries,a commercial bank is clearly distinct from e.g. a savings institutions or a savings and loan as-sociation. However, all three would fall within our definition of a bank as an institution issuingloans financed by deposits. The facts that e.g. thrifts in the U.S. mainly issue loans in the form of mortgages, or savings institutions in Germany are obliged to serve common welfare, are technicaldetails with little relevance for our purposes. 4 See e.g. Schmidt et al. (1999) for a study countering the common arguments of disintermedi-ation and supporting the importance of banks. 5 See e.g. Berger et al. (1999) and a May 2006 special issue of The Economist titled “Thinkingbig: A survey of international banking”. 6 See Hackethal (2004) for an overview and Decressin et al. (2003) for a detailed analysis of theGerman banking system. 2  business exhibits peculiarities that do deserve a special treatment in the approachto its valuation. Although this problem obviously does not require a separate andnovel pricing theory, certain deviations from standard methods seem not only ap-propriate but also necessary to us; to say it with Damodaran’s (2002) words: “Thebasic principles of valuation apply just as much for financial service firms as theydo for other firms. There are, however, a few aspects relating to financial servicefirms that can affect how they are valued.” 7 We will demonstrate both why andhow standard valuation approaches should be modified to account for bank-specificbusiness risks. Specifically, we address interest rate risk as a major characteristicof the banking business. The bank faces this type of risk not only directly in theprocess of maturity transformation but also indirectly in the determination of pricemargins and the attraction of business volume, all affecting the value of the bank.The high interest-rate sensitivity of a bank’s market value has been noted manytimes before in the literature; for example, early empirical studies supporting such arelationship are Flannery and James (1984 a  ) for U.S. banks and Bessler and Booth(1994) for German banks. Accordingly, there exist several authors who have takenup this finding and suggested special bank valuation approaches. However, in theprocess of reviewing these approaches, we will show that their models do not reachvery far in incorporating bank-specific risks. Hence, to our knowledge, there existsno common framework to value a bank which adequately accounts for these features.We propose an alternative and new valuation model for banks based on termstructure models of the interest rates. These models allow us to directly account forinterest rate risk but let us avoid the problem of having to explicitly forecast inter-est rate developments, a problem inherent in all other approaches. Originally, termstructure models were developed for the valuation of interest-rate sensitive deriva-tives. In the same spirit, we model banks as a portfolio of interest-rate contingentclaims and value bank equity as a call option on the portfolio value. In other words,we build on Merton’s (1974) structural model of the firm and extend its standardasset process of the firm for an application to the dynamics of the banking firm.For expository reasons, we will set up our model first in discrete time to gain anintuition for the bank’s business model and will then derive a valuation model in acontinuous-time setting.The paper proceeds as follows. In Section 2, we review the existent literature onbank valuation and identify shortcomings of the present approaches. In section 3, wereview the bank’s business model and motivate a distinct approach to its valuation.We feel that this is necessary given the fact that this problem has attracted littleattention in the literature so far. In the fourth section, we sketch a simple version of our model in discrete time and in section 5, we extend this model to the mathematicsof continuous time in order to derive a solution. Section 6 concludes. 7 Damodaran (2002), p. 603. 3  2 Survey: Literature on bank valuation 2.1 Why banks are special Little has been written on the valuation of banks. This fact allows for two conclu-sions: Either this question is of minor relevance and the valuation of banks deservesno special attention, or, alternatively, bank valuation exhibits particularities andproblems that have not found appropriate attention in the literature so far. Inseizing this problem, we follow the latter view and rely on the few existing paperscontributing to this issue and on those explicitly mentioning the valuation of banksas one of the unresolved issues in financial research, as e.g. Copeland et al. (2005)do. 8 In corporate finance, it is not unusual to specify valuation models for particulartypes of firms. For example, to mention just two of them, Brennan and Schwartz(1985) propose a real-options based valuation approach to natural resource compa-nies, explicitly modeling the options to temporarily close, reopen and shut-down themine, depending on the market price of the resource and Kronimus (2002) develops amodel suitable to the traits of young, fast-growing firms, including little or negativecurrent earnings but fast revenue growth. These models do not aim at introducing anew paradigm in asset pricing theory. Rather, the common feature of these modelsis the attempt to better grasp the underlying characteristics of the business—onwhich equity is the residual claim—as when compared to standard approaches. Forthe same reasons, one can argue for a special valuation approach for banks.The characteristics of the banking business motivating a distinct valuation ap-proach can be subsumed in four categories. First, due to their central role for theeconomy, banking is typically a heavily regulated industry, covering a wide rangeof provisions, such as e.g. market entry, deposit insurance, reserve requirements, orcapital structure. 9 Second, banks operate on both sides of their balance sheets, ac-tively seeking profits not only in lending but also in raising capital, a duality whichhad been practiced for long but had not been fully understood by economists un-til the late 19th century: “A Banker is a trader whose business consists in buyingMoney and Debts, by creating other debts.” 10 From a financial accounting pointof few, this implies relatively few fixed assets, resulting in a low operating lever-age, and relatively high financial leverage, resulting in a comparably higher earningsvolatility. 11 Third, and as a consequence of the previous point, banks are exposedto credit default risk, but in contrast to other firms, they also actively seek this kindof risk as part of their business model. Last but not least, the profit and the valueof the bank is strongly dependent on interest rate risk.Tackling each of these four points is of unequal complexity. Solving the first 8 See Copeland et al. (2005), p. 872. 9 See e.g. Carey and Stulz (2006). 10 MacLeod (1875), p. I:275. 11 It can be shown that banks optimally operate at high leverage because of deposit insuranceschemes granted to them in almost all industrialized countries, which is essentially a put optiongiven to the bank, see e.g. Buser et al. (1981). 4
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