The Bank Capital Regulation (BCR) model

Transcription

1 The Doctorissimes, 20/11/2014 supervisor: Raphael Douady co-supervisor: Duc Khuong Nguyen The Hye-jin CHO Department of Economics Universit Paris 1 - Panthon Sorbonne hyejin.cho@malix.univ-paris1.fr November 17, 2014

2 The Practical need - OECD Statistical data Cost of Banking Crisis from 1970 to 2007 The average net recapitalization cost to the government was 6% of GDP, fiscal costs associated with crisis management averaged 13% for GDP (16% of GDP if expense recoveries are ignored), and economic output losses averaged about 20% of GDP during the first four years of crisis. Prevention method by the government The estimated midium term impact of Basel 3 implementation on GDP growth would be in the range of 0.05% to 0.15% per year.

3 The Academic need - Stabilization of Financial Economics Incomplete Methodology Microeconomics theory of banking could not exist before the foundation of the economics which information were laid in the early 1970s. Freixas and Rochet (1999) claim that a general equilibrium approach enables one to explain the specific characteristics of the banking industry. This approach is particularly well developed from simple general equilibrium models containing a banking sector under the complete financial market hypothesis (Arrow, 1953) The research aims to articulate fundamental concepts to solve problems of a sudden micro financial shock in the short run with the long run macro stabilization with a balanced perspective between macroeconomics and microeconomics.

4 Literature The Economic approach for capital adequacy regulation Michaelsen-Goshay (1967), Krouse (1970), Parkin (1970), Haugen and Kroncke (1970), Pyle (1971), Hart and Jaffee (1974), Kahane and Nye (1975) Bank s problem approach (commercial, reserve bank) Cost of Deposit Insurance Merton (1978) Dynamic banking model, deposit as uncertainty variable, OHARA (1983) Reserve management modeling, Santomero (1984) Capital regulation on bank asset portfolio risk, Furlong-Keeley (1989) Financial intermediaries and Liquidity trader, Gorton-Pennachi (1990)

5 Literature The Financial Market approach Regulatory capital requirement, Berger-Herring-Szego (1995) Bank lending and money supply, Thakor (1996) Bank shareholder value and market risk, Kupiec-Obrien (1997) Macruprudential approach One bank model at the bank capital and risk-taking, Milne-Whalley (1998) Dynamics of variables in the general equilibrium, Diaz (2005) Procyclicality of Capital requirement in a general equilibrium and equity issuance cost, Covas-Fujita (2010) Financial Regulation in General Equilibrium, Goodhart-Kashrap-Tsomocos (2011) Macroprudential capital regulation in general equilibrium, Nelson-Pinter (2012)

6 The Freixas-Rochet (1999)

7 The Only minimum capital requirement regulation doesn t work (Kahane, 1977) The minimum capital requirement improves the intermediary s condition and increases its probability of ruin? The model (Kahane, 1977) checks this calculation with the ruin constraint and given standard deviation of rate of return at the portfolio composition of liability, stock and bonds. Why does the minimum capital requirement regulation induce for banks to operate riskier portfolio?

8 The (Cho,2014) conditions and pressure of required capital The expected rate of return of 17% the standard deviation of 27% the expected rate of return on equity is 7% Effects of increasing the equity at the portfolio composition) 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 %, %)

9 The (Cho,2014) Result Even though, there is pressure to raise the required equity every period, liability is same every period. The bank tries to meet the bank capital condition regulated by the financial intermediaries. The bank should operate much more riskier portfolio comparing to the previous period as following.

10 The Bank money and GE Bank money movement at the general equilibrium (Cho, 2014)

11 The Why GE for regulation? Why the General Equilibrium (GE) method is useful in the regulation domain? Still, the part of Regulation in Financial Economics is the untouchable field. Categorization of the domain about the bank capital regulation(bcr) - Different domain from Bankrupcy (involuntary process) and Liquidity (Leverage for debt management) under the emergency situation of financial crisis or economic recession - Aiming at the agent management on the on-balance sheet and off-balance sheet risk (containing counterparty risk) and equilibrium of economic stabilization

12 The Saving preference, Real assets, Consumptions Savings containing real assets Max u(c 1, C 2 ) C 1 + s Ω P sb h s + D h + S h s Ω P sb h s D h = W 1 C 2 = Π f + Π b + (1 + r) s Ω P sb h s + (1 + r D )D h + (1 + r h )S h (1 + r) s Ω P sb h s (1 + r D )D h Savings without real assets Max u(c 1, C 2 ) C 1 + P 1 B 1 + D 1 = W 1 R 1 + C 2 + (1 + r 1 ) P 1 B 1 + (1 + r 1 )D 1 P 2 B 2 D 2 = W 2 also, C 1 = (W 1 S 1 ) + (S 1 P 1 B 1 + D 1 ) Why we need the condition of real assets?

13 The Saving preference, Real assets, Consumptions Empirical balance when the capital of a household economy is concerned Ref: European Central Bank, the 4th quarter in 2013 (billion euros, growth rate) Loans- insurance corporations and pension funds house purchase (653.2, -5.3) (3858.1, 0.7) other financial intermediaries other loans (1854.1, -3.1) (796.7, -1.6) non-financial corporations consumer credit (1870.7, 6.7) (576.1, -3.0) government (440.8, -1.8) non-euro area residents (2522.9, -11.2)

14 The Saving preference, Real assets, Consumptions Ambiguity, completeness, regulation methods - Portfolio analysis Suppose that s {G, B}, G=Good, B=Bad. In the case 1, risk aversion is as below. (resp. risk-taking case) Ω = {G, B}, C 1 + s Ω P s=bb h s=b + Dh + S h s Ω P s=g B h s=g Dh = W 1 Incompleteness preference-initial GDP Ω = {G,B, no choice}, no choice can be selected by the choquet expectation CEv(u(x)) = min core(v)e (u(x)) where core(v) = { S : (A) v(a) for all A S} C D h + S h 0 D h = W 1 and D h offset, hence C 1 + C r h = W 1, Initial GDP is caused by partition of initial endowment which is combination of consumption set.

15 The Borrowing constraints Concerns 1. Moral Hazard problem (Boyd-Chang-Smith, 2014) 2. Quality of physical capital to face a shock variable (Nelson-Pinter, 2012) 3. Capital structure with income and control right (Dewartripont-Tirole, 2012) 4. Competitiveness of technology shock (Fujita, 2010) 5. Internal source than external financing (Diaz, 2005)

16 The Borrowing constraints The borrowing composition of firms imparted dynamics -Preference of Real assets: to maintain Real Assets D h + s Ω P sb h s. -Internal financing: Regardless of equilibriums, firms prefer to loan from central banks (so called as bonds) than commercial banks. -Ambiguous aversion: Among the D h and s Ω P sb h s, firms prefer to have D h because of financial stability and preference about certainty. -Financial size: to reflect the tendancy of banks toward the big size with Real Assets. -Going cern of entities: to operate the dynamics of the debt-to-equity ratio D and maintain the economic entity of Real E Assets D + E in the economy of countries.

17 The Borrowing constraints Hightlight on quality of physical capital and conservative business cycle (1) containing banks and federal banks in the banking model and (2) adding the real asset variable. imply the capital concept is naturally inducing the working capital concept. Adding the shock variable to the quality of physical capital (Nelson-Pinter 2012, Gertler-Karadi 2011, Gertler-Kiyotaki 2010) is hard to be measured and needed to be predicted with a lot of unexpected uncertain situation. The regulation is fixed in the expected situation. Also, the conservative business cycle is deduced. If we assume that multiplier µ exists, µ(d h + B h ) > D h + B h L fr > L fr. This assumption exactly reflects the preference of safetier capital type like real assets > a government bond (lower interest rate on a bond than a loan) > a loan.

18 The Demand deposit of Bank Demand deposit, money supply, fractional banking system The bank chooses its supply of loans to firms D h + B fr L fr, its demand for deposits D h, and the borrowing B fr L fr in a way that maximized its profit: Max Π b (P b ) Π b = r L Bank (D h + s Ω P sbs h L fr ) r L f r ( s Ω P sbs fr L fr ) r D D h The bank maximizes the profit by choosing its supply of loans L +, its demand for deposits D and the issuance s Ω P s B b s Max Π b (P b ) Π b = r L L + + r s Ω P sb b s r D D L + = s Ω P sb b s + D

19 The Demand deposit of Bank Talking about capital regulation without capital Without equity: A context which capital circulation within banks is required by other main factors of economy. The problem of banks is presented without equities of banks in fairly balanced debits and credits of banks. Under fractional banking system, commercial banks and reserve banks: This main issue has been to handle the demand deposit in the banking area and it related to the money supply closely. Under the fractional reserve banking, deposit is important indicator for economy because of money multiplier effect. Demand deposit and M1 of money supply: moneysupply = currency + deposits, demand deposit which has highest liquidity among deposits on the balance sheet of banks is directly related to the M1 of central banks.

20 The Demand deposit of Bank Why equities are not balanced at the equilibrium? liquidity mismatch of loans, deposits and equities exists -Dewatripont-Tirole (2012), Diamond-Dybvig (1983): deposit insurance of the prevention of banks runs. -Covas-Fujita (2010): the bank can raise funds through either deposits or equity so holding equity involves the equity issuance cost. -Diaz model (2005) : firms only source of financing is bank lending the bank can claim the full amount of firm s cash flow. bank equity motion, upper limit of dividend (the bank can turn equity into dividend with restriction), balance sheet constraint. -Goodhart-Kashrap-Tsomocos (2012) : shadow banking. The securitized loans, called mortgage backed securities (MBS) can be sold to the non-bank and the non-bank will finance the purchase with an repo loan from the bank.

21 The Federal Reserve Banks and general equilibrium (GE) The final decision to improve the profit level of all agents The Federal Reserve Banks chooses its investment level I and its financing (through real assets D h + s Ω P sbs h, liabilities to bank D h + s Ω P sbs h L fr (or Liabilities to central bank L fr ) in a way that maximizes its profit: Max Π f (P f ) Π f =f (I ) + r f (D h + s Ω P sbs h ) r L Bank (D h + s Ω P sb h L fr ) r L fr L fr I = S h Where f denotes the production function of the representative firm. r f is the premium of firm s real assets. r L Bank, r L fr are interest rates on bank loans and federal reserve bank loan. D h denotes for bank deposits. Bs h denotes for securities. Especially Bs fr denotes for securities of federal reserve banks. L fr are loans claimed by the firm to the federal reserve bank.

22 The Bank regulation: STEP 1 Previous deposit affects optimized equity capital [β = restriction of borrowing] Then, Borrowings can be executed between Deposit 1 and Restriction β [balance sheet equality constraint] D n = B n OEC n

23 The Bank regulation: STEP 1: Previous deposit affects optimized equity capital K > 0, KAHANE (1977) The opportunity set does not pass through the origin. (the vector of Deposit D, Borrowing B, Optimized Equity Capital = 0 give an infeasible solution) K = 0, Controversy with Hart and Jaffee(1974) possible by substantial degrees of leverage. Optimized Equity Capital can not be 0 (Cho, 2014) OptimizedEquityCapital = K Deposits = K K + β

24 The Bank regulation: STEP 1: Previous deposit affects optimized equity capital (1) The bank size can be bigger by the population effect, (2) The going concern of the balance sheet principle is fulfilled at multiple equilibriums. (Cho, 2014) Gorton-Winton (1995):bank size is given Theorem of Modigliani-Miller: the size and composition of banks balance sheets have no impact on other agents. The BCR model concerns As population grows, insured deposits will increase. Then, the bank size should grow so bank size growth concern should be measured.

25 The Bank regulation: STEP 2: kindex for the indicator of risk taking k index : k is the index to decline to increase the risk at the portfolio of commercial banks. The deposit is fixed at total 1 and borrowings have the constraint can not be negative value beyond the minimum borrowings β. k = Deposits + OptimizedEquityCapital Borrowings + OptimizedEquityCapital = 1 + K K + β k index simulation If deposit=1, the minimum of required equity = 10%, borrowings = = = 2.75 If the minimum of required equity is raised from 10%, to 15%, k index was downed = = 2.55

26 Conclusion The Summary The minimum capital requirementis a necessary condition for banking sector stability to raise the quality, consistency and transparency of the capital base. However, it has friction with the portfolio management. By using effects of increasing the equity at the portfolio composition, reducing procyclicality (to the financial shocks) and promoting the countercyclical buffer are pursued. Conclusion (1) The combination of portfolio composition test, (2) deposit-equity optimization and (3) k index enables bounding the bank capital regulation problems.

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