Lecture 4: Bank Runs and Failures

Solvency vs. Liquidity

Rajesh Narayanan

LSU Business - Department of Finance

February 2026

The Central Question

Do Runs Cause Bank Failures?

The Diamond-Dybvig model showed bank runs can be an equilibrium.

But it leaves open a critical empirical question:

The Question

Do runs actually cause bank failures — or do banks fail because they are fundamentally insolvent?

This is not merely academic. The answer determines whether policy should focus on stopping panics or restoring solvency.

Why the Answer Matters

If failures are liquidity-driven:

• Deposit insurance and LOLR may suffice
• Central bank lending prevents costly failures
• Policy focus: stopping panics

If failures are solvency-driven:

• Banks must be well capitalized
• Liquidity support alone cannot prevent failure
• Policy focus: capital requirements and supervision

CLV’s Answer (Correia, Luck, and Verner, 2026)

Bank failures — both with and without runs — are almost always related to poor fundamentals. Runs can accelerate failure of already-weak banks, but rarely cause failure of sound institutions.

Part 1: Historical Evidence

160 Years of Bank Failures

Figure 1: Bank Failures, With and Without Runs, 1863–2024 (Correia, Luck, and Verner, 2026)

Four Key Takeaways

1. Repeated waves: Major failure spikes during the Panic of 1893, 1920s agricultural downturn, Great Depression, and GFC. Each crisis reignites the illiquidity vs. insolvency debate.

2. Pre-FDIC: Runs were common in failing banks. Median failing bank lost 14% of deposits before failure; one-quarter lost >20%.

3. Post-FDIC: Failures involving runs became rare. Failing banks lose only ~2% of deposits before failure.

4. Deposit insurance changed how banks fail: It removes run-discipline on insolvent banks. Modern failures are usually supervisory decisions, not market-driven runs.

Failing Banks Show Deteriorating Fundamentals

Figure 2: Failing banks exhibit deteriorating fundamentals irrespective of a run. Red = failures with run; Blue = failures without run; Yellow = survivors. National banks, 1863–1934. Source: CLV (2026).

What Figure 2 Shows

• Profitability (panel a): Declines steadily for failing banks starting five years before failure. Gradual onset rules out a sudden panic as primary trigger.

• Asset quality (panel b): NPLs deteriorate well before failure and accelerate in the final two years — direct signal of building fundamental weakness.

• Deposit reliance (panel d): Drifts gradually lower, consistent with depositors slowly reacting rather than a sudden run-driven cliff.

• The crucial finding: Banks that fail with a run (red) look virtually identical to those that fail without a run (blue).

The Bottom Line

Runs do not select healthier banks for failure — they strike already-weak ones.

Part 2: The CLV Framework

Setup

Two dates \(t \in \{1, 2\}\). A bank holds:

\[A = \underbrace{C}_{\text{cash}} + \underbrace{L}_{\text{loans}} = \underbrace{D}_{\text{deposits}} + \underbrace{E}_{\text{equity}}\]

Key assumptions:

• \(D > C\): bank cannot pay all depositors at once from liquid assets
• Loan return \(\theta\): observable to all depositors at \(t=1\)
• Sequential service: early withdrawers paid first
• Receivership: if \(w > C\) (withdrawals exceed cash), loans are sold at discount \((1-\rho)\theta L\)

The Key Friction

The receivership discount \(\rho > 0\) captures value destruction when loans are sold outside the bank — inalienability of banker human capital (Diamond, 1984).

Three Regions of Bank Health

The Two Thresholds

Solvency Threshold

\[\theta^{Solvency} \equiv \frac{D - C}{L}\]

Below this: bank is fundamentally insolvent. Run is consequence of insolvency, not cause. Withdrawing is a dominant strategy.

Liquidity Threshold

\[\theta^{Liquidity} \equiv \frac{D - C}{(1-\rho)L} > \theta^{Solvency}\]

Above this: bank can always meet obligations even in worst-case run. No run can be an equilibrium.

The Panic Region

\(\theta^{Solvency} \leq \theta < \theta^{Liquidity}\)

Self-fulfilling runs are an equilibrium here.

• If runs occur: bank fails (loan liquidation destroys value \(\rho\theta L\))
• If no run: bank survives

Run is the proximate cause of failure — bank would have survived without withdrawals.

Two approaches to pin down run probability:

1. Sunspot equilibria (DD 1983): arbitrary public signal coordinates beliefs — equal probability for all banks in range

2. Global games (G-P 2005): private noisy signals → unique threshold \(\theta^* \in (\theta^{Solvency}, \theta^{Liquidity})\)

Testable Predictions

H1: Weak fundamentals → failures more likely

\(\theta < \theta^{Solvency}\): run and failure are unavoidable. Note both thresholds decrease in capital ratio \(E/L\) — higher capital reduces both fundamental and run-triggered failures.

H2: Recovery rates reflect insolvency

Pro-rata recovery \((1-\rho)\theta L / (D-C)\) is increasing in \(\theta\). Lower recovery → more likely fundamentally insolvent.

H3: Interbank liquidity reduces panic region

Access to wholesale funding shrinks \(\theta^{Liquidity}\), reducing the range of \(\theta\) where runs can cause failure.

H4: Sleepy depositors mute runs

If enough depositors never withdraw, even insolvent banks can avoid run-driven closure at \(t=1\) — failure becomes predictable rather than sudden.

CLV’s Central Finding

Historical Evidence (1863–1934)

Actual bank failures clustered in the always-fails zone (low \(\theta\)), not the panic zone.

• Runs do not select healthy banks for failure
• The panic region was rarely populated in practice
• Both fundamentals and liquidity problems precede failure — but fundamentals dominate

But does this hold for modern banking?

The March 2023 banking crisis — failures of SVB, Signature, and First Republic — revealed features the traditional framework doesn’t fully capture. Three extensions challenge CLV’s historical conclusion.

Extensions: Modern Banking Challenges

What March 2023 Revealed

Four features of modern bank fragility not in the CLV framework:

1. Liquid assets, not illiquid loans: Failed banks held Treasuries and agency MBS — perfectly liquid (\(\rho \approx 0\)). In CLV, \(\rho = 0\) eliminates the panic region. Yet self-fulfilling runs occurred.

2. Deposit franchise dependence: Banks paid far below market rates → enormous intangible franchise values. This asset vanishes in a run — CLV’s balance sheet doesn’t include it.

3. Systematic rate-driven losses: Fed rate hikes reduced MTM values across the entire banking system simultaneously — not idiosyncratic low-\(\theta\) banks.

4. Uninsured deposit composition as key differentiator: Many banks had similar MTM losses, but only those with extreme uninsured concentration faced runs.

Extension 1: Deposit Franchise Runs

The Deposit Franchise Value

Banks pay deposit rates below market rates. The NPV of this below-market funding is the deposit franchise value \(F\):

\[F \approx \frac{(1 - \beta) \cdot r \cdot D^U}{\delta}\]

where \(\beta\) = deposit beta, \(r\) = market rate, \(D^U\) = uninsured deposits, \(\delta\) = discount rate.

\(F\) is large when…

• Deposit beta \(\beta\) is low (bank pays far below market)
• Uninsured deposits \(D^U\) are large
• Interest rates \(r\) are high (wider spread)

Critical property: \(F\) is a conditional asset — worth \(F\) when deposits stay, worth zero the instant they run.

How \(F\) Shifts the Boundaries

Incorporating franchise value into CLV:

	No-run value	Run value
CLV baseline	\(\theta L + C - D\)	\((1-\rho)\theta L + C - D\)
With franchise	\(\theta L + C + F - D\)	\((1-\rho)\theta L + C - D\)

The asymmetric impact on the two thresholds:

Threshold	Formula	Effect of \(F\)
\(\theta^{Solvency}\) (lower boundary)	\((D - C - F)/L\)	Shifts left by \(F/L\)
\(\theta^{Liquidity}\) (upper boundary)	\((D-C)/((1-\rho)L)\)	Unchanged (\(F=0\) in a run)

Result: The Run-Fragile Zone Widens

\[\underbrace{(\theta^{Liquidity} - \theta^{Solvency}(F))}_{\text{total run-fragile zone}} = \underbrace{(\theta^{Liquidity} - \theta^{Solvency})}_{\text{CLV panic region}} + \underbrace{\frac{F}{L}}_{\text{franchise extension}}\]

Four Regions Instead of Three

The franchise-dependent zone (purple): bank appears solvent because of \(F\), but this solvency is illusory — it evaporates the moment deposits run.

Why Does an Asset Widen the Panic Region?

Student’s natural intuition: \(F\) adds to equity → safer bank → smaller panic zone. This is right for unconditional assets. \(F\) is not unconditional.

	Going-concern equity	Run-state equity	Lower boundary	Upper boundary	Zone width
Regular capital \(\Delta C\)	\(+\Delta C\)	\(+\Delta C\)	Shifts left	Shifts left	Unchanged
Franchise \(F\)	\(+F\)	\(0\)	Shifts left \(F/L\)	Unchanged	Widens

Regular capital helps in both states → both boundaries move → zone unchanged.

Franchise helps in no-run state only → lower boundary shifts, upper stays → zone widens by \(F/L\).

The Deposit Franchise Paradox

A Natural Hedge That Creates New Fragility

When rates rise:

• Asset values fall (MTM losses on fixed-rate securities): \(\theta\) declines
• Franchise value rises (wider deposit spread): \(F\) increases
• Total going-concern value may be stable…

…but this hedge works only if deposits stay.

The Paradox

Banks with the largest franchise values are also the most fragile:

• Large \(F\) → wide franchise-dependent zone → more states of the world where a run is self-fulfilling
• Franchise-dependent zone widens when rates rise — precisely when MTM losses are largest

SVB Through the Franchise Lens

• Low deposit beta (\(\beta \approx 0.15\)): SVB paid far below market rates → enormous \(F\)
• 95%+ uninsured deposits: Nearly all of SVB’s franchise was runnable
• Long-duration assets: Heavy concentration in fixed-rate MBS and Treasuries

When the Fed raised rates aggressively in 2022:

1. Asset values fell sharply (over $15B in unrealized losses) — \(\theta\) declined
2. Franchise value \(F\) rose (wider deposit spread) — offsetting losses on paper
3. SVB had positive GAAP book equity (not book-value insolvent in regulatory sense)… but MTM losses (~$34B) exceeded book equity (~$16B) → MTM insolvent
4. The March 2023 run destroyed the franchise, instantly revealing the insolvency

Contrast with Citigroup: Large uninsured deposits, but high \(\beta\) → small \(F\) → narrow franchise-dependent zone → not exposed to this type of run.

Extension 2: Solvency Runs with Liquid Assets

The Puzzle

CLV: the panic region exists because \(\rho > 0\) (fire sales destroy value).

If assets are perfectly liquid (\(\rho = 0\)): \(\theta^{Solvency} = \theta^{Liquidity}\) → panic region vanishes.

Jiang, Matvos, Piskorski, and Seru (2024)

A panic region can arise even when \(\rho = 0\) through a different mechanism: partial destruction of the deposit franchise by uninsured depositor runs.

This explains March 2023: the failed banks held liquid Treasuries and MBS. Asset illiquidity was not the source of fragility — franchise dependence was.

Extended Balance Sheet

Add liquid securities \(S\) (Treasuries, agency MBS) at book value:

\[C + S + L = D^I + D^U + E\]

Two key variables:

• \(\theta_S = r_0/r_f\): securities fundamental — ratio of coupon rate to current market yield. When the Fed raises rates (\(r_f > r_0\)), \(\theta_S < 1\).

• MTM loss \(= (1-\theta_S)S\): unrealized loss on securities portfolio — directly observable in public filings.

\(S\) is perfectly liquid (\(\rho = 0\)). Loans \(L\) still carry CLV discount \(\rho\).

Two Channels of Value Destruction

A run now destroys value through two channels simultaneously:

Channel	Mechanism	Value destroyed
CLV fire sale	Illiquid loans sold in receivership	\(\rho\theta L\)
Franchise destruction	Uninsured depositors leave → franchise proportionally destroyed	\(\frac{D^U}{D}F\)

Traditional vs. Modern Banks

• Traditional bank (\(S \approx 0\)): CLV’s fire-sale mechanism dominates
• Modern bank (\(L \approx 0\)): Jiang’s franchise mechanism dominates — panic region exists even with \(\rho = 0\)
• Bank with both: Total wedge \(\rho\theta L + \frac{D^U}{D}F\) — larger than either alone

The New Panic Region (Jiang et al.)

Setting \(L = 0\) (all assets liquid), the three-region structure survives despite \(\rho = 0\):

\[\theta_S^{Solvency} = \frac{D - C - F}{S} \qquad \theta_S^{Liquidity} = \theta_S^{Solvency} + \frac{D^U F}{DS}\]

Width of the panic region:

\[\theta_S^{Liquidity} - \theta_S^{Solvency} = \frac{D^U \cdot F}{D \cdot S}\]

Panic region is wider when:

• More uninsured deposits (\(D^U\) ↑)
• Larger franchise value (\(F\) ↑)
• Smaller securities portfolio (\(S\) ↓)

Key Insight

Liability structure, not asset structure, creates the scope for self-fulfilling runs.

The Fragility Index \(s^*\)

Jiang et al. generalize by allowing fraction \(s \in [0,1]\) of uninsured depositors to be “awake” (willing to run); \((1-s)\) are “sleepy.”

\(s^*\) = minimum fraction of awake depositors that makes a self-fulfilling run possible:

\[s^* = \frac{(\theta_S S + C + F - D) \cdot D}{F \cdot D^U}\]

Interpretation:

• \(s > s^*\): self-fulfilling run possible
• \((1 - s^*)\): fragility index — lower \(s^*\) → more brittle
• Banks with more uninsured leverage, lower capitalization, or larger MTM losses → lower \(s^*\)

Numerical Example

Bank with \(C = \$10\)B cash, \(S = \$90\)B Treasuries at 3% coupon (\(L = 0\)), funded by \(D^I = \$10\)B, \(D^U = \$80\)B, \(E = \$10\)B.

Rates rise from 3% to 4%: \(\theta_S = 3/4 = 0.75\). MTM value of securities = \(\$67.5\)B (unrealized loss: \(\$22.5\)B). Wider spread pushes \(F = \$22.5\)B.

No-run value: \(67.5 + 10 + 22.5 - 90 = \$10\)B ✓ (franchise perfectly hedges asset loss)

Run value (all uninsured depositors run, \(s=1\)): \[10 - \frac{80}{90} \times 22.5 = 10 - 20 = -\$10\text{B} \quad \text{(fails!)}\]

Fragility index: \[s^* = \frac{10 \times 90}{22.5 \times 80} = 0.5\]

Even if only half of uninsured depositors run, the bank fails.

Empirical Magnitude

Jiang et al. mark-to-market the entire U.S. banking system as of Q1 2023:

• Aggregate MTM losses: ~$2.2 trillion below book values — on the order of total bank capital
• Average asset value decline: ~10% across all banks
• 2,315 banks (with $11 trillion in assets) had MTM assets below total non-equity liabilities
• With all uninsured depositors running: 1,619 banks would have insufficient assets to cover insured deposits (shortfall to FDIC: ~$300B)
• With only half running: ~186 banks ($300B in assets) would fail

SVB Was Not an Outlier on Losses

10% of banks had larger unrealized losses. What distinguished SVB was extreme uninsured leverage — \(D^U\) in the 99th percentile. Over 78% of SVB’s assets were funded by uninsured deposits.

Extension 3: Financial Fragility

Why G-P Is Still Needed

Extensions 1 and 2 characterize the panic region — its location, width, and determinants. But both face the same limitation as CLV’s baseline:

Multiple Equilibria Remain

Within the panic region, two pure-strategy equilibria coexist:

• Run equilibrium: deposits leave → franchise destroyed → bank fails
• No-run equilibrium: deposits stay → bank survives

Neither DSSW nor JMPS provides an equilibrium selection mechanism. For any bank inside the panic region, a run is possible but not inevitable — depositor beliefs determine the outcome, and both models leave this indeterminate.

G-P completes the framework by introducing private noisy signals that destroy the common knowledge sustaining multiple equilibria → unique run threshold \(\theta^*\) inside the panic region.

G-P tells us not just that a panic region exists and how wide it is, but where within it the run threshold falls.

The Goldstein-Pauzner Link

Recall: global games pins down a unique run threshold \(\theta^*\) inside the panic region.

Goldstein and Pauzner (2005) show:

\[\theta^* = \theta^{Solvency} + \alpha \cdot \underbrace{(\theta^{Liquidity} - \theta^{Solvency})}_{\text{width of panic region}}\]

where \(\alpha \in (0,1)\) depends on the payoff structure.

The Key Result

Wider panic region → higher \(\theta^*\) → runs triggered at better fundamentals → failure more likely for any given \(\theta\).

GP interpret panic region width as the measure of financial fragility.

Three Frameworks Compared

Framework	Source of fragility	What creates panic region	Key parameter
CLV	Weak fundamentals (\(\theta\) low)	Asset illiquidity (\(\rho > 0\))	Receivership discount \(\rho\)
Drechsler et al.	Franchise dependence	Total franchise destruction (\(F\) lost)	Deposit beta \(\beta\), \(D^U\)
Jiang et al.	MTM losses + uninsured leverage	Partial franchise destruction (\(\frac{D^U}{D}F\) lost)	Uninsured leverage \(D^U/D\), \(F\)

The Run Threshold Across Frameworks

Framework	Panic region width	Run threshold rises with…
CLV	\(\frac{\rho(D-C)}{(1-\rho)L}\)	Higher \(\rho\)
Jiang (\(L=0\))	\(\frac{sD^UF}{DS}\)	Higher \(D^U/D\) or higher \(F\)

DSSW vs. JMPS: A Key Institutional Distinction

Both papers share the same basic premise: \(F\) exists only while depositors stay. But they differ in how much franchise is destroyed in a run.

	Who runs	Franchise destroyed	Mechanism
Drechsler et al.	All runnable depositors	Entire \(F\)	Run closes bank → franchise gone completely
Jiang et al.	Only uninsured depositors	Fraction \(\frac{D^U}{D} \cdot F\)	FDIC guarantees insured deposits → they never run

FDIC insurance immunizes the franchise on insured deposits from run risk. Only the \(D^U/D\) fraction is at stake — which is why Jiang et al.’s panic region width \(\frac{D^U F}{DS}\) shrinks toward zero as \(D^U \to 0\).

Different Emphases

• DSSW: Risk management dilemma — franchise hedges rates but the hedge collapses in a run; treat \(F\) as contingent
• JMPS: Empirical measurement — two banks with identical MTM losses can differ sharply in vulnerability based solely on \(D^U/D\)

Three Equivalent Views of Fragility

Higher uninsured leverage \(D^U/D\) affects fragility measures in ways that initially appear contradictory:

Measure	Effect of higher \(D^U/D\)	Direction	Meaning
Panic region width	Wider	↑	More \(\theta_S\) values lead to run failure
Run threshold \(\theta_S^*\)	Higher	↑	Runs triggered at better fundamentals
Fragility index \(s^*\)	Lower	↓	Fewer awake depositors needed to trigger run

These are not contradictory — they measure fragility from different angles:

• Higher \(\theta_S^*\): Bank A faces runs over a wider range of fundamentals
• Lower \(s^*\): For any given \(\theta_S\), a smaller coordination shock suffices

Synthesis

Fundamental or Panic?

A Natural Question

If JMPS and Drechsler et al. center everything on solvency, are the 2023 failures fundamental runs rather than panics?

No — they remain self-fulfilling. Each vulnerable bank had two genuine equilibria:

• No-run equilibrium: deposits stay → bank holds assets to maturity, earns franchise rents → survives (going-concern equity positive)
• Run equilibrium: deposits leave → franchise destroyed and/or liquid assets sold at MTM → fails (run-state equity negative)

A fundamental failure has only one equilibrium: bank fails regardless of depositor behavior. Here, depositor beliefs determine the outcome.

The G-P Connection

These models are in the same tradition as Goldstein and Pauzner (2005) — self-fulfilling runs on “solvent but weak” banks:

Zone	Fundamentals	Outcome
Always fails	Too weak: insolvent in all states	Failure regardless of beliefs
Panic zone	Intermediate: viable going concern, insolvent if run	Determined by depositor beliefs
Always survives	Strong: solvent even in liquidation	Survival regardless of beliefs

Critical difference from G-P: G-P’s panic zone arises from asset illiquidity (\(\rho > 0\)). JMPS and Drechsler et al. generate the same three-zone structure with fully liquid assets (\(\rho = 0\)) — through MTM losses and contingent franchise destruction.

This is precisely why March 2023 was a puzzle: liquid assets should have eliminated the panic zone, yet self-fulfilling runs still occurred.

Unified Interpretation

What the Three Frameworks Together Tell Us

• CLV establishes that fundamental asset quality (\(\theta\)) is the primary driver historically. Actual bank failures cluster in the always-fails zone, not the panic zone.

• Drechsler et al. show apparent solvency can rest on a fragile intangible (\(F\)) that the run itself destroys — widening the run-fragile zone below CLV’s \(\theta^{Solvency}\).

• Jiang et al. show monetary tightening simultaneously reduces asset quality (\(\theta_S\) falls system-wide) while franchise \(F\) creates both a hedge and new vulnerability.

Two senses of solvency that must be kept apart:

Concept	Threshold	Implication
Unconditional solvency	\(\theta \geq \theta^{Liquidity}\)	Runs cannot cause failure
Conditional solvency	\(\theta^{Solvency}(F) \leq \theta < \theta^{Liquidity}\)	Runs are the proximate cause of failure

CLV’s thesis holds for the first definition. Modern extensions expand analysis to the second.

Key Takeaways

1. CLV’s central finding: Bank failures are overwhelmingly driven by poor fundamentals — runs strike already-weak banks, not sound ones.

2. The CLV framework: Three regions (always fails / panic / always survives) defined by \(\theta^{Solvency}\) and \(\theta^{Liquidity}\). Higher capital shrinks both.

3. Deposit franchise (Drechsler et al.): Adding \(F\) widens the run-fragile zone (asymmetric — \(F = 0\) in a run). Larger franchise → more fragile in a paradoxical way.

4. Liquid asset solvency runs (Jiang et al.): Panic region survives even with \(\rho = 0\), created by partial franchise destruction. Liability structure — not asset structure — drives fragility. \(\frac{D^U}{D}\) is the key.

5. G-P link: Wider panic region → higher run threshold → more likely failure. Financial fragility = panic region width. Runs in 2023 were self-fulfilling panics on conditionally solvent (but weak) banks.

References

Primary

• Correia, Luck, and Verner (2026). Review of Financial Studies (forthcoming)
• Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. JPE, 91(3), 401–419.

Extensions

• Drechsler, Savov, Schnabl, and Wang (2025). Deposit franchise runs.
• Jiang, Matvos, Piskorski, and Seru (2024). Monetary tightening and U.S. bank fragility. Journal of Finance.
• Goldstein, I., & Pauzner, A. (2005). Demand deposit contracts and the probability of bank runs. JF, 60(3), 1293–1328.

Empirical tests

• Chen, Goldstein, Huang, and Vashishtha (2022). Liquidity transformation and fragility in the US banking sector. Journal of Finance.
• Gorton, G. (1988). Banking panics and business cycles. Oxford Economic Papers.