Banking Lecture 2 Alberto Zazzaro Universit` a Politecnica delle Marche Money and Finance Research Group (MoFiR) home page: http://utenti.dises.univpm.it/zazzaro e-mail: [email protected]

AY 2013/2014 – First term

A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Financial intermediation in the saving-investment process 3

Why do intermediaries exist?
In altre parole, per spiegare l’esistenza degli intermediari

Intermediariesoccorre allow dimostrare agents to che make transactions at lower costs and allocate resources efficiently (i.e., greater agents’ utility)

Agent A

Intermediary TCAI

Agent B

TCIB

TCAB TC1 +TCif2 = TCI < TC Intermediation is an efficient solution TCAI + TCIB


UiNI intermediari dispongano di capacità professionali e di una i i A. Zazzaro

(Univpm – MoFiR) tecnologia

Banking –talmente Lecture 2 efficienteAYda 2013/2014 – First term di scambio consentire di

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Financial intermediation in the saving-investment process

Types of financial intermediaries Brokers Buy and sell securities on behalf of investors – reduce search costs Dealers Trade securities for its own account – reduce search and waiting costs Collective investment schemes Pool money from many investors by issuing securities which are representative of a bundle of marketable securities they buy – reduce diversification costs Banks Hold non-marketable, illiquid assets (loans) that are funded largely by issuing very liquid liabilities (deposits) which are withdrawable on demand – reduce liquidity and information costs A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

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Financial intermediation in the saving-investment process

Why do banks are special? Liability side Bank deposits are repayable on demand at their face value and are used as immediate substitute for money By collecting deposits from a large number of investors, banks diversify risk of deposit withdrawal and may invest in illiquid assets Asset side Loans are non-marketable assets with a great content of private information By financing their activity with demand deposits, banks have incentives (and exclusive information) to act as information producer and delegated monitor A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

The intuition

Investments returns are long-term, while consumption needs are uncertain and subject to idiosyncratic shocks As long as consumption shocks are not perfectly correlated across individuals, banks may efficiently invest savings long-term, providing depositors with insurance against idiosyncratic consumption shocks

A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

The model set up The economy lasts three periods, t = 0, 1, 2, and produces one good There is a continuum of agents of measure 1 each endowed with one unit of good at time 0 Agents get utility from consumption and are sufficiently risk averse u 0 (c) > 0; u 00 (c) < 0;

−cu 0 (c) ∂cu 0 (c) > 1 ⇔ < 0; u 00 (c) ∂c

At t = 1 agents experience a consumption shock and learn whether they are ”impatient”, i.e., they derive utility only from consumption at t = 1, or are ”patient”, i.e., they derive utility only from consumption at t = 2 Liquidity shocks are not publicly observable and an insurance market cannot open A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

The model set up (cont’d) The probabilities of being impatient and patient (the shares of impatient and patient in the population) are p and 1 − p With no discounting, the expected utility of each individual at t = 0, as well as the social welfare, is U = pu(c1 ) + (1 − p)u(c2 ) p is common knowledge; consumption shocks are unobservable The good can be stored or can be invested in an amount 0 ≤ I ≤ 1 in a long-run technology The investment provides R > 1 units of consumption at t = 2, but L < 1 units of consumption if it’s terminated early at t = 1 A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

Optimal allocation

max U = pu(c1 ) + (1 − p)u(c2 ) c1 ,c2

s.t.

pc1 = 1 − I (1 − p)c2 = IR

max L = pu(c1 ) + (1 − p)u(c2 ) − λ[pc1 + (1 − p) c1 ,c2

c2 − 1] R

 ∂L 0   ∂c1 = pu (c1 ) − pλ = 0 λ ∂L 0 ∂c = (1 − p)u (c2 ) − (1 − p) R = 0   ∂L2 c2 ∂λ = pc1 + (1 − p) R − 1 = 0 u 0 (c1 ) = Ru 0 (c2 ) A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

Optimal allocation (cont’d)

Given that R > 1 and u 00 (·) < 0 c1∗ < c2∗ Given that

∂cu 0 (c) ∂c

R · u 0 (R)

Therefore, given that u 00 (·) < 0 1 < c1∗ < c2∗ < R

A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

Autarky

c1 = 1 − I + LI = 1 − (1 − L)I ≤ 1 c2 = 1 − I + RI = 1 + (R − 1)I ≤ R

Consumers cannot replicate the optimal allocation

A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

Financial markets

Assume that after the liquidity shocks occur a financial market opens where agents can trade their present and future goods Let B be a bond which yields with certainty a unit of good at t = 2 and b its price c1 = 1 − I + bRI 1−I c2 = + RI b

A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

Financial markets (cont’d) If b > 1/R (i.e., if bR > 1) all agents prefer to invest long-term and sell the bond when they know to be impatient. If b < 1/R (i.e., if 1/b > R) all agents will prefer to store their goods and buy the bond when they know to be patient In equilibrium: b = 1/R Therefore c1 = 1 c2 = R

Financial markets cannot replicate the optimal allocation A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

Banks The optimal allocation can be implemented by a bank offering the following deposit contract D ∗ : In exchange for one unit of good at time 0, pay c1∗ on deposits withdrawn at t = 1 and c2∗ on deposits withdrawn at t = 2 Bank balance sheet Assets Loans = 1−

pc 1*

Liabilities Deposits = 1

Reserves = pc 1*

A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

Banks: efficient equilibrium

Impatient investors have no interest to withdraw at t = 2 and patient have no interest to withdraw at t = 1 The contract D ∗ and the asset allocation reported in the balance sheet are a Nash equilibrium

A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

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Liability side: banks as consumption smoothers

Diamond and Dybvig 1983

Banks: bank–run equilibrium

When there is uncertainty concerning p, R or there is lack of confidence in the bank, another possible equilibrium is all depositors withdraw at t = 1 Assume that a patient investor believes that a fraction x of other patient investors wants to withdraw at t = 1 He anticipates that the bank will be forced to liquidate part of its long-term investments at a loss in order to pay c1∗ at t = 1 and, hence, that it cannot pay c2∗ to 1 − x patient depositors The optimal strategy for patient and impatient investors is to withdraw at t = 1, and the Nash equilibrium is ”bank run” (all consumers withdraw at t = 1 and the bank is liquidated)

A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

AY 2013/2014 – First term

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Liability side: banks as consumption smoothers

Extensions and criticisms to D&D

Remedies Narrow banking: banks must hold an amount of liquidity equal to demand deposits, i.e., 100% reserves [or banks can liquidate some assets in the case of unexpected withdrawals] max c1 ,c2

s.t.

U = pu(c1 ) + (1 − p)u(c2 ) c1 ≤ 1 − I c2 ≤ IR

[c1 ≤ 1 − I + LI ] [c2 ≤ 1 − IR]

which cannot replicates the optimal allocation Suspension of convertibility (to establish a threshold above which the convertibility of deposits is suspended) feasible if p (the fraction of impatient depositors) is known with certainty if p˜ is a random variable and π is the threshold, then if p > π impatient are rationed if p < π a bank run is possible

Deposit insurance A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

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Liability side: banks as consumption smoothers

Extensions and criticisms to D&D

Equity-funded banks – Jacklin 1987 In D&D, demand deposits are assumed non-tradable and depositors are satisfied according to a sequential service (first-come-first-served) rule Jacklin (1987) shows that a bank financed by tradable equities, which distribute a dividend d to each investor in t = 1 and R(1 − d) in t = 2, can achieve the social optimal allocation, like a bank financed by non-tradable deposits, without being subject to panics Proof Let q be the price of the share; a depositor endowed with one unit of money may consume

A. Zazzaro

(Univpm – MoFiR)

c1

= d +q

c2

= R(1 − d) +

d R(1 − d) q

Banking – Lecture 2

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Liability side: banks as consumption smoothers

Extensions and criticisms to D&D

Jacklin ’87 – Proof (cont’d) In equilibrium, q is such that the supply and demand of bank’s shares are equal d d p = (1 − p) q = (1 − p) q p substituting for q in c1 and c2 we have R(1 − d) d c1 = c2 = p 1−p d is determined by maximizing individual utility U subject to the above expressions for consumption max c1 ,c2

s.t.

U = pu(c1 ) + (1 − p)u(c2 ) c1 = c2 =

d p

R(1−d) 1−p

which is the same maximization program as in D&D and replicates the optimal allocation max c1 ,c2

s.t. A. Zazzaro

(Univpm – MoFiR)

U = pu(c1 ) + (1 − p)u(c2 ) pc1 +

(1−p) c2 R

Banking – Lecture 2

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Liability side: banks as consumption smoothers

Extensions and criticisms to D&D

Criticisms and extensions In D&D, investment returns are assumed certain and bank runs purely speculative and inefficient; actually, returns are uncertain and runs may have a fundamental origin and be efficient Gorton (1985) shows that if there is asymmetric information on the value of bank’s assets, the suspension of convertibility may allow banks to transmit, at a cost, information on the true expected returns to depositors Chari and Jagannathan (1988) assume that some patient depositors receive a signal on the bank’s performance; the others observe the deposit withdrawals at t = 1; if the asset liquidation value is larger than the expected return conditional on the signal the bank run is efficient

Multiplicity of banks, bank-specific liquidity shocks and interbank market (Bhattacharya and Gale 1997) A. Zazzaro

(Univpm – MoFiR)

Banking – Lecture 2

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Other liability-based theories

Banks as liquidity providers

Gorton and Pennacchi (1990) show that if uninformed traders recognize the fact that they lose money when they trade securities with better-informed traders, a demand arises for liquid and safe securities like bank deposits (i.e., securities that can be unexpectedly sold by uninformed traders without a loss to more informed traders)

A. Zazzaro

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Syllabus

References

Freixas X. and J.-C. Rochet (2008), The microeconomics of banking, Boston: The MIT Press, 2nd edition, Sections 2.2, 7.1, 7.2, 7.4, 7.6 Gorton G. and A. Winton (2003), Financial intermediation, in Handbook of the economics of finance, edited by G.M. Constantinides, M. Harris and R.M. Stulz, Amsterdam: Elsevier, chapter 8

A. Zazzaro

(Univpm – MoFiR)

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