Measuring Liquidity Mismatch in the Banking Sector

• DOI: http://doi.org/10.1111/jofi.12591
• Author: ARVIND KRISHNAMURTHY,CHARLES‐HENRI WEYMULLER,JENNIE BAI
• Published date: 01 February 2018
• Date: 01 February 2018

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 1 •FEBRUARY 2018

Measuring Liquidity Mismatch

in the Banking Sector

JENNIE BAI, ARVIND KRISHNAMURTHY, and CHARLES-HENRI WEYMULLER∗

ABSTRACT

This paper constructs a liquidity mismatch index (LMI) to gauge the mismatch

between the market liquidity of assets and the funding liquidity of liabilities, for

2,882 bank holding companies over 2002 to 2014. The aggregate LMI decreases from

+$4 trillion precrisis to −$6 trillion in 2008. We conduct an LMI stress test revealing

the fragility of the banking system in early 2007. Moreover, LMI predicts a bank’s

stock market crash probability and borrowing decisions from the government dur-

ing the financial crisis. The LMI is therefore informative about both individual bank

liquidity and the liquidity risk of the entire banking system.

LIQUIDITY PLAYS AN ENORMOUS ROLE in financial crises. In the classic model of

Diamond and Dybvig (1983), the illiquidity of bank assets coupled with the

liquidity promised through bank liabilities leaves banks vulnerable to runs

and financial crises. During the 2007 to 2009 financial crisis, the U.S. gov-

ernment provided several trillion dollars of reserves to the financial sector to

forestall and ameliorate a liquidity crisis.1Regulators have taken steps to im-

prove the liquidity of banks since the financial crisis. For instance, the Basel

∗Jennie Bai is with McDonough School of Business at Georgetown University. Arvind Krish-

namurthy is with Stanford University Graduate School of Business and NBER. Charles-Henri

Weymuller is with French Treasury. We thank Michael Roberts (the Editor), two referees, Viral

Acharya, Christa Bouwman, Markus Brunnermeier, Allen Berger,Adam Copeland, Darrell Duffie,

Michael Fleming, Itay Goldstein, Gary Gorton, Samuel Hanson, Song Han, Larry Harris, Ben-

jamin H´

ebert, Yi Li, Angela Maddaloni, Antoine Martin, Stefan Nagel, Mitchell Petersen, Klaus

Schaeck, Philipp Schnabl, Mark Seasholes, David Skeie, Philip E. Strahan, and seminar partic-

ipants at AFA (2016), WFA (2014), EFA (2014), SFS Finance Calvacade (2014), FDIC Annual

Conference (2014), BIS Research Network Meeting (2014), European Bank Association’s Annual

Financial Stability Conference (2014), Mitsui Finance Symposium (2015), the Role of Liquidity in

the Financial System Conference (2015), Stanford University, New York University, Copenhagen

Business School, Georgetown University, and University of Rhode Island for helpful comments.

We also thank participants at the BIS, European Central Bank, International Monetary Fund,

the Federal Reserve Board, Federal Reserve Bank of New York, Federal Reserve Bank of Atlanta,

Deutsche Bundesbank, Bank of France, Bank of England, and the Department of the Treasury’s

Office of Financial Research. Jonathan Choi, Jay Im, Jiacui Liu, and Yiming Ma provided excel-

lent research assistance. Arvind Krishnamurthy received a Research Grant from Goldman Sachs

Global Markets Institute from 2012 to 2015 to study ECB policy. The authors declare that they

have no relevant or material financial interests related to the research in this paper.

1Fleming (2012) notes that, across its many liquidity facilities, the Federal Reserve provided

over $1.5 trillion of liquidity support during the crisis. This number is much higher if one includes

other forms of government liquidity support. Lending by the Federal Home Loan Bank peaked at $1

DOI: 10.1111/jofi.12591

51

52 The Journal of Finance R

III committee has implemented minimum liquidity standards for commercial

banks, including the liquidity coverage ratio (LCR) and the net stable funding

ratio (NSFR), and the Federal Reserve has incorporated a liquidity stress test

(the Comprehensive Liquidity Assessment and Review (CLAR)) as part of its

oversight of large banks.

These policy responses have run ahead of research and raise important ques-

tions for researchers to answer. First, we lack an agreed-upon framework for

examining when government regulation of private liquidity choices is desir-

able, and what instruments should be used to implement liquidity regulations.

A small but growing literature has sought to address these questions (see Holm-

strom and Tirole (1998), Caballero and Krishnamurthy (2004), Farhi, Golosov,

and Tsyvinski (2009), Perotti and Suarez (2011), Allen (2014), Diamond and

Kashyap (2016)). Second, we lack an agreed-upon framework for how to mea-

sure the liquidity of financial firms and the financial sector. Beyond simple

intuitions for special cases (e.g., long-term loans are illiquid assets, while cash

is liquid, and short-term debt liabilities leave a bank prone to liquidity risk,

while long-term debt liabilities reduce liquidity risk), we lack a general system

for measuring liquidity that can handle a sophisticated financial sector.

As Allen (2014) and Diamond and Kashyap (2016) note, there is a striking

contrast between the analysis of capital and liquidity regulations. With capital,

there is a consensus on how to measure capital and why it should be regulated,

although disagreement persists on the optimal level of capital requirements.

With liquidity, there is little consensus beyond the recognition that liquidity is

hard to measure.

In this paper, we develop and implement a liquidity measurement system.

This paper builds on earlier theoretical work by Brunnermeier, Gorton, and

Krishnamurthy (2012) and is also related to Berger and Bouwman’s (2009)

empirical approach to measuring liquidity. Adopting the terminology in Brun-

nermeier, Gorton, and Krishnamurthy (2012), the “liquidity mismatch index”

(LMI) measures the mismatch between the market liquidity of assets and

the funding liquidity of liabilities. The LMI is based on a stress liquidity-

withdrawal scenario: all claimants on the firm are assumed to act under the

terms of their contract to extract the maximum liquidity possible, and the

firm reacts by maximizing the liquidity it can raise from its assets. The net

liquidity under this scenario gives the LMI for the firm. Brunnermeier, Gor-

ton, and Krishnamurthy (2012) derive their liquidity metric in settings with

a fixed liquidity stress horizon (i.e., overnight). We extend their measure to

encompass dynamic settings: the LMI today is the appropriately “discounted”

value of the expected LMI tomorrow. The recursive construction captures the

liquidity of different maturity liabilities as, for example, a two-day liability

today will become a one-day liability tomorrow. Our approach also accounts

trillion in September 2008. The Federal Deposit Insurance Corporation insurance limit increases

in the crisis provided further guaranteed support of $336 billion as of March 2009 (He, Khang,

and Krishnamurthy (2010)). The U.S. Treasury also offered $431 billion of funding through the

Troubled Asset Relief Program (TARP) (see page 3).

Measuring Liquidity Mismatch in the Banking Sector 53

for the time-varying state of liquidity conditions, which we achieve by linking

the liquidity stress horizon to asset market measures of market and funding

liquidity. Existing measures, including Basel’s liquidity ratios and the Berger

and Bouwman (2009) metric, restrict measurement to a fixed liquidity stress

horizon.

A good liquidity measure must be theoretically coherent and shed light on

data. The recursive principle and incorporation of market prices favor our con-

struction theoretically. The bulk of this paper shows that the LMI performs

well empirically. First, we show that the LMI is useful from a macropruden-

tial perspective. A liquidity metric should capture liquidity imbalances in the

financial system, offering an early indicator of financial crises. It should also

quantitatively describe the liquidity condition of the financial sector and the

amount of liquidity the Fed may be called upon to provide in the event of a

financial crisis. The LMI performs well on each of these dimensions. Another

important feature of the LMI is that it can be aggregated across banks to

measure the liquidity mismatch of a group of banks or of the entire financial

sector. Liquidity measures that are based on ratios, such as Basel’s LCR, do

not possess this aggregation property. The LMI is also well suited to stress

test analysis. The market liquidity of assets and funding liquidity of liabilities,

which form the LMI, can be described in terms of their exposures to a set of

underlying factors. In our implementation, we use repo market haircuts to ex-

tract the asset liquidity factor and the spread between the Treasury bill rate

and the Overnight Indexed Swap rate (hereafter the OIS-Tbill spread) as the

funding liquidity factor. A stress test can be conducted by shocking the haircut

factor and the OIS-Tbill spread and then measuring the change in the LMI of

a bank or of the financial system. In a one-sigma (1σ) shock at the beginning of

2007, for example, we show that the aggregate liquidity of the banking sector

dips by nearly $1 trillion below zero, providing an early warning signal of the

fragility of the financial sector. In 2007Q2, a 3σshock takes the LMI of the

banking sector to −$4.71 trillion. Our stress test and its predictions provide an

anchor for estimating the Fed’s liquidity provision during a systemic/aggregate

liquidity crisis and capture the banking sector’s liquidity risk.

Our second set of empirical criteria arises from microconsiderations. We

argue that a good liquidity measure should capture liquidity risk in the cross

section of banks, identifying which banks carry the most liquidity risk. We

show that our measure performs well, and better than other measures, in this

dimension. We examine the cross section of banks and show that banks with

a lower LMI before the crisis have higher crash risk during the peak of the

financial crisis. Banks with a lower LMI are also more likely to borrow from

Federal Reserve facilities and the Troubled Asset Relief Program (TARP), and

they receive larger liquidity injections. The LMI thus helps describe the cross

section of liquidity risk in the financial sector. For regulatory purposes, our

approach can help identify systemically important institutions on a liquidity

dimension.

We compare our liquidity measure to two Basel III metrics: namely, the LCR

(BCBS (2013)) and the NSFR (BCBS (2014)). As noted above, the Basel ratios