Bank Funding Risk, Reference Rates, and Credit Supply: Cooperman, Duffie, Luck, Wang & Yang (2025)

What this is. The paper’s core results, the equilibrium model of credit line provision, and the empirical evidence on how banks fund credit drawdowns: enough to know what it found and how, without reading all 52 pages. To replicate or extend it, read the full source at the original.

TL;DR

Revolving corporate credit lines create a debt-overhang cost for bank shareholders: because borrowers draw more heavily when funding markets are stressed, banks must sometimes fund drawdowns with expensive unsecured wholesale debt, diluting legacy shareholders. Credit-sensitive reference rates like LIBOR partially offset this by reducing borrower incentives to draw precisely when bank funding costs are high. The LIBOR-to-SOFR transition removes this offset. Using a calibrated equilibrium model and confidential Federal Reserve data (FR 2052a, FR Y-14Q), the authors show that SOFR-linked lines lead to higher spreads (about 15 bps), smaller credit line commitments (roughly 6% lower for a baseline bank), and a 2.6% welfare loss. The adverse impact is offset at banks that expect drawn funds to be left on deposit, which happened at large universal banks during COVID but not at regional banks during the GFC.

The paper relates to Kashyap, Rajan, and Stein (2002), who identify the liquidity coinsurance synergy between deposits and credit lines; the authors add a new debt-overhang complementarity channel to this synergy. It also extends Jermann (2019), who shows LIBOR-linked loan revenues insure banks against funding risk, to an equilibrium credit provision setting. Empirically, it builds on Ivashina and Scharfstein (2010) on GFC drawdowns, Acharya and Mora (2015) on bank funding pressures, and Gatev and Strahan (2006) on flight-to-safety deposit inflows. In the conclusion, the authors discuss the AXI credit-sensitive reference rate proposed by Berndt, Duffie, and Zhu (2023) as a potential LIBOR successor.

Core results

Magnitudes and significance are as reported; \*, \*\*, \*\*\* = 10%, 5%, 1%. Locators point into the source PDF.

#	Result	Locator	Magnitude
R1	During COVID, each dollar of credit line drawdown is associated with 94 cents deposited at the same bank, insulating shareholders from funding costs	Table IV Panel A, col. 1, p. 24-25	Coeff. on Delta Draws x COVID = 0.94*** (0.34); baseline coeff. on Delta Draws = 0.07 (0.04); total = ~1.01 during COVID
R2	During the GFC (post-Lehman), each dollar of C&I loan growth required ~$4 of new wholesale funding (no deposit offset)	Table V col. 3-4, p. 28	Coeff. on DeltaC&ILoans x Lehman = 4.33*** (0.41) in levels (col. 3); normalized Lehman interaction = 0.90* (0.47) per unit assets (col. 4)
R3	LIBOR-to-SOFR transition reduces equilibrium aggregate credit line commitments by 5.9% for baseline bank	Table VI col. Baseline, p. 38; Figure 5 right, p. 34	-5.87% (baseline theta=1.0, D=0.2); range: +4.64% (low-overhang) to -11.36% (high-overhang)
R4	Transition reduces expected drawn credit by 2.77% for baseline bank	Table VI, p. 38	-2.77% (baseline); +1.12% (low-overhang); -5.20% (high-overhang)
R5	The equilibrium spread on drawn credit rises ~15 bps and the drawn-rate spread rises 51.7 bps over the reference rate for baseline bank	Table VI, p. 38; p. 6	Change in drawn spread s* = +51.7 bps; expected cost of drawn credit rises ~15 bps; SOFR lines ~24 bps more expensive than LIBOR lines in normal times (Figure 5 left, p. 34)
R6	Welfare falls 2.62% for baseline bank; the welfare-maximizing reference rate has ~72% of LIBOR’s credit sensitivity	Table VI, p. 38; p. 39	Welfare change: -2.62% baseline, -4.98% high-debt-overhang, +1.16% low-debt-overhang; optimal lambda* = 0.72 for baseline

Overall (paper’s conclusion). The transition from LIBOR to SOFR increases the ex-ante expected cost banks must charge on revolving credit, reducing the equilibrium supply of credit lines. The magnitude depends on how much of future drawdowns banks expect to receive back as deposits. The adverse effect is concentrated at high-funding-spread, low-deposit-retention banks (predominantly large regional banks), while well-capitalized banks with strong deposit franchises may gain market share. The welfare-maximizing reference rate is more credit-sensitive than risk-free SOFR but need not be as credit-sensitive as LIBOR.

Theory / model

The model has a three-date structure (Figure 1, p. 11). At time 0, a bank offers a menu of credit line contracts $\{(L, s(L)) : L \geq 0\}$ distinguishing line size $L$ and contractual spread $s(L)$ over the floating reference rate $R$. The credit-sensitive rate is $R = r + W$ (LIBOR form, for credit-spread benchmark $W$); the risk-free rate is $R = r$ (SOFR form). At time 1, the reference rate $R$, the bank’s unsecured wholesale credit spread $S$, and the borrower’s liquidity shock $\psi$ are realized. The borrower draws $q \leq L$ and deposits $d \leq q$ at the same bank. At time 2, the bank is solvent or not.

The borrower’s optimal draw quantity solves (eq. 1, p. 13):

$$Q(L) = \underset{0 \leq q \leq L}{\sup} \; b(q, \psi) - q\delta(1 + R + s(L)) \tag{1}$$

where $b(q, \psi)$ is a reduced-form liquidity benefit with marginal benefit $b_x(x, y)$ increasing, differentiable, and strictly concave in $x$. The optimal draw has a threshold structure: $Q(L) = L$ if the marginal liquidity benefit is high enough, and $Q(L) = B(\delta(1+R+s(L)), \psi)$ where $B(\cdot, y)$ is the inverse of $b_x(\cdot, y)$.

The market value of credit lines to legacy bank shareholders is (Proposition 1, eq. 7, p. 14):

$$G(L) = p_1\bigl(\delta Q(L)(1+R+s(L)) - Q(L)\bigr) - p_1\delta(1-\varphi-C)Q(L)S - (1-p_1)CQ(L) \tag{7}$$

where $p_1 = P_1(X \geq 0)$ is the bank’s solvency probability at time 1, $\varphi = d/q$ is the fraction of drawn funds deposited at the bank, $C$ is the regulatory capital ratio, and $S$ is the bank’s unsecured wholesale credit spread. The second term is the debt-overhang cost: the bank must fund $(1-\varphi-C)Q(L)$ of drawdowns with expensive new wholesale debt at spread $S$. Under Bertrand competition ($E[G(L)] = 0$), the equilibrium spread is (eq. 8, p. 14):

$$s(L) = \frac{E\bigl[p_1 Q(L)\bigl(1 - \delta(1+R) + \delta(1-\varphi-C)S\bigr) + (1-p_1)CQ(L)\bigr]}{E\bigl[\delta p_1 Q(L)\bigr]} \tag{8}$$

This spread rises in $\text{Cov}(S, Q(L))$: the key debt-overhang wedge. A credit-sensitive reference rate ($R = r+W$ with $W \approx S$) reduces drawdowns exactly when $S$ is high, cutting this covariance. A risk-free reference rate removes this attenuation.

Identification. The empirical section uses the GFC (Ivashina and Scharfstein (2010)) and COVID recession as quasi-natural experiments that shift the LIBOR-OIS spread to historically extreme levels, allowing the authors to compare how banks funded drawdowns under each episode. The calibrated model is then identified by fitting the distribution of credit line utilization in the FR Y-14Q data across normal times and the COVID recession.

Method

The paper proceeds in three steps. First, the equilibrium model of Section II identifies the theoretical mechanism. Second, confidential FR 2052a and FR Y-14Q data are used empirically to pin down bank funding cost composition and drawdown funding, building on panel-regression and difference-in-differences. Third, the model is calibrated via nonlinear least squares to historical LIBOR-linked credit line behavior and the model is used to simulate the LIBOR-to-SOFR transition.

Calibration of borrower demand. The liquidity benefit is specified as (eq. 11, p. 30):

$$b(q, \psi) = \frac{\psi^\alpha q^{1-\alpha}}{1-\alpha} \tag{11}$$

for price elasticity $1/\alpha$, baseline $\alpha = 1/25$ (elasticity of 25). The optimal draw is therefore (eq. 13, p. 33):

$$Q(L) = \min\!\bigl((K(W) + \epsilon)^+(1+R+s)^{-1/\alpha}, L\bigr) \tag{13}$$

where $K(W)$ is the common component of the borrower liquidity shock (a nonlinear increasing function of LIBOR-OIS spread $W$) and $\epsilon$ is an idiosyncratic shock. The deposited fraction of drawn funds is a logistic function of LIBOR-OIS (eq. 12, p. 32):

$$\Phi(x) = \frac{D}{1+e^{-m(x-w_0)}} \tag{12}$$

with baseline parameters $D = 0.2$, $m = 0.1$, $w_0 = 146.1$ bps. The risk-neutral probability of a GFC-like crisis is set to $p = 4\%$, calibrated to daily LIBOR-OIS observations from January 2005 to April 2021.

Aggregate equilibrium quantities in the continuum-of-borrowers model satisfy (eq. 14-15, p. 33):

$$M \cdot E[Q(L) \mid W] = M \cdot E\!\left[\min\!\left((K(W)+\epsilon)^+(1+R+s)^{-1/\alpha}, L\right) \;\middle|\; W\right] \tag{14}$$ $$P[Q(L) = L \mid W] = P\!\left[(K(W)+\epsilon)^+(1+R+s)^{-1/\alpha} \geq L \;\middle|\; W\right] \tag{15}$$

Empirical specifications

Funding of drawdowns during COVID (eq. 9, p. 24). Using monthly FR 2052a data (20 largest BHCs, July 2017 to April 2022, $N = 1{,}111$, 20 banks), the authors estimate:

$$\Delta y_{bt} = \tau_t + \gamma_b + \beta_1 \Delta\text{Drawdowns}_{bt} + \beta_2 \Delta\text{Drawdowns}_{bt} \times \text{COVID}_t + \epsilon_{bt} \tag{9}$$

where $y_{bt}$ is the change in corporate deposits, FHLB advances, unsecured wholesale funding, or total deposits. $\text{COVID}_t$ takes the value one during March and April 2020. Bank and time fixed effects are included. Robust standard errors are clustered at the bank level. The coefficient $\beta_1 + \beta_2$ measures the marginal funding response per dollar of drawdown during COVID; $\beta_1$ measures the non-COVID response (Table IV, p. 25).

Funding of drawdowns during GFC (eq. 10, p. 27). Using weekly FR 2416 data (30 commercial banks, December 2007 to May 2009, $N = 1{,}765$), the authors estimate:

$$y_{bt} = \tau_t + \gamma_b + \beta_1 \Delta C\&I\text{Loans}_{bt} + \beta_2 \times \Delta C\&I\text{Loans}_{bt} \times \text{Lehman}_t + \epsilon_{bt} \tag{10}$$

where $\text{Lehman}_t$ takes value one from September 15, 2008 through end of 2008. The dependent variable is either total deposits or wholesale short-term funding (WHSLE). Month and bank fixed effects. Robust standard errors (Table V, p. 28).

Both regressions test whether drawdowns generated deposit inflows (low marginal funding cost) or required new wholesale funding (high marginal funding cost). During COVID, banks needed essentially no new external funding because drawdowns were left on deposit; during the GFC, the same drawdowns forced banks to raise costly wholesale debt.

Datasets used

Dataset	Role in paper	Wiki page
FR 2052a (Federal Reserve confidential)	Daily/monthly bank balance sheet, funding composition by counterparty and product type; main panel for COVID empirics (20 BHCs, July 2017-April 2022)	no page yet
FR Y-14Q Schedule H1 (corporate loans) and H2 (CRE)	Loan-level credit commitments and utilization; calibration target for borrower demand and line draw distribution	FR Y-14Q (confidential)
FR 2416 (Federal Reserve, weekly)	Weekly balance sheet for 30 banks; GFC drawdown-funding regression (Dec 2007-May 2009)	no page yet
FR 2420 (Federal Reserve, transaction-based)	Corporate deposit and wholesale funding rates (overnight rates, CDs, fed funds); sensitivity of funding costs to LIBOR-OIS	no page yet
FRED	LIBOR-OIS spread, SOFR, effective federal funds rate	FRED
FR Y-9C / bank call reports	Public balance sheet data merged with FR 2052a for context	no page yet
FHLB Des Moines historical fixed-rate advance file	FHLB advance rates for funding cost benchmark	no page yet
Bloomberg	Long-term bank debt floating-rate and LIBOR-referenced shares	no page yet

Sample: Empirical analysis spans December 2007 to April 2022; calibration uses LIBOR-OIS observations from January 2005 to April 2021.

When to read the full paper

Use the original if you are: (i) pricing revolving credit facilities under SOFR to account for debt-overhang costs, and want the calibrated equilibrium spread formula (Section IV.B); (ii) studying bank balance sheet dynamics during the GFC vs. COVID using FR 2052a or FR 2416 data (Sections III.E-F and Tables III-V); (iii) evaluating alternative credit-sensitive reference rates such as AXI, BSBY, or Ameribor from a welfare-maximizing standpoint (Section V); or (iv) studying how bank capitalization and deposit franchise strength mediate the impact of reference-rate transition on credit supply heterogeneity (Section IV.C and Table VI).

Attribution and rights

Source: peer-reviewed, The Journal of Finance 80(1), February 2025, pp. 5-56. Accepted March 4, 2024; published online December 20, 2024. This distillation was extracted by an LLM on 2026-06-06 and is not human-verified or independently reproduced. The paper is paywalled (Wiley/AFA); only textual extracts are reproduced here.

Cooperman, Harry, Darrell Duffie, Stephan Luck, Zachry Wang, and Yilin (David) Yang. “Bank Funding Risk, Reference Rates, and Credit Supply.” The Journal of Finance 80, no. 1 (February 2025): 5-56. DOI: 10.1111/jofi.13411. © 2024 the American Finance Association. All rights reserved. This page presents distilled extracts only; redistribution of the verbatim article is not permitted.