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Banking
Banking
Banking
Banking
Banking
Banking
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Banking

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  • 1. FINANCIAL ECONOMICS Christophe Chamley Risk-neutral probabilities Exercises Financial intermediation Banks The Diamond-Dybvig model Diamond, Douglas, W. and Philip H. Dybvig (1983). “Bank Runs, Deposit Insurance, and Liquidity,” Journal of Political Economy, 401-419. ! Bank runs have been common in monetary history. ! Commercial banks that accept demand deposits are subject to bank runs ! Depositors with demand-deposit (checking) accounts are entitled to withdraw heir full deposits in cash without notice. ! Bank runs occur when depostors rush to weithdraw cash because they expect the bank to run out of funds. ! Before a bank runs out of funds, it pays depositors in full. ! After a bank runs out of funds, it pays nothing. ! Therefore, if depositors fear a bank run, they have a large incentive to be among the first to withdraw their funds. 2 "
  • 2. Commercial Banks vs Mutual Funds ! Commercial banks ! The assets are often no liquid, (mortgages-investment in housing) ! If banks are forced to liquidate their assets prematurely in order to pay depositors, they must do so at a loss. ! But they must pay depositors in full (if they have the funds). ! Mutual funds ! Financial institutions taht sell shares in mutual funds,.. ! promise their clients only the current market value of the underlying securities ! If clients wish to withdraw funds, the institution sells the securities and pays the client whatever the securities fetched on the market. ! These institutions cannot run out of funds. ! There is no advantage to be the first to withdraw fund. ! Runs on mutual funds do not occur. 3 Bank runs as a self-fulfilling prophecy ! If depositors fear a bank run, a bank run is likely to occur, even if the bank is solvent (assets ! liabilities) ! If a bank run occurs, the bank may be forced to liquidate assets at a loss ! The bank may then become insolvent 4
  • 3. Investment banks ! Something like this may have happened to the investment bank, Bear Stearns. ! Investment banks do not take deposits, but they do borrow to finance risky investments. ! After lenders began to fear the solvency of Bear Stearns, ! they refused to lend Bear Stearns to pay off its existing debts, ! and BS was forced to sell illiquid assets at a great loss. ! Some commentators say that BS had become insolvent before the bank run began. ! But BS management claims that it became insolvent because of the run. ! Issue Like commercial banks, but unlike mutual funds, investment banks finance risky investments with fixed liabilities. 5 Why do we need banks ! Why do we need conventional banks that have liquid liabilities (e.g., demand deposits) but illiquid assets (e.g., mortgages, loans to firms)? ! Why not only mutual-fund-type “banks”? ! Banks that want to offer liquid demand deposits could invest in liquid assets like treasury bills (T-bills). ! Banks that want to give a better, but not completely guaranteed, return could invest in the mondy market. ! Other securities businesses could offer mutual funds. ! Diamond/Dybvig argue that it is economically useful to convert illiquid assets into liquid assets,... ! but in so doing, banks run the risk of bank runs. 6
  • 4. Banks Banks and liquidity: the Diamond/Dybig model (simplified) ! Production ! capital investment and return T =1 T =1 T =2 0 4  −1  1 0 ! Production ! Diamond, Douglas, capital investment and return W. and Philip H. Dybvig (1983). “Bank Runs, Deposit Insurance, and Liquidity,” Journal of Political Economy, 401-419. 7 Banks Production ! Capital investment and returns T =1 T =1 T =2 0 4  −1  1 1 0 ! The same long-trm productive investment is available to everyone at time 0. Diamond, Douglas, W. and Philip H. Dybvig (1983). “Bank Runs, Deposit Insurance, and Liquidity,” Journal of Political ! An investment of 1 unit at time T=0 yields 4 unites at time T=2. Economy, 401-419. ! but if production is interrupted at T=1, then the investment yields only 1 unit, i.e. the investor gets back only his original input. ! This investment is an illiquid asset, becasue you have to sacrifice most of the return in order to cash in early. 8
  • 5. T =1 T =1 T =2 0 4  −1 T =1  =1 T =2 T T = 1 T = 1 T =0 2 The agent’s state 1  0 4 T = 1  0= 1 T = 2 4  T  −1 1 There is a CARA utility function with coefficient 2: U (C) = 1−  −1 ! Suppose all agens are expected-utility maximizers, with utility in aC   1 0   0 4  for C ≥ period that is CARA with coefficient 2. single 1. 1  0 −1 1 There is a CARA utility function with coefficient 2: U (C) = 1−1   1 0 There is a CARA utilitystates for with agent, θ = 1 or (C) = 1− C There are two possible function the coefficient 2: U 2. for C ≥ 1. C for C ≥ 1. CARA utility function with coefficient 2: U (C) = 1− 1 There is a Agents learn their state at the beginning of period 1. C for C ≥ 1. two possible states for the agent, θ = 1 or 2. There are There are two possible states for the agent, θ = 1 or 2. The utility of the agent is (2 − θ)U (c1 ) + (θ − 1)U (c2 ) There are two the agentstates − θ)U (cagent, θ = 1 or 2 ) The utility of possible is (2 for the 1 ) + (θ − 1)U (c 2. The utility of the agent is (2 − θ)U (c1 ) + (θ − 1)U (c2 ) 1 2 Let π be the probability of state θ = 1 for the agent. The π be the probabilityis (2 − θ)U =11 for(θ − 1)U (c2 ) Let utility of the agent of state θ (c1 ) + the agent. Let π be the probability of state θ = 1 for the agent. 2 His expected utility is His expected utility is Let π be the probability of state θ = 1 for the agent. His expected utility is π 1−π E[U (c1 , c2 )] = 1 − π − 1 − π. His expected utility is(c1 , c2 )] = 1 − π1 −1 −2π . E[U c c E[U (c1 , c2 )] = 1 − c1− c2 . 1 2 c1 c2 9 1 π 1−π2 E[U (c1 , c2 )] = 1 − 1 − . Diamond, Douglas, W. and2Philip H.cDybvig 21 1 c2(1983). “Bank Runs, Diamond, Douglas, W. and Philip H. Dybvig (1983). “Bank Runs, Diamond,Deposit Insurance, and H. Dybvig (1983). “Bank Runs, Douglas, W. and Philip Liquidity,” Journal of Political Deposit Insurance, and Liquidity,” Journal of Political Economy, 401-419. Deposit Insurance, and Liquidity,” Journal of Political Economy, 401-419. Diamond, Douglas, W. and Philip H. Dybvig (1983). “Bank Runs, Economy, 401-419. Deposit Insurance, and Liquidity,” Journal of Political Economy, 401-419. 1 A world without banks 1 ! Each aent receives 1 at time T=0 and1invests it. ! At T=1, an agent in sate 1 has no choice but to liquidate the 1 investment for 1 and consume it. ! His utility is 0. ! If the agent learns he is in state 2, he receives 4 in period 2. ! His utility is 3/4. ! The agent’s expected utility is 1/2. 10
  • 6. Insurance 11

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