# **Box 2: “Bank Runs, Deposit Insurance and Liquidity”**<sup>**1/**</sup>

Economic literature has tried to explain the existence of banks, struggling with two important questions: (i) Why is there a demand for bank <mark>(sight)</mark> deposit contracts when depositors know that there is a small but still positive probability of bank runs which are likely to result in a partial or total loss of wealth if banks are forced into ‘fire sale’ liquidation? (ii) Why do banks issue bank (sight) deposit contracts while engaging in the transformation of liquid deposits into less or illiquid assets, knowing that this term-transformation leaves banks vulnerable to runs and the risk of failure?.

The classic paper by Diamond and Dybvig provides an answer to these two questions, demonstrating that: (i) Bank deposit contracts can lead to a superior allocation of wealth and resources for depositors and banks, **provided confidence is maintained.** They demonstrate that there are multiple equilibria, with different levels of confidence, including the undesirable state of a bank run. As they indicate, the “illiquidity of assets provides the rationale both for the existence of banks and for their vulnerability to runs” (p. 403). If the optimal risksharing among depositors in normal times is disrupted by a run on the bank--given the sequential nature of bank deposit contracts (first-come, first-served)--depositors have the incentive to withdraw their money as fast as they can under the expectation that late comers will be faced with partial or total loss. This outcome results from the expectation that the face value of deposits will be larger than the liquidation value of the bank’s assets if bank owners are forced to liquidate assets in a rush. Under these circumstances, the only “feasible contract” that allows banks both to prevent runs and to provide optimal risk sharing is to suspend the convertibility of deposits (as witnessed during the Argentina crisis of 2001 with the infamous “corralito”).

If the bank is solvent, the suspension of convertibility--when withdrawals are excessive--removes the option of at least some depositors withdrawing funds and, in that way, restoring a ‘good equilibrium’. A second mechanism which can be used to achieve the same result is for the government to offer a deposit guarantee funded by the power of taxation. To the extent that this insurance offers a credible promise of no-loss, it will not need to be fulfilled and a ‘bad equilibrium’ can be avoided. The third option to stabilize bank deposit contracts is to design a lender of last resort facility, able to provide the same guarantee of the deposit insurance system. The fourth intervention (although not a direct financial tool) of a preventive nature has to do with a regulatory regime to contain liquidity risks.

In other words, banks are intrinsically vulnerable to shifts in expectations. Once confidence is lost and, in the absence of suspension of convertibility of deposits into cash, fire sales of bank assets become a self fulfilling prophecy for bank insolvency, resulting in losses for depositors.

Diamond and Dybvig’s approach assumes that the liquidity crisis results from a shift in expectations “which could depend on almost anything”, and it is not related only to the bad quality or loss of the underlying assets. So the fragility of the ‘good equilibrium’ is such that anything that causes depositors to anticipate a run will lead to a run. In spite of this fragility, bank deposit contracts are demanded as a form of insurance that allows depositors to request their deposits to finance their consumption as needed. The liquidity demand is driven by uncertainty and/or the presence of asymmetric information.

> 1/ <mark>Douglas W. Diamond and Philip H. Dybvig,</mark> _<mark>Journal of Political Economy</mark>_ <mark>, 1983, Vol.91, no.3.</mark>

38. **_Volume and composition of balance sheet_**<sup>_30_</sup> . On the liability side of the balance sheet, bank analysts should look at deposits: types, amounts, concentration, possibility of withdrawals (contractual versus behavioral); and inter-bank lines of credit and loans: size, maturities, other restrictive covenants, and rollover possibilities. On the asset side of the balance sheet a bank 30 Banque de France, Financial Stability Review,” Liquidity Regulation and the lender of last resort”, February 2008