The Bank Capital Regulation (BCR) Model

Transcription

1 Te Bank Capital Regulation (BCR) Model Hyejin Co To cite tis version: Hyejin Co. Te Bank Capital Regulation (BCR) Model. Alex Nicolls (University of Oxford); Simon Taylor (University of Cambridge); Wim A. Van der Stede (London Scool of Economics); Mattew Haig (University of London); Heimo Losbicier (University of Applied Sciences Upper Austria); Jua Kansikas (University of Jyvaskyla, Finland); Barbara Verardo (University of Oxford, World Bank Wasington DC); Elisabet Mensc (Universität Linz, Austria); Alex Murdock (London Sout Bank University). 14t FRAP - Finance, Risk and Accounting Management Perspectives Conference, Sep 2014, oxford, United Kingdom. Otmar M. Lener, 14 ( ), pp.696, 2014, Proceeding in Finance and Risk Perspective (2014).. HAL Id: al ttps://al.arcives-ouvertes.fr/al Submitted on 25 Sep 2014 HAL is a multi-disciplinary open access arcive for te deposit and dissemination of scientific researc documents, weter tey are publised or not. Te documents may come from teacing and researc institutions in France or abroad, or from public or private researc centers. L arcive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recerce, publiés ou non, émanant des établissements d enseignement et de recerce français ou étrangers, des laboratoires publics ou privés.

2 Te Bank Capital Regulation (BCR) Model Hye-jin Co Department of Economics, University of Paris 1, Panteon-Sorbonne, Room 502, Maison des Sciences Economiques, , Boulevard de l'hopital Paris FRANCE Abstract. Te motivation of tis article is to induce te bank capital management solution for banks and regulation bodies on commercial banks. Te goal of te paper is intended to mitigate te risk of a banking area and also provide te rigt incentive for banks to support te real economy. Keyword. Demand Deposit, On-balance-seet risks and off-balance-seet risks, Portfolio composition, Minimum equity capital regulation. Part I Introduciton In Europe, after te Basel 1 (1988) accord, te banking supervision Accords in Basel, Switzerland, Basel 2 (1999) and Basel 3 (2010) ave been evolved. Te issuer, te Basel Committee on Banking Supervision (BCBS), advised about credit risk ( ) at te Basel 1 and amended about market risk ( ) wit te Basel 1 Amendment. In te revised framework of te Basel 2, operational risk ( ) was introduced and enanced at te Basel 3 ( ). In tis overall perspective, tese Basel Capital Rules ave been enanced up to te Basel 3. For example, te scope of operational risk is enlarged. Tis requires some reasonable motivation since banks face te situation to manage te cost to follow banking capital regulation rules. Of particular significance is tat te government needs to regulate banks to prevent panic from te systemic banking crisis. Muc interest as been aroused in cascading failure of bank run prevention. For example, Friedman and Scwartz (1963) observe large costs imposed on te economy of United States caused by bank runs in te 1930s. Upon on muc more recent data, in systemically important banking crises of te world from 1970 to 2007, te average net recapitalization cost to te government was 6% of GDP (Gross Domestic product). Fiscal costs associated wit crisis management were averaged 13% for GDP (16% of GDP if expense recoveries are ignored), and economic output losses were averaged about 20% of GDP during te first four years of te crisis. Oterwise, if te government decides to adopt te Basel capital regulation framework, te adoption cost will influence te economy of countries. Eiter ouseolds or banks, related parties to economy sould pay for te Basel capital regulation as te preventive metod in te banking business cycle. An OECD (Te Organisation for Economic Cooperation and Development) study released on 17 February 2011, estimated tat te medium-term impact of te Basel III implementation on GDP growt would be in te range of 0.05% to 0.15% per year. Economic output would be mainly affected by increase in banks lending spreads, as banks pass a rise in bank funding costs, due to iger capital requirements, to teir customers. Terefore, te situation is tat banks are struggling to manage te regulation cost and te government wants to defend about nationwide contagion of oter banks.

3 Part II Te macroprudential approac to financial regulation covering onbalance-seet and off-balance-seet (OBS) Insofar as systemic risk is concerned, risks tat firms, ouseolds and reserve banks and commercial banks face are igly linked to eac oter. Seen from tis point of view, te banking industry and te monetary policy ave particular relevance to systemic risk. Undoubtedly, it goes witout saying tat financial contagion problems troug international banks sould be measured in te manner of systemic risk management. Wit te macroprudential approac, it is igly probable tat systemic risk is explained by te static model of te general equilibrium. Because on-balanceseet and off-balance-seet (OBS) risks are structually segmented annually or periodically by financial statements containing te balanceseet. Even toug domino effects or contagions can be understood as movements aving te future tendency to figure out solutions toward te future, scope of regulation sould be articulated by categorization of on-balance-seet and off-balance-seet (OBS) risks in te static model. Tus te macroprudential approac to financial regulation covering on-balance-seet and off-balance-seet (OBS) risks is intimately linked wit te general equilibrium (GE) approac. On-balance-seet risks are presented in a fourfold manner and are divided into credit risk, market risk, liquidity risk and systemic risk. Assets of banks ave credit risk and market risk. Credit risk is te risk tat a borrower will default on any type of debt by failing to make required payments. Market risk is te risk of losses in positions arising from movements in market prices. In case of liquidity risk, tere are two major situations. One is emergency capacity of banks. Wen an illiquidity event takes place, an affected bank typically must borrow funds at interest rates exceeding tose paid by oter institutions. Anoter is about te stability of te banking system in case of inducing a large number of depositors to seek witdrawals. I would say liquidity risk in regard of demand deposit is on-te-balance-seet risks of banks. Credit, market and liquidity risk are portrayed in considerable individual details but systemic risk is negative externality or adverse spillover effect stemming from transaction in wic tey were not participants. Distinguised from credit risk containing sovereign risk (government risk), counterparty risk (unincorporated entities risk exposed to financial risk, usually referring to governments, national banks), systemic risk is te risk of collapse of an entire financial system or te entire market, as opposed to risk associated wit any individual entity, group or component of a system. George G. Kaufman and Kennet E. Scott (2003) define systemic risk in imprecise terms as below: Systemic risk refers to te risk or probability of breakdowns in an entire system, as opposed to breakdowns in individual parts or components, and is evidenced by comovements (correlations) among most or all te parts. Darryll Hendricks (2009), wo is a practitioner, suggests a more teoretical definition from sciences in wic te term originated: A systemic risk is te risk of a pase transition from one equilibrium to anoter, muc less optimal equilibrium, caracterized by multiple self-reinforcing feedback mecanisms making it difficult to reverse.

4 Banks engage in a number of activities tat yield income, entail expenses and manage risks from on-balance-seet risks to off-balance-seet risks. Depending on bank caracteristics, Banks extend loan commitments, security loans and trade derivative securities. Troug extended loan commitments, te borrower as a guarantee of Figure II.1 Vanoose Asset/Liability of banks credit at a given interest rate wenever desired during te specific period. Te bank receives interest income on te portion of te credit line tat te borrower draws upon, and te bank receives non-interest income on te unused portion. Wereas a loan commitment obligates a bank to bring a loan onto its balance seet upon customers requests, securitization permits a bank to remove loans from a balance seet. Trading derivative securities also proved to be significant source of revenues. Tis claim is supported by te survey of David Van Hoose (2010), by te end of 2008, United States banks eld a notional amount of derivatives totally more tan 190 trillion dollar, of wic about 150 trillion dollar of derivatives exposure was comprised of interest rate contracts. In relation to wat I ave previously said, te general equilibrium (GE) approac is useful to understand te overall mecanism of financial transaction and economic policy. Te opposite mecanism of assets and liabilities on bank caracteristic in te figure II.1, is different from usual balance seets of firms. Tat is, banks regardless of central banks or commercial banks ave caracteristic tat loans are assets of banks and deposits are liabilities.

5 Figure II.2 Freixas-Rocet (1999) All of tese figures are empasized by capital circulation of te Freixas-Rocet model (1999) in te figure II.2. In conjunction wit te Freixas-Rocet model, te equilibrium is detected wit te general equilibrium approac wit direct relevance to circulation of securities and stability of deposits. In te paper, te general equilibrium appoac is upgraded wit an adroit mixture of te balance seet concept evaluating te value of economic entities and te income statement concept considering te profit to support te existence of financial entities. Part III Model 1. Saving preference of Consumers A microeconomic teory of banks ad not been existed before te microeconomic foundation related to banks in te early 1970s. I would suggest add a banking sector at te Arrow general equilibrium model (1953) under te complete financial market assumption. Te main purpose of te model as been to explore solutions about te problem of ouseolds, firms, banks and regulation bodies. Te two-period model (t=0,1,2) wit a unique pysical good initially owned by consumers in te economy in wic a continuum of ex-ante identical agents is eac endowed wit one unit of goods at te period t=0, and tis good is to be consumed at eac period of t=1 and t=2. Te consumer cooses er consumption profile (C 1, C 2 ) and te allocation of er savings S between bank deposits D and securities Σ s Ω P s B s, in a way tat maximize er utility function µ under er budget constraints: Max µ(c 1, C 2 ) C 1 + Σ s Ω P s B s + D + S - Σ s Ω P s B s D = W 1 C 2 = Π f +Π b +(1+r) Σ s Ω P s B s + (1+r D )D + (1+r )S -(1+r) Σ s Ω P s B s -(1+r D )D Were W1 for er initial endowment of te consumption good, Π f +Π b for respectively profits of te firm and of te bank (distributed to te consumer-stockolder at t=2).

6 B denotes for securities, D for bank deposits. S denotes for savings. r, r D, r are interest rates paid by securities, deposits and savings. For eac future state of te world s (s ω) one can determine te price P s te contingent claim tat pays one unit of accounts in state s and noting oterwise. Te consumer as a well-defined set of desires ( preference ), wic can be represented by a numerical utility function. In addition, we assume tat te consumer cooses optimally, in te sense tat tey coose te option wit te igest utility of tose available to tem. It implies tat a consumer is solving an optimization problem. An optimization problem as tree key components. a. Selected object Te consumer cooses er consumption profile (C1, C2 ) and allocation of er savings S between bank deposits D and securities B. If real assets S - Σ s Ω P s B s D is non-negative, it implies real assets are sufficient to support te ouseold economy. b. Te objective function Te consumer maximizes er utility function µ. µ is assumed to be increasing and concave. Notice tat preferences are contingent states and do not fit te standard Von Neumann-Morgenstern representation. Incompleteness of preference becomes apparent tat decision makers cannot make a decision in te ambiguous situation. However, even toug one individual or one factor doesn t decide, te regulator decides te policy wit a foretaste of wat is to come after annual closing accounts. c. Constraints Cas-in-advance 0<D W 1, Te paper will be based on te Cas-in-advance constraint. Tis approac tat was introduced by Clower (1967) is te requirement tat eac consumer or firm must ave sufficient available cas before tey can buy goods. Price of security under Uncertainty Σ s Ω P s B s (resp. Σ s Ω P s B s f, Σ s Ω P s B s b ) implies te price of securities by te absence of arbitrage opportunities. A bank issues (or buys) a security (intepreted as a deposit or a loan) caracterized by te array B s (s Ω) (resp. B s f, B s b ) of eac payoff in all future states of world ω Interior Solution Te consumer s program (P ) as an interior solution only wen interest rates are equal: r = r D Preference of Savings In te Arrow-Debreu model, money is redundant in te market. Houseolds are indifferent about te composition of savings. In te paper, te ouseold as preference to increase te budget to collect savings S and affected by risk levels of securities, deposits and real assets. Savings S is te sum of Securities Σ s Ω P s B s, Deposits D and Real Assets S -(Σ s Ω P s B s +D ). d. Arguments Tere are concerns about savings tat are substituted into consumption by te ouseold like Covas-Fujuta (2010). Diaz (2005) adds no capital requirement at basics

7 to reduce consumption and increase savings by te ouseold. Haslag (2001) assumed tat return to money is positively related to te money growt rate tat is a random variable, gross real returns to savings are random. His realized gross real return to savings indicates tat te gross real return to savings is a weigted sum of capital and fiat money (wic derives its value from government regulation or law, so called as fiat currency ). Te weigt is te sare of agent s asset. In te Waller model (2004), Savings are very passively selected by te ouseold depending upon decisions at te previous period. Middle-aged agents ave already earned teir wage income, as te wage during period t was determined by te previous period s interest rates (a level of te capital stock). Also, tey ave already decided ow muc to consume and save (since savings are a fixed fraction of wage income), but tey ave not yet decided ow to allocate teir savings between capital and fiat currency. Wat tese middle aged agents want at tis point is just te igest possible interest rate between period t and t + 1, so tat tey can obtain te best possible return on teir savings and can tus consume as muc as possible during teir period of old age. In te tird period of life, retired agents consume teir savings and exit te model. Practically, Cristensen-Me-Moran (2011, Bank of Canada) mentioned, at te timing of events, ouseolds deposit savings at banks tat use tese funds as well as teir own net wort to finance te entrepreneur s projects. In te investment frame, exiting (failing to return from te project) agents sell teir capital for consumption goods and surviving agents buy tis capital as part of teir consumption-savings decision. However, in reality, even toug te agent as a ouse, tey need to spend expenditure for renting, maintenance and extension of ouses. Savings and real asset portion are large enoug to make te loan from banks. It is ard to explain price fluctuation of ouses and savings on te economy by depending upon te interest rate of capital stock and deposit, or perfect substitution of consumption. For ouseolds, te preference of savings is te matter about existence of ouseold economy making future benefits and directly affecting to te welfare of any individual. House-price appreciation by te model of Goodart-Kasrap-Tsomocos (2012) is impressive. Reducing deposit defaults induces more savings circulated by te bank and less self-insurance and by te end, te reduction in self-insurance reduces te number of ouses for sale in a good state, wic means tat ouse-price appreciation in te boom is iger tan oterwise. Most of all, te market incompleteness wit deadweigt costs of default distorts te ousing market. Wealty agents endowed wit ouses make teir saving decisions accounting for te possibility tat deposits will not be fully repaid. Wen default penalties for banks are low, ten ouseolds internalize risks putting less wealt into te banking system and old more in te form of ouses. Tis coice increases te supply of ouses tat is available in boom, wic lowers ouse prices and raise welfare for agents entering te ousing market at tat time. To insure tat ouse price reduction in te bad state of te world, ouseolds P and F are also presumed to ave lower wealt. Likewise, te non-bank is endowed wit lower capital in period 1 as well as in te bad state of te world. Tis model describes te ouse bubble penomenon interestingly. In te model of Lucas (1995), to support te incompleteness of markets, e pointed out savings tat te young split teir savings between bank deposits, wic promise a fixed nominal return, and a bank equity, wic yields an uncertain real dividend. In addition, because a constant fraction of initial wealt is saved, tere is no

8 distortion due to fixed nominal interest payments on deposits. Hence regardless of deposits, te bank equity is related to te real effect of monetary policy. In te paper, at te framework of securities, deposits and real assets wit savings, firstly, te relation between savings and real assets (especially ouses) can be muc more attaced. Secondly, deposits included in te total saving amount wic are escaped from te one-sided tinking tat deposits are equal to savings and can be perfectly substituted to consumption. Tirdly, Securities at uncertainty are affecting to te investment portfolio of ouseolds. Tese dynamics are explained by te following academical detail. Houseolds coose (C1, C2, S1, S2, R1 ) taking prices (W1, W2 ) as given. Formally, if we consider te 4-factor model containing banks, because banks ave te special financial structure aving deposits as liabilities and loans as assets, we need to ave te different mindset from generally accepted accounting principles about debit and credit accounts. Te general equilibrium (GE) diagram is similar wit te balance seet. Distinguisably, te money flow in te paper starts at te bank transaction wic is deposits and borrowings as liabilities and claims to corporate as assets. Ten, deposits of ouseold are te amount to be accumulated in banks. Conveniently, riskier investments tan deposits for ouseold are categorized as securities. Savings are moving in te real ouseold economy by capital circulation of securities, deposits and real assets. In addition, te welfare of eac ouseold is moving from dynamics of accumulated savings. In te overlapping generation model, wealt is always given and manages te ouseold economy easily by eac generation. In reality, one wo didn t get a ouse as a legacy, se sould spend quite a long time to ave a ouse or rent a ouse. Attention about fundamental wealt related to non-working capital of a ouseold economy sould be empasized. If te consumer spends is income entirely, te total amount W1 may be spent totally and can be bounded. In tis manner, te ouseold always as teir fundamental welfare to manage te ouseold economy and consumption can be naturally deduced from te framework of ouseould economy. Tat is, W1 is te budget constraint and te market information is incomplete so we cannot deduce te real variable of consumption in reality. W1 and incompleted market information are not enoug to deduce te real variable of consumption. In terms of te working capital, we are not so surprised to know tat capital as various liquidities. For example, a ouseold wants to spend money on a daily basis but sould reduce te amount of money by spending it to ave fundamental living basis like ouses. In te paper, te financial budget constraint is bounded witin te W1 except for S1 because S1 is te summation of securities, deposits and real assets. Tese are vital factors to operate ouseold economy related to financial markets. Te working capital concept at te ouseold economy is evoked witin te general equilibrium in te paper. In te perspective tat te industrial caracteristics of banks mainly operated by capital, it makes sense to us tat consideration about te ouseold economy sould be balanced wit te working capital concept of banks. Ten, wy we need to define return R1 in tis model? Simply, we tink of tree variables of W for endowment, S for savings and C for consumption. We assume tat te concept of te golden-rule saving rate in Capter 1 of Barro and Sala-i-Martin, n denotes for te constant exogenous population growt rate, and d is for te constant exogenous rate of depreciation of capital. We know te ouse saving rate is 5% (usually

9 2-11%, OECD, Economic Outlook n.91, June 2012). Te amount of savings in te economy sould grow as population grows. To support tis insured saving amount caused by population growt, te return sould be enoug to make profits to cover te insurance expense in te economy wit te general equilibrium (GE) perspective. Ten, we can assume te worst senario like a bank-run case. Even toug te fix amount of saving deposits is secured, te loss amount induced from total savings by te end - insured savings will go to te consumption part. In tis overall perspective of an equilibrium, insuring savings of ouseolds seems plausible to support te economy of ouseolds, yet it requires furter understanding about te profitable dynamic mecanism to operate te economic cycle. I would say te original form is mainly based on te BCR general equilibrium model diagram presenting as te balanceseet format as it can be because on-balance-seet factors are reflected by two regards - te money flow perspective (profit) and te economic status perspective (net present value). Original form (savings containing real assets) Max µ(c 1, C 2 ) C 1 + Σ s Ω P s B s + D + S - Σ s Ω P s B s D = W 1 C 2 = Π f +Π b +(1+r) Σ s Ω P s B s + (1+r D )D + (1+r )S -(1+r) Σ s Ω P s B s -(1+r D )D Simplified form for calculation (savings containing real assets) Max µ(c 1, C 2 ) C 1 =W 1 -S 1 C 2 =R 1 +W 2 -(1+r)S 1 -S 2 We ave te first order condition of consumption at period 1 and 2 as below.!!! = µ (C 1, C 2 ) - λ = 0!!! = µ (C 1, C 2 ) - λ = 0 We know te Lagrange multiplier is 0 as λ = 0, by te!, te first order condition of savings at period 1 and by te!, te first order condition of return from initial!! investment. In addition, we get λ(1+r 1 ) = 0 by te!, te first order conditon of savings at period 1. Terefore, wat is get from cecking te first order condition of ouseold problem is tat ouseolds consume today or tomorrow regardless of a banking money flow and it is not affected by te return of initial savings. µ (C 1, C 2 ) = 0 denotes as time indifference about consumption preference. Houseolds operate te ouseold economy related to banks regardless of consumption for today or tomorrow. We conclude consumption coice is not affected by return of initial savings r 1 at te frame of banking money flow related to ouseold. Te ouse expense portion in deposits eld wit MFIs (Monetary Financial Institutions) is te asset tat can induce te future benefit and considered as priority to invest for a long time. For example, among loans to ouseolds of MFIs (5231 billion euros), loans for ouse purcase are 74%, billion euros in Note tat we!!!!

10 focus on te money transaction started from te bank balance seet, in te concept of savings, House fee is deduced from S -Σ s Ω P s B s -D Were is te period of ouseold. If we suppose te ouse fee is not contained in savings as below. Simplified form for calculation (savings witout real assets) Max µ(c 1, C 2 ) = 0 C 1 + Σ 1 Ω P 1 B 1 + D 1 = W 1 R 1 +C 2 +(1+r) Σ 1 Ω P 1 B 1 + (1+r 1 )D 1 -(1+r) -Σ 2 Ω P 2 B 2 -D 2 =W 2 Also, C 1 = (W 1 S 1 )+(S 1 - Σ 1 Ω P 1 B 1 + D 1 Te first-order condition!!! = µ (C 1, C 2 ) - λ = 0!!! = µ (C 1, C 2 )- λ = 0!!! λ = 0!!! - λ (1+r 1) = 0!!! λ = 0 µ (C 1, C 2 )=0! Σ! Ω!!!!! - λ (1+r 1) = 0! Σ! Ω!!!!! λ = 0!!! = λ (Σ 1 Ω P 1 B 1 + D 1 ) = 0 In conclusion, µ (C 1, C 2 )=0 (time indifference about consumption preference) is te same condition regardless of real assets weter it is contained in savings or not. Consumption coice is not affected by te interest rate r 1 for initial savings (same condition regardless of real assets weter is contained in savings or not) and summation of securities and deposits Σ 1 Ω P 1 B 1 +D 1. Evidently, tis condition appears in tis banking model wen we ignore real assets wic is most stable in te ouseold economy and can be interpreted as te big portion expense and te intangible asset producing future benefits. Terefore, wit te condition tat real assets are contained in savings, we can explain te ouse economy affected by te proportion of securities and deposits. First intention to coose te general equilibrium model in te paper is to offer understandable metod to te academic field and professional field. In te practice, te reserve bank as many metods and even tey want more metods togeter in te weigted way. As I can do, I am intending to use real variables tan random variables and a lot of Lagrange metods wic is very general way to use te general equilibrium. Te saving composition matter is more specifically supported by te following empirical data. Te deposit amount traded is different depending upon factor composition of economic models. For example, te European Central Bank announces te Euro areas deposit amounts for te 4t quarter in 2013 in te Euro areas. Gross saving amount of ouseolds is billion euros (growt rate: 2.4). Deposits by non-financial corporations are billion euros. (growt rate: 6.7). Deposits by Insurance

11 corporations and pension funds (financial intermediaries) are billion euros. (growt rate: -5.3). Deposits by oter financial intermediaries are billion euros (growt rate -3.1). Deposits by government are billion euros (growt rate: -1.8). Deposits by non-euro area residents are billion euros (growt rate: -11.2). Terefore, witout consideration about deposits by non-financial corporations (1870.7), te comparison between deposits by ouseold (2521.3) and deposits by financial intermediaries ( =2507.3) is naive explanation. Loans for ouse purcase is billion euros. (growt rate: 0.7). It is Longterm liability affecting te existence of ouseold economy. In addition, te total (7341.7) of deposits by insurance corporations, pension funds (653.2, -5.3), oter financial intermediaries (1854.1, -3.1), non-financial corporations (1870.7), government (440.8), non-euro area residents (2522.9) are. Also, total (7752.2) of deposits by ouseold (2521.3, 2.4) and Loans for ouse purcase (3858.1, 0.7) and oter loans (796.7, -1.6), consumer credit (576.1, -3.0) are. Loans for ouse purcase (3858.1, 0.7) oter loans (796.7, -1.6) consumer credit (576.1, -3.0) total Empirical balance wen te capital of a ouseold economy is concerned Ref: European Central Bank, te 4t quarter in 2013 (billion euros, growt rate) insurance corporations and pension funds (653.2, -5.3) oter financial intermediaries (1854.1, -3.1) non-financial corporations are (1870.7, 6.7) government (440.8, -1.8) non-euro area residents (2522.9, -11.2) total Savings S are te sum of Securities Σ s Ω P s B s, Deposits D, Real assets S - Σ s Ω P s B s D. Houseolds try to control te balance of assets and liabilities because in te situation of uncertainty, to maintain enoug Deposits D for te economic existence of ouseolds, ouseolds need to invest on securities as of Σ s Ω P s B s posed on uncertainty conditions. Mainly, real assets imply te budget for ouses wic can afford to manage te residence and invested real assets. For example, if te ouseold as an apartment and tere is te redundancy after spending te investment on securities and deposits, it can be te maintenance fee for ouse decoration or big furniture purcases. Te importance of portion for ouses is considerable. Oterwise, if real assets are negative, ence, savings of ouseolds are less tan te amount of securities and deposits. Even toug, te amount of operation in te ouseold is enoug wit securities and deposits. In te conservatism on te ouse budget, we can consider te effect on ousing. In te paper, Houses of ouseolds is considered as future economic assets tat support eac member of ouseolds to make productions. Troug te general equilibrium approac, te link from te bank problem to te ouseold problem is naturally connected. Also, te following tecnical finding by usage of same accounts at te ouseold problem induces direction of regulation on banks like te portfolio analysis and inital GDP consideration. Te following are tecnical findings wit saving preference.

12 Suppose tat s G, B, G=Good, B=Bad. In te case 1, risk aversion is a s below. (resp. risk-taking case) Ω= G, B, C 1 +Σ s Ω P s=b B s=b +D +S -Σ s Ω P s=g B s=g -D =W 1 In tis case, portfolio analysis sould be detected by regulation because te situation can be canged depending on te status. In te case 2, incompleteness preference can be considered. Ω= G, B, no coice, no coice can be selected by te coquet expectation CEν(µ(x)) = min Π core(ν) E Π (µ(x)) were core(ν) = Π ΔS : Π(A) ν(a) for all A S C 1 +0+D +S -0-D =W 1 and D offset, ence C 1 +!!!!!! =W Initial GDP is caused by partition of initial endowment tat is combination of consumption set. Hence, regulation direction is originated from initial GDP in tis case. 2. Borrowing composition of Firms - Additional session is in te Part IV.6 Te firm cooses its investment level I and its financing (troug Real Assets Σ s Ω P s B s + D, Liabilities to banks Σ s Ω P s B s + D -L fr (Or Liabilities to central banks L fr ) in a way tat maximizes its profit: Max Π f (P f ) Π f =ƒ(i)+r f (Σ s Ω P s B s + D )-r L bank (D + Σ s Ω P s B s -L fr )-r L fr L fr I=S =D +Σ s Ω P s B s Were ƒ denotes te production function of te representative firm. r ƒ is te premium of firm s real assets. r bank fr L, r L are interest rates on bank loans and federal reserve bank loan. D denotes for bank deposits. B denotes for securities. Especially B fr denotes for securities of federal reserve banks. L fr are loans claimed by te firm to te federal reserve bank. For eac future state of te world s (s ω), one can determine te price P s of te contingent claim tat pays one unit of accounts in a state s and noting oterwise. I is te investment level and S denotes for savings. Interior Solution P ƒ as an interior solution only wen: r ƒ= r L bank =r L fr Te Modigliani-Miller (MM) teorem projects a teme of a teorem on capital structure. Te basic teorem states tat, under a certain market price process (te classical random work) and an efficient market, in te absence of taxes, bankruptcy costs, agency costs and asymmetric information, te value of a firm is unaffected by ow tat firm is financed. Firms are indifferent about te composition of borrowings. Given te proposition II of te Modigliani-Miller (MM) teorem, a iger debt-to-equity ratio leads to a iger required return on equity because of te iger risk involved for equity-olders in a company wit debt. r E =r 0 +!! (r 0-r D ) were r E is te required rate of return on equity or cost of equity, r 0 is te company unlevered cost of capital (ie. Assume

13 no leverage, r D is te required rate of return on borrowings or cost of debt and! is te! debt-to-equity ratio under two assumptions: (1) no transaction costs exist. (2) individuals and corporations borrow at te same rates. However, on te surface, given same ratios of!, two different sized banks are distortly intepreted. Even toug tis proposition is! induced in te absence of te bankrupcy costs, merges of banks like too big to fail, so called te size game among big banks, are considerable. Tus it is certainly wort inquiring D+E beind it s apprant dynamics of!!. Te BCR model provides a key wit wic to unlock riddles of firms borrowing compositions. Te borrowing composition of firms imparted dynamics wit te preference to maintain Real Assets Σ s Ω P s B s + D. Regardless of equilibrium, firms prefer to loan from central banks (so called as bonds) tan commercial banks. Among te D and Σ s Ω P s B s, Firms prefer to ave D because of financial stability and preference about certainty. Te model reflects te tendancy of banks toward te big size wit Real Assets. In te economic existence respect of banks, banks ave responsibility to operate te dynamics of te debt-to-equity ratio! and maintain te economic entity of Real Assets! D+E in te economy of countries. Given te firm s problem, we ave ambiguity about cange of firms because of investments or loan status. Precise explanation about te relation wit commercial banks and central banks sould be offered. In te general equilibrium (GE), firms coose labor cost and manage te capital for production or business process but labor effect is ard to be clarified wit certain connection of commercial banks and federal banks. Hence, te transaction like loan movements (i.e. liabilities to banks, liabilities to central banks, investments) can be selected to explain in tis paper. Additionally, Investments is regarded as Real assets to support existence of business entities. It implies firms want to acquire investment budget to maintain real assets tat can be requisite for existence of firms. Terefore, by aving borrowing preference to ave muc more stability between liabilities to banks and central banks (so called as bonds), firms pursue to obtain stability to acquire te investment up to te stability of Investments wic can be equal to Real Assets. Tus, we can explain dynamics of investments and loans wit te firm s property. Tere are many arguments to explain te ambiguity of firms wit informational asymmetry, sock absorbed by effective capitals, securities, tecnical socks, and interest rates on loans and borrowing constraints. Boyd-Cang-Smit (2004) points out two informational asymmetry problems of firms: Te moral azard problem arises because any borrower s project coice is not observable. Also, te costly state verification (CSV) problem arises because, for eiter type of projects, te return of investments cannot be freely observed by any agent oter tan te project owner. In te Nelson-Pinter (2012) model, at te production function of cobb-douglas standard form, tere is a sock variable to te quality of pysical capitals. Wen we face te unanticipated exogenous declines in te productive capacity of pysical capitals, available Effective capitals for use in te production is diminised. Tis intends to consider te effect on banks since banks old claims on pysical capitals directly on teir balance seets, tis will be loss for banks, wic must be absorbed or passed on to outside creditors.

14 In te Dewartripont-tirole (2012) model, e argues tat securities are caracterized not only by income rigts but also by control rigts. Optimal corporate coices are te time- inconsistency. Investors in control of corporate coices must face an incentive tat differs from firm-value maximization. So a banking manager as no financial resources to cover an investment cost and turns to investors for financing. Te capital structure - tat is, te allocation among investors of contingent cas-flow and control rigts - is designed at tis financial stage. Covas Fujita (2010) mentioned tat te tecnology sock is distributed as standard normal distribution. Labor and capital rental markets are assumed to be competitive. Diaz (2005) tinks tat since interest rates on loans are greater or equal tan te discount rate, firms prefer to use internal sources (i.e. cas flows) rater tan external financing. In addition, e induces tat capital depreciation is paid out of firm s cas flow and net investment is entirely financed wit debting. In te model of Nuno- Tomas (2013), tey assumed tat te firm can only borrow from banks located on te same island. In te static model of general equilibrium (GE), if we know te GDP endowment as te exogenous factor, we can calculate more at te firm s problem. Indeed, te analysis about GDP like Consumption to GDP, Government Expenditure to GDP, Fixed Capital Formation to GDP, Export to GDP, Net Export to GDP, Money to GDP except for inflation rate and nominal interest rate are used wit te general equilibrium (GE) approac. Te effort to figure out ambiguity of firms and overal perspective analysis display a coerent structural and compositional understanding. Ten, ow we can measure te firm s productivity relating to te banking area in general equilibrium (GE)? Te classical viewpoint tat tere are tree basic factors of production, (land, labor and captal) at te production function. Total-factor productivity (TFP) is different from te traditional calculation measured by inputs of labor and capital. Te TFP calculation is measured as a Solow residual affecting in total output and not caused by inputs. Te equation Y = A K α L β in Cobb-Douglas form represents total output (Y) as a function of total-factor productivity (A), capital input (K), labor input (L), and te two inputs respective sares of output (α and β are te capital input sare of contribution for K and L respectively). Te problem is tat units of A do not admit a simple economic intepretation. We ave two ways to calculate TFP (Cen, 2011). Firstly, we obtain te TFP measurement by estimating a production function. Secondly, we establis a model to find te determinant of TFP and uncover weter financial factors exert any effects on TFP. Materials and energy are secondary factors because tey are from land, labor and capital. It can be puzzled weter duplicated or missed amounts are existed in te general equilibrium (GE). Te equity portion as capitals is in te liabilities of firms and te wage portion as expense is in te eliminated account of firms. Wit tis production function measure, we are talking about te exact asset amount of firms tat is te part of equity at te same time. Let s go back to te definition of te production function. Factors of production are inputs to te production process. Finised goods are te output and te relationsip of input and output is te production function. Te important point is tat we cannot exaggerate too muc about money. Indeed, te classical viewpoint is tat money is not contained in capital because it is not directly

15 produce any good so it is ard to be related to consumptions of goods at te problem of ouseold. In te paper, firstly, we are focusing on capital including te financial capital. Financial capital is raised to operate and expand a business and it is net wort (assets minus liabilities) including money borrowed from oters. Originally, Capital means goods tat can elp produce oter goods in te future, te result of investment. Considering a labor is not realistic because te number of employees at te firm is ard to be considered at te banking problem. Already we consider equity (asset-liability) is te result after considering labor cost. Redundant firm size variable can evoke te biased information if we pursue obtain te general equilibrium (GE) in tis model. It s true tat wage is te large portion of input at te firm and sould be considered distinguisly. However, for te special industry like banking, we need to clarify needed variables to figure out te problem in te academic field for future and in te realistic world for present. If we contain banks and federal banks in te banking model, we add te real asset variable. It implies te capital concept is naturally inducing te working capital concept. Adding te sock variable to te quality of pysical capital (Nelson-Pinter 2012, Gertler- Karadi 2011, Gertler-Kiyotaki 2010) is ard to be measured and needed to be predicted wit a lot of unexpected uncertain situation. Also, te conservative business cycle is deduced. If we assume tat multiplier µ exists, µ(d +B )>D +B -L fr >L fr. Tis assumption exactly reflects te preference of safetier capital type like real assets > a government bond (lower interest rate on a bond tan a loan) > a loan. 3. Demand Deposit of Bank Scope of Bank Domestically cartered commercial banks, country brances and agencies of foreign banks, Edge Act corporation. Te bank cooses its supply of loans to firms D +B fr +L fr, its demand for deposits D, and te borrowing B fr -L fr in a way tat maximized its profit: Max Π b (P b ) Π b = r L Bank (D +Σ s Ω P s B s -L fr ) - r Lfr (Σ s Ω P s B s fr -L fr ) r D D were r L Bank, r Lfr are interest rates on bank loans and federal reserve bank loan. D denotes for bank deposits. R D is te interest rate paid by deposits. B s denotes for securities. Especially B s fr denotes for securities of federal reserve banks. L fr are loans claimed by te firm to te federal reserve bank. Te bank maximizes te profit by coosing its supply of loans L +, its demand for deposits D - and te issuance Σ s Ω P s B s b. Max Π b (P b ) Π b = r L L + + r Σ s Ω P s B s b r D D - L + = Σ s Ω P s B s b +D - Te part of banks problem provides a context wic capital circulation witin banks is required by oter main factors of economy. Te problem of banks is presented witout equities of banks in fairly balanced debits and credits of banks. Tis main issue as been to andle te demand deposit in te banking area and it related to te money

16 supply closely. In te data of Board of Governors of te Federal Reserve System, demand deposit and money stock data ave been collected from Demand Deposit, Currency and Related items (J.3, Semi montly) in 1960 to Money Stock Measures in Under te fractional reserve banking, deposit is important indicator for economy because of money multiplier effect. In te formula of moneysupply=currency+deposits, demand deposit wic as igest liquidity among deposits on te balance seet of banks is directly related to te M1 of central banks. Diamond and Dybvig model (1983) explains wy bank runs occur at an undesirable equilibrium and wy banks issue demand deposits tat are more liquid tan teir assets by providing better risk saring among people wo need to consume at different random times. Te key to describe te rationality bot for te existence of banks and for teir vulnerability to runs is te illiquidity of assets, especially by te demand deposit. His conclusion on te bank runs as better indicator of economic distress tan money supply is too quick because tere is te duplicated section of deposits and money supply. A bank run is te sudden witdrawal of deposits of just one bank and money supply contains te currency section. In case of bank runs, te government of country sould prepare te recovery solution for economy. Regularly, given information about money supply, te government can figure out about bot moving of currency and deposits. Krugman (2006) points tis out tat deposits are usually considered part of te narrowly defined money supply, as tey can be used, via cecks and drafts, and a means of payment for goods and services and to settle debts. Te money supply of a country is usually eld to consist of currency plus demand deposits. In most countries, demand deposits account for a majority of te money supply. To explain te correlation between deposit (demand deposit) and money supply, bank runs can be interpreted as te sudden constraint of deposit and money supply. We researc on indicators of economic crisis so economic crisis is not te indicator to analyse te status of economy. Gorton and Pennacci (1990) assume tat te uniqueness of demand deposits roles as a desirable medium of excange so te existence of demand for privately produced riskless trading securities induces issuing demand deposits by banks. Actually, under te fractional reserve banking, a bank deposit is not a bailment tat implies pysical possession of personal property. It moves safely upon te banking revenue process. Firstly, te property of customer was deposited. In turn, te customer receives an asset called te deposit account. Finally, te deposit account is te liability of te bank on its balance seet. On te balance seet of Liabilities of all commercial banks in te United States ( ), 70% is te deposit account. Te circulation of deposits is important in economy. David Vanoose (2010) categories te deposit into tree sections like transaction deposit, large-denomination time deposit, saving deposits and smalldenomination time deposits, at te United States commercial bank liability and equity capital. Transaction deposit contains non-interest-bearing demand deposits. Transaction deposit is 6% among total liabilities and equity capital of bank balance seet. Dewatripont-Tirole (2012) points out tat deposit insurance is te prevention of banks runs following te Diamond-Dybvig (1983). In te model of Boyd-Cang-Smit (2004), even toug project return is safe because of a large number of borrowers, e assumes possibility for banks to fail. Regardless of a single borrower and aggregate of borrower, potential bankers can suggest needless to operate te bank.

17 In te model of Covas-Fujita (2010), te bank can raise funds troug eiter deposits or equity so olding equity involves te equity issuance cost. Diaz model (2005) also try to select te considerable sources. For example, firms only source of financing is bank lending te bank can claim te full amount of firm s cas flow. Te equity of banks moves under upper limit of dividend (under te ypotesis tat te bank can turn equity into dividend wit restriction) because of balance seet constraint. Goodart-Kasrap-Tsomocos (2012) mentioned sadow banking. Te securitized loans, called mortgage backed securities (MBS) can be sold to te non-bank and te non-bank will finance te purcase wit a repo loan from te bank (tat will ave te MBS as collateral) 4. Federal Reserve Banks and general equilibrium (GE) Te Federal Reserve Bank cooses its investment level I and its financing (troug real assets D +Σ s Ω P s B s, Liabilities to bank D +Σ s Ω P s B s -L fr (or Liabilities to central bank L fr ) in a way tat maximizes its profit: Max Π b (P b ) Π f = f (I) + r f (D +Σ s Ω P s B s ) - r L Bank (D +Σ s Ω P s B s fr -L fr ) r L fr L fr I=S Were ƒ denotes te production function of te representative firm. r f is te premium of firm s real assets. r L Bank, r L fr are interest rates on bank loans and federal reserve bank loan. D denotes for bank deposits. B denotes for securities. Especially B fr denotes for securities of federalreserve banks. L fr are loans claimed by te firm to te s federal reserve bank. For eac future state of te world s (s ω), one can determine te price P s of te contingent claim tat pays one unit of account in state s and noting oterwise. I is te investment level and S denotes for savings. Interior Solution P f as an interior solution only wen: r f = r L Bank = r L fr 5. General Equilibrium (GE) General equilibrium (GE) is caracterized by a vector of interest rates (r, r D, r, r f,, r L Bank, r L fr ) and tree vectors of demand and supply levels (C 1, C 2, Σ s Ω P s B s, D ) for te consumer, (I, Σ s Ω P s B s, D, L fr ) for te firm, (L fr, Σ s Ω P s B s, D, Σ s Ω P s B s fr ) for te bank and (D, Σ s Ω P s B s, L fr ) for federal reserve banks. Eac agent beaves optimally. (i.e., is or er decisions solve P, P f or P b respectively. Eac market clearing I=S (Good market) D (Firm) - D (Firm) + D (Houseold) - D (Houseold) + D (Bank) - D (Bank) (Deposit market) L fr (Firm) - L fr (Firm) - L fr (Bank) + L fr (Firm) + L fr (FR:Federal Reserve Banks) - L fr (FR) (Credit Market) B s (Firm) - B s (Firm) + B s (Houseold) - B s (Houseold) + B s fr (Bank) - B s fr (Bank) + B s fr (FR) - B s fr (FB) (Financial market) It is clear in tis model tat te only possible equilibrium is suc tat all interest rates are equal: r = r L = r D

18 (result) Arrow (1953) If firms and ouseolds ave unrestricted access to perfect financial markets, ten at te competitive equilibrium, banks make zero profit and te size and composition of balance seet (banks) ave no impact on oter economic agents. (result) Co (2014) If some accumulated variables are not negative, for example, te components Investment I, Savings S, L fr are not negative, tere is te equilibrium in te economy and te existence of eac factors like firms, Houseoulds, Banks, Federal Reserve Banks is fulfilled. Te size of banks is affecting on eac agent because equity capitals depend on previous deposits (additional explanation in Part IV, 7). Depending te cange of bank size influencing on total deposits D, te liability of firms is affected by liabilities to banks D +Σ s Ω P s B s fr -L fr, deposits of ouseold D and real assets of ouseolds and firms. Tis is supported by te following te process of equity capital multiplication.

19 Part IV Effects of Equity Capital Regulation 6. Additional explanation about te borrowing composition of firm s problem Te portfolio composition effected by te minimum equity capital regulatoin. In te model of Kaane (1977), te minimum capital requirement causes an unintended result: it worsened, rater tan improved te intermediary s condition and increases its probability of ruin. He cecks tis calculation wit te ruin constraint and given standard deviation of rate of return at te portfolio composition of liability, stock and bonds. In tis paper, wit te portfolio of risky portfolio and stable portfolio, explanation will be easier to be understood wy minimum equity regulation induces for banks to operate riskier portfolio. In addition, it intends to reduce procyclicality (to te financial socks) and promote te countercyclical buffer. If we assume tat te bank manages a risky portfolio wit an expected rate of return of 17% and a standard deviation of 27%. Te expected rate of return on equity is 7% and even toug, tere is pressure to raise te required equity every period, liability is same every period. Te bank tries to meet te bank capital condition regulated by financial intermediaries so te bank sould operate muc more riskier portfolio comparing to te previous period as following. Effects of increasing te equity at te portfolio composition Period Required Equity, Liability Portfolio composition (risky portfolio, stable portfolio) 1 12 (12%), 88(88%) (-61.6%, 161.6%) 2 13 (13%), 88(87.12%) (-61 %, 161 %) 3 14 (14%), 88(86.72%) (-60.4 %, %) To calculate te portfolio composition, we calculate te expected value (Mean). Mean 0.12(12/100) = (13/101) = (14/102) = Suppose tat te bank decides to invest in te portfolio aving a proportion Y of te total investment budget so tat te overall portfolio will ave an expected rate of return as above. We know an expected rate of return of a risky portfolio Rp is 17% and an expected rate of return of a stable portfolio is 7%. Hence, we get te risky portfolio proportion Y. R f + (R p R f )) Y Proportion Y Y = Y = Y =