What Banks Do and Why Banks Exist
LSU Business - Department of Finance
February 2026
By the end of this lecture, you should be able to:
Part 1: What Is a Bank?
Part 2: The Demand for Liquidity
Part 3: How Banks Create Liquidity
Part 4: Can Markets Replicate Banking?
Definition: Bank
A bank is a financial institution that intermediates funds between savers and borrowers.
This definition, while accurate, doesn’t tell us much about:
To understand these questions, we need to look at what banks actually do.
Banks perform valuable activities on both sides of their balance sheet:
Assets (Uses of Funds)
Liabilities (Sources of Funds)
Key Insight (Doug Diamond)
Banks create value through their activities on both sides of the balance sheet, not just one.
Monitoring and screening borrowers
Banks specialize in evaluating creditworthiness and monitoring loan performance.
Why is this valuable?
Why is this Valuable?
Individual savers lack the expertise, scale, and incentives to monitor borrowers effectively. Banks solve this by delegating the monitoring function to a specialized intermediary.
Creating money-like deposits
Banks offer deposit accounts that function as a medium of exchange and store of value.
Key features of deposits:
Redeemable on demand at par: You can withdraw $100 any time and get exactly $100
Accepted for payments: Deposits can be transferred to pay for goods and services
Stable value: Unlike equity or bonds, deposits don’t fluctuate in nominal value (information insensitive debt)
Why Is This Valuable?
Individual savers face uncertain liquidity needs but cannot efficiently self-insure. Banks solve this by pooling liquidity risk across many depositors and providing liquidity insurance — offering liquid deposits backed by illiquid assets. This is liquidity creation: banks create more liquidity than exists in the underlying assets.
Everything we’ve described so far — monitoring borrowers, creating liquid deposits — generates real social value:
How? Through maturity transformation:
But there is a catch
The very feature that makes deposits valuable — redeemable on demand — means the bank must always be ready to pay out. Yet its assets are locked up in long-term loans. This mismatch is the source of banking’s fragility.
Maturity transformation is how banks create value. It is also how they become fragile.
The value it creates
. . .
Example:
The fragility it creates
. . .
The worst case:
Central Question
Maturity transformation is socially valuable but inherently fragile. Why do banks engage in it? What problem are they solving that makes the risk worthwhile?
We have seen that banks create value on both sides of the balance sheet:
In this lecture, we focus on the liability side — how banks create liquidity and provide insurance against uncertain liquidity needs. This is the Diamond-Dybvig model.
In the next lecture, we’ll examine the fragility this creates (bank runs), and then in later lectures, we’ll return to the asset side to study delegated monitoring in detail.
The fundamental economic problem that gives rise to banking:
Consumers face uncertainty about when they will need to consume.
The tradeoff:
Diamond (2007)
“The bank can do what no individual can do for himself — it provides a better set of outcomes across all future scenarios.”
Three periods: \(t = 0, 1, 2\)
Technology:
Two investment technologies available:
Short-term (liquid) investment
Long-term (illiquid) investment
Key relationship: Long-term investment dominates for patient investors: \[ R > r_1 \cdot r_2 = r_2 \]
Intuition
Ex ante identical consumers
Each consumer has initial wealth = 1 at \(t=0\)
Uncertainty about consumption timing:
At \(t=1\), consumers learn their type:
Consumer Types
Expected utility at \(t=0\): \[ EU = \pi \cdot u(c_1) + (1-\pi) \cdot u(c_2) \]
where \(u(\cdot)\) is increasing (\(u' > 0\)), strictly concave (\(u'' < 0\)), with Inada conditions.
Assumption 1: Ex Ante Homogeneity
All consumers are identical at \(t=0\). They don’t know whether they’ll be impatient or patient.
Assumption 2: No Aggregate Uncertainty
Exactly fraction \(\pi\) of consumers will be impatient. The only uncertainty is who will be impatient, not how many.
Assumption 3: Types Are Private Information
At \(t=1\), each consumer learns their type, but the bank cannot observe it directly.
Why these assumptions matter:
Diamond’s numerical example (Diamond 2007):
Let \(\pi = 1/4\), \(R = 2\), \(U(c) = 1 - 1/c\)
Strategy 1: Invest entirely in the illiquid asset
\[EU(\text{illiquid}) = \tfrac{1}{4}\underbrace{\left(1 - \tfrac{1}{0}\right)}_{-\infty} + \tfrac{3}{4}\left(1 - \tfrac{1}{2}\right) = -\infty\]
Strategy 2: Invest entirely in the liquid asset
\[EU(\text{liquid}) = \tfrac{1}{4}(1-1) + \tfrac{3}{4}(1-1) = 0\]
Neither pure strategy works well! We need a mixed portfolio.
Optimal individual portfolio: split between liquid and illiquid
With \(\pi = 1/4\), \(R = 2\), \(U(c) = 1 - 1/c\):
Risk-neutral comparison (expected payoff):
A risk-neutral investor clearly prefers illiquid assets.
But risk-averse investors care about utility, not expected payoff:
Key Insight (Diamond 2007)
Risk aversion — not expected returns — drives the demand for liquidity. A risk-neutral investor would never hold liquid assets. Risk-averse investors hold them as insurance against early consumption needs.
What happens without financial intermediation?
Each consumer individually chooses investment portfolio: \((x, y)\)
Payoffs:
Consumer’s problem at \(t=0\): \[ \max_{x, y} \quad \pi \cdot u(x) + (1-\pi) \cdot u(x r_2 + y R) \quad \text{s.t.} \quad x + y = 1 \]
First-order condition: \[ \pi \cdot u'(c_1^A) = (1-\pi) \cdot R \cdot u'(c_2^A) \]
Key Inefficiency
In autarky, each consumer must hold both assets. Impatient consumers waste the high returns from illiquid assets.
A bank offers a deposit contract \((r_1, r_2)\) that specifies:
Key features:
Budget constraint (with both constraints binding):
\[ r_2 = \frac{(1 - \pi \cdot r_1) R}{1-\pi} \]
Diamond’s 100-Investor Example
With 100 investors, \(\pi = 1/4\): exactly 25 withdraw at \(t=1\), 75 wait until \(t=2\).
Bank invests \(25 r_1\) in liquid assets, rest in illiquid. Patient depositors get: \[r_2 = \frac{(1 - \tfrac{1}{4} r_1) \cdot R}{3/4} = \frac{(4 - r_1) R}{3}\]
The bank maximizes expected utility: \[ \max_{r_1, r_2} \quad \pi \cdot u(r_1) + (1-\pi) \cdot u(r_2) \quad \text{s.t.} \quad (1 - \pi \cdot r_1)R = (1-\pi) r_2 \]
First-order condition: \[ u'(r_1) = R \cdot u'(r_2) \]
Diamond’s Framing
“The bank sets the marginal utility of consumption of the person who withdraws early in line with the marginal cost of providing liquidity — which is \(R\) times the marginal utility of the person who waits.”
Each dollar paid early costs the bank \(R\) dollars of forgone long-term return.
Solving: From \(u'(r_1) = R \cdot u'(r_2)\) and the budget constraint:
\[ (1-\pi) r_2 = (1 - \pi \cdot r_1) R \]
These two equations pin down \((r_1^*, r_2^*)\).
Proposition: Optimal Deposit Contract
The optimal banking contract satisfies: \[ u'(r_1^*) = R \cdot u'(r_2^*) \]
Equivalently: \(\dfrac{u'(r_1^*)}{u'(r_2^*)} = R\)
Interpretation:
Efficiency condition: Marginal utility of early consumption equals marginal cost of liquidity (\(R \cdot\) marginal utility of late consumption)
Full insurance: The bank equalizes the marginal utility per unit of real resources across states
Comparison to autarky:
Since \(\frac{(1-\pi)R}{\pi} > R\) (when \(\pi < 1\)), autarky has too large a gap in marginal utility. The bank narrows this gap through cross-subsidization.
Autarky
Banking
Diamond (2007)
“Each investor needs all or none of the liquidity from their investment. But the bank knows that only fraction \(\pi\) will need liquidity. This is the fundamental source of the bank’s advantage.”
Result: \(r_1^* > c_1^A\) and welfare under banking exceeds autarky (when RRA \(> 1\)).
What if early liquidation is costly but possible? (Diamond 2007)
Suppose the illiquid asset can be liquidated at \(t=1\) for \(\tau\) per unit invested, where \(0 < \tau < 1\).
Bank’s asset management:
When \(\tau > 0\), the bank holds:
Only fraction \(\pi\) withdraw early, so the bank needs exactly \(\pi \cdot r_1\) in liquid reserves.
Individual’s opportunity with early liquidation:
An individual who invests \(1 - r_1\) in the illiquid asset and \(r_1\) in liquid can, if patient, consume: \[ r_2^{\text{individual}} = r_1 + (1-r_1) \cdot \frac{R - \tau}{\tau} = 1 + \frac{(1-r_1)(R-1)}{\tau} \]
But the bank offers: \[ r_2^{\text{bank}} = \frac{(1 - \pi \cdot r_1) R}{1-\pi} \]
Example: \(\pi = 1/4\), \(\tau = 1/2\), \(R = 2\)
With \(r_1 = 1.28\) (optimal bank contract):
Why the Bank Dominates
The individual who sets aside \(r_1 > 1\) for early consumption must over-invest in liquid assets. If patient, they have excess liquidity and insufficient long-term investment.
The bank exploits the fact that only fraction \(\pi\) actually withdraw early — it holds far less in liquid reserves than any individual would need.
Risk aversion (concavity of \(u\)) drives the entire insurance motive:
With concave utility (\(u'' < 0\)):
In the DD context:
Starting from autarky where \(c_1^A < c_2^A\): \[ u'(c_1^A) > u'(c_2^A) \]
Insurance improves welfare by raising \(r_1^*\) above \(c_1^A\) (taking from patient, giving to impatient).
Key Insight
Critical Requirement
For banking to improve on autarky (i.e., \(r_1^* > 1\)), we need RRA \(> 1\).
Proof. With CRRA utility \(u(c) = \frac{c^{1-\gamma}}{1-\gamma}\), the FOC \(u'(r_1^*) = R \cdot u'(r_2^*)\) gives: \[ (r_1^*)^{-\gamma} = R \cdot (r_2^*)^{-\gamma} \implies \frac{r_2^*}{r_1^*} = R^{1/\gamma} \]
Substituting into the budget constraint: \[ r_1^* = \frac{R}{(1-\pi) R^{1/\gamma} + \pi R} \]
For \(r_1^* > 1\): \(R > (1-\pi) R^{1/\gamma} + \pi R\), which simplifies to \(R > R^{1/\gamma}\), i.e., \(R^{(\gamma-1)/\gamma} > 1\).
Since \(R > 1\), this holds iff \(\gamma > 1\).
Summary:
Consider the \((c_1, c_2)\) space:
Budget constraint (resource feasibility): \[ \pi \cdot c_1 + (1-\pi) \cdot c_2/R = 1 \]
Indifference curves: \(\pi \cdot u(c_1) + (1-\pi) \cdot u(c_2) = \bar{U}\)
Optimum: Highest indifference curve tangent to budget constraint
Banking expands the budget constraint by efficiently allocating the long-term investment.
The Diamond-Dybvig model generates a natural term structure:
Since \(\frac{u'(r_1^*)}{u'(r_2^*)} = R\) and \(u\) is concave, we have \(r_2^* > r_1^*\) when \(R > 1\).
Upward-Sloping Term Structure
Long-term deposits pay higher returns because:
In practice, banks offer a menu of deposit products:
This menu allows depositors to self-select based on their liquidity needs.
The Diamond-Dybvig model provides theory — but how much liquidity do banks actually create?
Berger and Bouwman (2009) construct the first comprehensive measures of bank liquidity creation.
Research Question
How much liquidity do banks create? How does it vary by bank size? What’s the relationship between capital and liquidity creation?
Data: Virtually all U.S. banks, 1993-2003
Three-step methodology:
Step 1: Classify each balance sheet item as liquid, semi-liquid, or illiquid
Step 2: Assign weights
| Category | Assets | Liabilities | Off-Balance Sheet |
|---|---|---|---|
| Illiquid | +0.5 | -0.5 | +0.5 |
| Semi-liquid | 0 | 0 | 0 |
| Liquid | -0.5 | +0.5 | -0.5 |
Intuition: Banks create liquidity (+) by transforming illiquid assets into liquid liabilities. Holding liquid assets or issuing illiquid debt destroys liquidity (-).
1. CAT FAT ⭐ (preferred)
2. CAT NONFAT
3. MAT FAT
4. MAT NONFAT
Why Category over Maturity?
Banks’ ability to securitize/sell loans matters more than loan maturity. A 30-year mortgage may be quite liquid if easily securitized.
1. Liquidity creation is substantial
2. Large banks dominate
3. Capital-liquidity relationship depends on size
Large banks:
Small banks:
Diamond-Dybvig Theory:
Berger-Bouwman Measurement:
Evidence:
Policy Implication
Capital requirements may affect liquidity creation differently for large vs. small banks — important for regulatory design.
Jacklin, Charles J. (1987)
“Demand Deposits, Trading Restrictions, and Risk Sharing.” In Contractual Arrangements for Intertemporal Trade, ed. E.C. Prescott and N. Wallace, University of Minnesota Press.
Main question: What happens if agents can trade securities at \(t=1\)? Can markets replicate the DD banking contract?
So far we’ve compared:
Autarky
DD Banking Contract
Jacklin asks: what about markets open at \(t=1\)? Where does this fall?
What can be traded?
Each agent starts with portfolio \((x, 1-x)\). At \(t=1\):
Impatient types sell all \(t=2\) claims at price \(p\): \[c_1^M = x + p(1-x)R\]
Patient types buy \(t=2\) claims: \[c_2^M = \frac{x}{p} + (1-x)R\]
Market clearing gives \(p = \frac{(1-\pi) x}{\pi (1-x) R}\), and consumption: \[ c_1^M = \frac{x}{\pi}, \qquad c_2^M = \frac{(1-x)R}{1-\pi} \]
Optimal portfolio FOC: \[ u'(c_1^M) = R \cdot u'(c_2^M) \]
Same condition as DD! So why isn’t the market allocation identical?
The market imposes an additional constraint the DD bank does not face.
With open markets, a patient depositor can:
If \(r_1 \cdot R > r_2\), patient depositors deviate. For the contract to survive: \[ r_2 \geq r_1 \cdot R \implies r_1 \leq \frac{r_2}{R} \]
But DD optimum has \(r_1^* > r_2^*/R\) — violated! Markets unravel the bank.
Market Equilibrium
The IC constraint binds: \(c_1^M = c_2^M / R\). Combined with the budget constraint: \[ c_1^M = 1, \qquad c_2^M = R \]
Proposition: Ranking of Allocations
\[ U^{\text{Autarky}} < U^{\text{Market}} < U^{\text{DD}} \]
In summary: \(c_1^A < 1 = c_1^M < r_1^*\). Markets get you to the no-arbitrage boundary; only the bank can go beyond it.
Diamond acknowledges Jacklin’s point but argues that trading restrictions are exactly what makes banking valuable:
The Consensus
Jacklin is right about the mechanism: trading restrictions are necessary for optimal insurance.
But this creates a new problem: the same restrictions that enable insurance also make banks fragile. If depositors lose confidence \(\to\) bank runs (Lecture 3).
Banks use several mechanisms to implement the DD contract:
1. Non-Transferable Deposits
2. Penalties for Early Withdrawal
CDs impose penalties eliminating the arbitrage incentive: \[ \text{Penalty} = r_1^* \times R - r_2^* \]
Patient depositor who withdraws early and reinvests nets exactly \(r_2^*\) — no gain from deviating.
3. Monitoring and Verification
Partial verification of liquidity needs (medical emergencies, job loss). Not fully enforceable but helps.
The Jacklin critique became reality in 2008:
Traditional banking: Non-tradable deposits, penalties, FDIC insurance \(\to\) relatively stable
Shadow banking (money market funds, repo): Tradable securities, no penalties, no deposit insurance \(\to\) highly vulnerable
What happened: Reserve Primary Fund “broke the buck” (September 2008) — held Lehman Brothers debt, NAV fell below $1, massive withdrawals spread to other money market funds.
The Lesson
Bank-like claims + Tradability = Fragility
If you want deposit-like insurance, you need deposit-like restrictions: non-tradability, penalties for early redemption, or insurance/guarantees.
Narrow banking proposal: Banks hold only liquid, safe assets (Treasury bills)
Proponents argue:
Critics (Diamond-Dybvig view):
Key Takeaway
The banking structure we observe — illiquid deposits funding illiquid loans — is not an accident:
The same features that make banking valuable also make it fragile:
Good equilibrium:
Bad equilibrium:
Lecture 3 will cover: Multiple equilibria, suspension of convertibility, deposit insurance, and the lender of last resort.
Main Insights from Lecture 2
Banks as liquidity providers: Banks exist to insure depositors against idiosyncratic liquidity shocks
Risk aversion drives demand: Without concave utility, there is no demand for liquidity insurance (Diamond 2007)
Optimal contract: \(u'(r_1^*) = R \cdot u'(r_2^*)\) — marginal utility of early consumption equals marginal cost of liquidity
Banks dominate autarky: Individual needs all-or-nothing liquidity; bank knows fraction \(\pi\) will need it
Markets cannot replicate banking: Tradable claims unravel the insurance (Jacklin 1987)
Trading restrictions are essential: Illiquidity of deposits is a feature, not a bug — but it creates fragility
Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. Journal of Political Economy, 91(3), 401-419.
Diamond, D. W. (2007). Banks and liquidity creation: A simple exposition of the Diamond-Dybvig model. Federal Reserve Bank of Richmond Economic Quarterly, 93(2), 189-200.
Jacklin, C. J. (1987). Demand deposits, trading restrictions, and risk sharing. In E. C. Prescott & N. Wallace (Eds.), Contractual Arrangements for Intertemporal Trade (pp. 26-47). University of Minnesota Press.
Diamond, D. W. (1987). Discussion of Jacklin’s paper. In E. C. Prescott & N. Wallace (Eds.), Contractual Arrangements for Intertemporal Trade. University of Minnesota Press.
Berger, A. N., & Bouwman, C. H. S. (2009). Bank liquidity creation. Review of Financial Studies, 22(9), 3779-3837.
Bryant, J. (1980). A model of reserves, bank runs, and deposit insurance. Journal of Banking & Finance, 4(4), 335-344.
Diamond, D. W. (1984). Financial intermediation and delegated monitoring. Review of Economic Studies, 51(3), 393-414.
Haubrich, J. G., & King, R. G. (1990). Banking and insurance. Journal of Monetary Economics, 26(3), 361-386.
Tirole, J. (2006). The Theory of Corporate Finance. Princeton University Press. Chapter 12.
Freixas, X., & Rochet, J. C. (2008). Microeconomics of Banking (2nd ed.). MIT Press.
FIN 7650 Banking - Lecture 2