Principles of Banking (II): Microeconomics of Banking (3) Bank Capital

Transcription

1 Principles of Banking (II): Microeconomics of Banking (3) Bank Capital Jin Cao (Norges Bank Research, Oslo & CESifo, München)

2 Outline 1 2 3

3 Disclaimer (If they care about what I say,) the views expressed in this manuscript are those of the author s and should not be attributed to Norges Bank.

4 The role of bank capital Besides raising funds from depositors and money market, part of funding comes from bank owner s own pocket equity, or bank capital; Similar as in non-financial firms, equity is certificate of ownership A bank is owned by its shareholders, and profit is distributed among shareholders as dividends; After paying dividends, the retained earnings can be used to increase equity; Equity also bears loss: shareholders are wiped out when loss incurs. Bankruptcy happens when equity falls to zero; What s the role of capital in aligning banks incentives? Why is it claimed that banks hold too little capital?

5 Modigliani-Miller (M&M) Theorem Benchmark: Modigliani-Miller Theorem Theorem (Capital structure irrelevance principle) If (1) capital markets are perfect, (2) information is complete and symmetric, and (3) there are no taxes, bankruptcy costs or agency costs, a firm s value (i.e., the value of claims over the firm s income) is independent of its financial structure and only depends on the present value of future returns. Proof. Consider two identical projects, which need the same input and generate the same return R. We may set up two firms, each running one of the projects, and are different in financial structure: Firm U ( unleveraged ) is funded by equity (E U ) only, and firm L ( leveraged ) is funded by both equity (E L ) and debt (D L ). The value of the firms: V U = E U and V L = E L + D L respectively.

6 Modigliani-Miller (M&M) Theorem (cont d) Proof. (cont d) Suppose an investor has two alternative strategies: (A) Buy x% of equities of firm U, which costs x%e U and returns x%r; (B) Buy x% of equities and x% of debts of firm L, which costs x%e L + x%d L and returns x% (R interest payment) + x% (interest payment) = x%r. Two strategies give the same return. In equilibrium, no-arbitrage condition requires the cost of two strategies to be the same, too: x%e U = x%e L + x%d L, or E U = E L + D L V U = V L. If such firm is a bank, M&M implies that the bank s value doesn t depend on its funding sources, whether it s funded by issuing equity and / or raising debts (through bonds, deposits, interbank borrowing...). But...

7 Why M&M fails in banking? First observation, in reality banks funding sources are quite diversified. Easy to explain: strong incentive to balance between funding cost and liquidity risks (due to reasons such as incomplete market); Second, banks hold a certain ratio of equity (bank capital). Same as firms, equity certifies ownership but is it the only reason why banks need certain level of equity? Role of bank capital? Third, banks usually hold less equity than firms (or, higher leverage ratio), and it is often argued that banks equity ratio is too low. Why do banks prefer debt to equity?

8 The role of bank capital Asymmetric information generates severe incentive problems in banking (making M&M fail), when banks (agensts) are supposed to work for consumers (principals) interests; Bank capital aligns banks incentives and induces them to behave properly As stakes in banks business, capital makes banks skin-in-the-game : misbehavior hurts banks, too; As a signaling device, high capital ratio means a bank can absorb more losses, lower likelihood of being bankrupted so that it can borrow at lower interest rate;

9 Why is banks capital ratio too low? In reality banks are much more leveraged than firms; or Banks have strong preferences for debt so that equity ratio is lower than what society desires Tax advantage: interest paid on debt is often tax deductible; Limited liability and separation of market: only limited number of investors can invest on bank equity. They gain all the rent in normal time, while in bankruptcy only lose up to the amount they invest; (Implicit) public guarantee: incentive to shift risks to insured depositors. Head I win, tail I don t lose; Hard to raise equity ratio because new equity dilutes incumbant owners ROE: debt overhang ; That s why banks often claim that capital is too costly.

10 A theory of bank capital Holmström and Tirole (1997) provides a theory on the role of bank capital, which answers two questions at the same times Why bond market and bank lending co-exist? Or, why do some firms directly borrow from bond market, while others borrow from banks? Entrepreneurs have the incentive to take too much risks ( moral hazard ), so need to put their own stakes ( capital ) in the projects. Only firms with enough stakes ( well capitalized ) can borrow directly from investors; Banks have special monitoring technology, avoiding borrowing entrepreneurs from excessive risk taking. Therefore, less capitalized firms can borrow from banks and access to funding. welfare improving;

11 A theory of bank capital (cont d) Why do banks need to hold capital? Double moral hazard problem Besides moral hazard on the firm side, banks suffer from the same problem, too: they are not guaranteed to do the monitoring job on behalf of depositors properly. They may shirk and avoid the monitoring cost; Therefore, banks are required to hold capital and align incentives should they shirk, the incurred loss would hurt themselves, too; Endogenous market structure: (1) best capitalized firms borrow directly from investors; (2) less capitalized borrow from banks; and (3) worst ones do not get funding.

12 Agents, technology and information Projects available incapital the availability economy, Holmstrom and Tirole each 1997 costs I as initial input The model and yields set upverifiable gross return y if it s successful. There are two types of projects All investment projects cost I unit of money and return y in case of success (verifiable) Good projects (G): probability of success is p G ; Good (G) projects have a probability of success p Bad projects (B): G is p B < p G, but it Bad (B) projects have a probability of success p gives private benefit B > 0 to the entrepreneur. B < p G, with p = p G p B, and give a private benefit B > 0 to the entrepreneur p G y Project G 1- p G Project B 1- p B 0 B (private benefit) p B y + B (private benefit) A. Zazzaro (Univpm MoFiR) Banking Lectures 4-5 AY 2013/2014 First term 18 / 35

13 Agents, technology and information (cont d) A continuum of risk-neutral entrepreneurs in the economy, each Owns wealth A, publicly observable, distribution following probability density function f (A); May choose between two types of projects, good (G) or bad (B). The choice is not observable; A continuum of risk-neutral consumers in the economy who are endowed with money and can buy risk-free assets with safe gross return R; Assumption: p G y > RI > p B y + B. Bad projects are not socially desirable, but preferred by entrepreneurs: moral hazard; Separation of markets: consumers cannot access the risky projects. M&M doesn t hold any more.

14 Case 1: direct lending Without intermediaries, consumers lend L C D directly to entrepreneurs. Assume funds are scarce: Consumers take rd C out of the projects return, when successful; Bad projects have negative net present value (NPV), so consumers only want to have good projects; First best only takes place if consumers know the choice, lend to good projects, and get r C,FB D = y when successful; However, entrepreneurs choice on projects is unobservable They always have the incentive to choose bad projects, pocketing private benefits and leave nothing to consumers: moral hazard; How can consumers avoid that and make sure that entrepreneurs always choose good projects?

15 Case 1: direct lending (cont d) Consumers can induce entrepreneurs to behave properly by Setting rd C such that entrepreneurs can earn more by choosing good projects; Such rd C aligns with consumers interests, it s incentive compatible: ( ) ( ) p G y r C D pb y r C D +B r C D y B = y B p G p B p < r C,FB Further, consumers participation constraint requires expected return from lending is higher than buying safe assets: D ; p G r C D RL C D L C D p G r C D R.

16 Case 1: direct lending (cont d) Suppose entrepreneurs compete for funds so that consumers can set highest possible rd C = y B p. A consumer s willingness to lend becomes L C D p G R ( y B p ) ; On the other hand, an entrepreneur must borrow for his initial input on the project A + L C D I A I p ( G y B ) = A (R). R p

17 Case 1: direct lending (cont d) What do we find from the exercise? When borrowers choice on projects is not observable, there is a chance for moral hazard: they ll opt for private benefit and screw out lenders; To induce desireable choice, lenders must give away some informational rent to borrowers: rd C < r C,FB D ; The incentive compatible solution is only second best; Only entrepreneurs with sufficiently high wealth ( well capitalized, A A (R)) can borrow: capital ensures a firm has enough skin-in-the-game and reduces lenders losses; Can we improve anything if banks are introduced?

18 Case 2: intermediated lending Suppose there are intermediaries called banks They have a special monitoring technology: after spending non-observable C, entrepreneurs private benefit falls to b < B if they operate bad projects; They start with initial wealth L B B, called capital, owned by share holders. They borrow from consumers and lend to entrepreneurs. Banks balance sheet Assets Liabilities Bank capital L B B Loan to entrepreneur L B Get the share rb B if loan performs Return y if project is successful Deposits L C B Get the share rb C if loan performs

19 Case 2: intermediated lending (cont d) Now the projects return will be split among banks (r B B ), depositing consumers (r C B ), and entrepreneurs (r E B ): y = r E B + r B B + r C B ; Again, moral hazard problem arises on entreprenuers side. To induce them to choose good projects, under banks monitoring, the incentive compatibility constraint (IC E ) must hold p G rb E p B rb E + b rb B + rb C y b p (IC E ) ; However, moral hazard also exists on banks side: how can one ensure banks do monitor at cost C?

20 Case 2: intermediated lending (cont d) Therefore, incentive compatibility constraint (IC B ) must hold for banks, too: to make sure they are better off by monitoring so that entrepreneurs choose good projects p G r B B C p B r B B r B B C p (IC B) ; More constraints? Yes, participation constraints for both banks (PC B ) and depositing consumers (PC C ) Banks expected return to equity (ROE) should be high enough to maintain share holders; Depositing consumers expected return should be higher than risk-free return.

21 Case 2: intermediated lending (cont d) Banks participation constraint: suppose share holders demand ROE at least as high as β >> R Here β is exogenously given. In reality, bank share holders do demand very high ROE typically around 15% for risk premium. p G r B B βl B B L B B (β) = p G r B B β = p G C β p (PC B) ; Bank competition ensures that (IC B ) and (PC B ) hold with equality. Depositing consumers participation constraint p G r C B RL C B L C B p G r C B R (PC C ).

22 Case 2: intermediated lending (cont d) Combining (IC E ), (PC C ) and (IC B ), one can see L C B p ( G y b + C ) ; R p Of course an entrepreneur must borrow for his initial input on the project A+L C B +L B B I A I L B B (β) p ( G y b + C ) = A (β, R) ; R p ) Comparing with A (R) = I p G R (y B p, it s easily seen that A (β, R) < A (R) if C is small enough.

23 Case 2: intermediated lending (cont d) Result: co-existence of various types of financing ff(aa) No finance Bank finance Direct finance AA(ββ, RR) AA(RR) AA Entrepreneurs with highest A won t borrow from banks: (1) by direct financing, the required expected return to consumers is weakly higher than R, while (2) by bank finance, the required expected return to depositing consumers is weakly higher than R, but to bank share holders is at least β >> R; therefore, the financing cost in (1) is lower.

24 Case 2: intermediated lending (cont d) Co-existence of various types of financing Entrepreneurs with AA > AA(RR) Direct finance Consumers Bank finance Banks Entrepreneurs with AA(ββ, RR) AA AA(RR) Assets Loans LL BB Liabilities BB Capital LL BB CC Deposits LL BB Consumers Entrepreneurs with 0 AA < AA(ββ, RR) No finance

25 Conclusion Bank capital is a desciplinary device for properly practicing monitoring Banks effort is not observable. Without descipline they would shirk and too many bad projects would be carried out: market breaks down; Capital thus makes banks skin-in-the-game: loss from bad projects would hurt banks so that they have the incentive to monitor properly; This provides access to funding for less well capitalized firms, who wouldn t otherwise be able to borrow directly from investors (due to the same moral hazard problem). Banking improves social welfare; Note: What is NOT covered here is that banks have incentives to hold less capital than socially optimal level.

26 References ( : Recommemded reading) Admati, A. and Hellwig, M. (2013), The Bankers New Clothes: What s Wrong with Banking and What to Do about It, Princeton University Press. Freixas, X. and Rochet, J.-C. (2008), Microeconomics of Banking (2nd Edition), MIT Press, Chapter Holmström, B. and Tirole, J. (1997), Financial intermediation, loanable funds and the real sector, Quarterly Journal of Economics 112, Modigliani, F. and Miller, F. (1958), The cost of capital, corporation finance and the theory of investment, American Economic Review 68,