Financial Institutions 1
Deposits
Prof. Dr. Oliver Spalt
Chair of Financial Markets and
Financial Institutions
Objectives of this Session
• Get an understanding of deposit contracts, which are key
liabilities banks hold
• Understand how deposits both, create value and induce
fragility in the banking system
• Learn how deposit insurance solves some important
problems, while potentially creating others
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The Importance of Deposits
(Mainly)
Deposits
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Example: Bank of America
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Major Types of Deposits
• Demand Deposits
– Checking account
• Infinitesimal maturity, i.e. depositors can withdraw at any time
• Can be used to make payments
– Money market accounts
• Similar to checking account, but pays interest at money market rates
– Savings account
• Amount that can be withdrawn in a certain period is often limited
• Cannot be used to make payments
• Pays higher interest rate than checking or money market accounts
• Term Deposits
– Certificates of Deposit
• Short to medium maturity (1, 3, 6 months, up to 1-5 years)
• Callable only at a cost
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Who Deposits and For How Long?
Example: Deutsche Bank
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Key Properties of Deposits
1. Deposits are debt contracts
2. Deposits have short maturity (often on demand)
3. Deposits are mainly nontraded
4. Sequential service constraint governs repayment of
deposit liabilities
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A Central Economic Problem for
Uninsured Depositors: Moral Hazard
• Depositors face classical problems related to debt contracts
and imperfect monitoring ability
• Problem 1: Bank has an incentive to increase asset risk
– Bank equity = call option on bank profits;
𝜕𝜕𝑉𝑉(𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶)
𝜕𝜕𝜕𝜕
>0
• Problem 2: Bank has incentive to undersupply monitoring
effort (effectively, this also increases risk)
• Problem 3: Bankers have an incentive to maximize private
benefits at the expense of depositors
– A version of the classical principal-agent problem
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Deposit Design Features as Partial
Remedies (Calomiris and Kahn, 1991)
• Short maturity
– Allows depositors to “vote with their feet”
– Large withdrawals are very costly to the bank…
• New capital to replace old deposits is likely more costly
• Insolvency is very costly to both, bank and bankers
– …hence, depositors’ ability to withdraw quickly disciplines bankers
• Sequential Service Constraint
– SSC = “First come, first served principle“ in withdrawals
– SSC makes “free-riding” on monitoring efforts by other depositors
unattractive, since free-riders risk being last in the queue
– SSC thus incentivizes all depositors to monitor the bank
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A Theory of Deposits and Bank
Runs: Diamond and Dybvig (1983)
• Classic paper that addresses the following questions:
–
–
–
–
Why do banks issue deposits?
Why may banks optimally mismatch asset and liability durations?
Why do depositors sometimes run on banks?
Why is deposit insurance useful?
• Key insights:
– Banks issue deposits to provide liquidity to risk averse investors who
demand liquidity
– Maturity mismatch induces optimal insurance scheme…
– …but at the same time, makes banks run prone
– Deposit insurance can be optimal mechanism to prevent runs
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The Model
• Three dates: T = {0, 1, 2}
• Without a bank, investors have access to the following asset:
– Invest 1 in T=0
– Get payoff r2 if you hold the asset until T=2
– If you liquidate the asset already in T=1, get payoff r1 < r2
• Liquidity can be defined here as: r1/r2
– The lower r1/r2, the lower liquidity
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Investor Types and Utility
Investors:
• Investors need to consume either in T=1 (“investor of type
1“), or T=2 (“investor of type 2“)
• In T=0, investors do not know their type
– But they know: being of type 1 has a probability of t
– Example: With 100 investors and t=0.25, there will be 25 investors
of type 1 and 75 of type 2, but investors only learn their type after
T=0 (investor type is noncontractible)
• Investors are assumed to be risk averse
• Expected utility: t*U(r1) + (1-t)*U(r2)
– Assume U(x) = 1 - 1/x (constant relative risk aversion with RRA=2)
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Comparing Assets By Liquidity
• Asset “I” (= illiquid asset): (r1=1,r2=2)
• Investor expected utility with t=0.25:
– EU = 0.25*U(1) + 0.75*U(2) = 0.25*0 + 0.75*0.5 = 0.375
– Expected Value = 0.25*1 + 0.75*2 = 1.75
• Asset “L” (= liquid asset): (r1=1.28, r2=1.813)
– By the above definition, asset L is more liquid than asset I
– EU = 0.25*U(1.28) + 0.75*U(1.813) = 0.391 > 0.375
– EV = 0.25*1.28 + 0.75*1.813 = 1.68 < 1.75
• The investor prefers the more liquid asset even though EV
of the illiquid asset is higher!
– Liquid asset effectively acts as an insurance device, since it
improves payouts in the bad state (which risk averse investors like)13
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The Value of Bank Liquidity Creation
• Assume that, without a bank, investors could spend 1 to
buy asset I, which yields EU = 0.375
• Alternatively, assume there is a bank which…
– collects 1 in T=0 from each investor as deposit
– invests proceeds in illiquid asset I
– offers liquid deposit contract: promise r1=1.28 and r2=1.813 if
investor (=depositor) withdraws in T=1 or T=2, respectively
Questions:
1. Would investors find deposit contract attractive?
– YES, because EU(L) = 0.391 > EU(I) = 0.375
2. Can bank offer this contract without running out of funds?
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The Banking Solution
• Continue example from above:
• T=0:
– Bank collects 100 from the 100 investors (“deposits”)
– Invests in 100 units of asset I (“loan portfolio”)
• T=1:
– If 25 depositors withdraw their money and receive 1.28 each, the
bank needs 25*1.28 = 32
– Hence bank liquidates 32 units of asset I, pays out 32, and retains 68
• T=2:
– The remaining 75 depositors demand payoff of 1.813 each = 136
– Payoff from 68 units of asset I in T=2 is 68*2 = 136
• The strategy is thus feasible for the bank!
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Main Takeaways
• The bank creates value by providing liquidity transformation
services (a form of QAT)
• By issuing liquid deposits, the bank can help risk averse
investors with uncertain future liquidity needs to reduce the
risk of low payoffs from early liquidation
– The liquid deposit contract acts as an insurance device
– Bank enlarges the investment opportunity set of investors
• Offering liquid deposits and investing in illiquid assets
(“loans”), creates, all else equal, a duration mismatch on the
bank’s balance sheet
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Runs and Panics
• Example Northern Rock:
• https://www.youtube.com/watch?v=sKjdT8I6TnE
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Two Equilibria and Bank Runs
• The “Good” equilibrium: type 2 depositors believe that all
other type 2 depositors will only withdraw in T=2
– Then only type 1 depositors will withdraw in T=1 and all results from
the example above obtain
• The “Bad” equilibrium: type 2 investors believe that all other
type 2 investors will withdraw early
– This is a bank run!
– In T=1, the bank can repay a maximum of 100, but depositors demand
128 –> The bank fails
• Liquidity transformation thus creates value for depositors
but induces bank fragility!
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What Triggers Runs?
• DD model is silent on how beliefs are formed
• Depositor beliefs could be random and irrational (“sunspots“)
– As long as beliefs across banks are not correlated, there may be a run on
single banks, but not a banking panic across banks
– However, banking panics could be indirectly induced: e.g., if banks are
interconnected then fire sales in one bank may drive down asset values
in other banks (systemic risks)
• More plausibly, changes in beliefs may be induced by the arrival
of bad news about the bank, the sector, or the economy
– Correlated changes in beliefs may induce widespread banking panic
– Similar indirect effects as for the sunspot case
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Potential Remedies
• Require bank to hold liquid assets and equity capital:
– Can attenuate but not eliminate the problem
• Suspension of convertibility: bank commits to stop paying out
in T=1 once the fraction t of type 1 depositors is served
– Common in the U.S. before 1933
– Problem: bank may not know the fraction of type 1 investors, so costly
mistakes are possible, if not likely
• Deposit insurance: insurance scheme that guarantees full
payout to type 2 depositors
– This completely eliminates the incentive to run
– Natural provider of deposit insurance: government (almost infinitely
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deep pockets)
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Deposit Insurance Adoptions
Source: Calomiris, C. W., & Chen, S. (2018). The Spread of Deposit Insurance and the Global Rise in Bank Asset Risk since
the 1970s (No. w24936). National Bureau of Economic Research.
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(N = 131)
Source: International Association of Deposit Insurers (2017)
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Source: International Association of Deposit Insurers (2017)
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Potential Problems With Deposit
Insurance
• In an effort to curing one problem, deposit insurance may
amplify another problem, moral hazard at the bank level:
1. Deposit insurance eliminates the need for depositor
monitoring and thus weakens market discipline
–
Incentive for bankers to increase risk and maximize private
benefits (bank equity is a call option on bank profits!)
2. It is hard to set deposit insurance premia right
–
E.g.: flat premia (seen in most countries!) incentivize banks to
maximize asset risk, and thus to exploit taxpayers (if DI is not fairly
priced) or other, less risky, banks (if they subsidize risky banks via
excessive premia)
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Empirical Evidence
Capital ratios for U.S. Credit
Unions around the
introduction of deposit
insurance in 1971
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The Deposit Paradox
• By issuing deposits, banks perform a socially valuable
function but, at the same time, induce banking fragility
• Deposit insurance can prevent runs, but, at the same time,
amplify moral hazard problems and bank risk taking
• Some of the regulatory apparatus we see today is geared
towards minimizing the problems which deposit insurance
amplifies:
– Capital requirements
– Asset portfolio restrictions
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Summary
• Deposits are core liabilities in banking
• By issuing liquid deposits, banks perform a valuable
social function, but, at the same time promote the
risk of bank runs
• Deposits and deposit insurance are central objects
for optimal regulatory policy
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