On the Independence of Assets and Liabilities: 

Evidence from U.S. Commercial Banks, 1990-2005*

Robert DeYoung** 

Capitol Federal Professor in Financial Institutions and Markets 

University of Kansas 

Lawrence, KS 66045 USA 

Chiwon Yom** 

Federal Deposit Insurance Corporation 

Washington, DC 20219 USA 

March 20, 2008 

Abstract: Traditional asset-liability management techniques limit banks’ abilities to structure their 

balance sheets—but more recently, financial innovations have allowed banks the chance to manage 

interest rate risk without constraining their asset-liability choices. Using canonical correlation analysis, 

we examine how the relationships between asset and liability accounts at U.S. commercial banks changed 

between 1990 and 2005. Importantly, we show that asset-liability linkages are weaker for banks that are 

intensive users of risk-mitigation strategies such as interest rate swaps and adjustable loans. Perhaps 

surprisingly, we find that asset-liability linkages are stronger at large banks than at small banks, although 

these size-based differences have diminished over time, both because of increased asset-liability linkages 

at small banks and decreased linkages at large banks. 

Key words: asset-liability management, canonical correlation, commercial banks, deregulation, 

technological change. 

JEL codes: G21, G32 

* Forthcoming in Journal of Financial Stability. 

** The views in this paper are those of the authors and do not necessarily reflect the views of the Federal 

Deposit Insurance Corporation. The authors have received helpful comments from seminar participants at 

the Bank of Finland/Journal of Financial Stability conference in Helskinki and session participants at the 

Western Economics Association meeting in Seattle. DeYoung is the corresponding author: Summerfield 

Hall, 1300 Sunnyside Avenue, Lawrence, KS 66045. Phone: 785-864-1806. Email: rdeyoung@ku.edu. 
1. Introduction

The savings and loan crisis of the 1970s and 1980s was the largest financial disruption in the 

United States since the Great Depression of the 1930s, and stood as the largest financial disruption in the 

United States until the subprime lending crisis of 2007-2008. While the crisis unfolded in several 

increasingly complicated stages and took over a decade to run its course, the initial cause of the crisis was 

quite simple: savings and loans (or thrifts) funded long-term fixed rate mortgage loans with short-term 

certificates of deposit and demandable deposit accounts. Under normal credit market conditions—that is, 

an upward sloping yield curve—this maturity mismatch was quite profitable, but it left thrifts vulnerable 

to interest rate risk. When U.S. interest rates spiked in the late 1970s thrifts’ cost of funds also spiked, 

resulting in negative interest margins which—coupled with capital losses from discounted loan sales, loan 

defaults in markets with falling real estate values, and imprudent risk-taking by thrift owner-managers 

desperate to generate profits—consumed the equity capital of hundreds upon hundreds of thrift 

institutions. Over a thousand thrifts became insolvent, with the ensuing bailout of the government safety 

net costing U.S. taxpayers approximately $125 billion. 

The thrift crisis was a wake-up call to U.S. banks and thrifts underscoring the importance of 

asset-liability management (ALM) for mitigating interest rate risk. In its most simple form, ALM 

requires banks to select a liability structure that matches the expected maturity or duration of their 

existing assets, thus immunizing bank earnings from interest rate movements. More recently, a variety of 

developments have allowed banks to mitigate interest rate risk without having to practice this strict form 

of ALM. Financial innovations such as interest rate derivatives, adjustable rate loans, and asset 

securitization have expanded the methods banks can use to manage interest rate risk both on and off the 

balance sheet, and have reduced the costs of doing so. Geographic deregulation has allowed banks of all 

sizes to grow larger, providing a wider set of investment and funding options for small banks and 

allowing midsized banks easier access to off-balance sheet risk-management tools and tactics. Expansion 

into non-traditional banking services securities brokerage and insurance sales, as well as a general shift 

away from portfolio lending and toward securitized lending and contingent credit contracts, have 

1
generated streams of off-balance sheet income which, in some cases, has reduced banks’ reliance on 

interest-based income and lessened the importance of asset-liability mismatch to their overall risk 

positions. 

Because these developments have arguably reduced the need for banks to practice strict ALM, the 

composition of banks’ assets and liabilities should have become measurably more independent over the 

past two decades. We ask and attempt to answer two basic questions related to the development and 

application of these potential risk-mitigation tools: Have bank assets and liabilities become measurably 

more independent over time? And if so, is the application of interest rate derivatives, adjustable rate 

loans, and other off-balance sheet tools empirically associated with increased asset-liability 

independence? While conventional wisdom suggests that the answer to both of these questions is “yes,” 

we are not aware of any systematic empirical investigation of these phenomena. 

We apply canonical correlation analysis to balance sheet data for U.S. commercial banks between 

1990 and 2005. Although canonical correlation analysis is seldom used in financial or banking research, 

it is a most appropriate tool for our purposes. Developed by Hotelling (1935, 1936), canonical correlation 

is a multivariate version of the familiar linear correlation analysis—more exactly, linear correlation is a 

special case of canonical correlation analysis in which the two vectors being examined each contain just a 

single variable. The technique measures the degree to which one set of correlated variables (say, the 

portfolio of loans, investments, and other assets held by banks) is useful for explaining the variance in 

another set of correlated variables (say, the mix of liabilities and equity capital used to fund bank assets). 

As such, the technique captures—in a single, summary measure—the essence of traditional asset-liability 

management: whether the maturity mix of banks’ liability accounts reflects the maturity mix of banks’ 

asset accounts. Moreover, the technique also identifies the most important underlying relationships 

between and among the individual elements in the two vectors, which allows us to infer which assets 

banks tend to match with which liabilities in the course of performing ALM. Finally, canonical 

correlation imposes no structure on the data and makes no assumptions about the causal direction between 

the two vectors; this flexibility is essential for our experiment, since some commercial banks have strong 

2
deposit franchises and search for profitable lending opportunities, while other commercial banks have 

strong lending programs and must search for funding. 

We have four main findings. First, we find that the strength of asset-liability linkages is 

positively related on average to bank size. This is a surprising result, as one may easily have expected 

that small banks would be the stalwart practitioners of on-balance sheet ALM. This result (a) suggests 

that small size and local geographic focus impart a granularity to individual loans and an inflexibility to 

deposit mix, both of which constrain on-balance sheet ALM, and (b) offers an explanation for the 

relatively low levels of financial leverage typically found at small banks, i.e., these banks hold extra 

capital against risk they cannot otherwise hedge on the balance sheet. 

Second, we find that overall asset-liability linkages have become systematically less correlated 

over time for large banks, but systematically more correlated over time for small banks. The former 

result is a sensible one, given that large banks (a) have easier access than small banks to many of the new 

tools for risk mitigation, (b) have accounted for the bulk of banking industry consolidation and thus have 

benefited more from size-related reductions in risk, and (c) have lately derived an increased portion of 

their income from fee-based activities which may potentially generate activity-based reductions 

(diversification) in risk.1

 The latter result likely reflects the increasing size of banks during our 1990-

2005 time period, which for small banks relaxes to some extent the constraints associated with asset 

granularity and deposit mix inflexibility. Regardless of the factors driving these changes, our evidence 

shows that the degree of asset-liability dependence has converged over time, i.e., different-sized banks 

have become more alike. 

Third, we find evidence that asset-liability correlations are weaker at banks that are 

disproportionate users of risk-mitigation tools such as interest rate swaps and/or adjustable rate loans, 

consistent with off-balance sheet risk-mitigation. We also find that asset-liability linkages are weaker at 

 

1

 According to industry wisdom, banks can reduce risk by replacing interest income with non-interest income, due to 

greater diversification, reduced exposure to interest rate movements, and less exposure to credit risk. However, 

researchers have found little evidence of such gains. For example, see DeYoung and Roland (2001), DeYoung and 

Rice (2004), and Stiroh (2004a, 2004b). 

3
banks that have relatively strong supervisory safety and soundness ratings, consistent with extant 

evidence that bank supervisors allow well-managed and/or safe-and-sound banks more risk-taking leeway 

(DeYoung, Hughes, and Moon 2001). 

Fourth, we find a number of systematic and economically intuitive relationships among 

individual asset and liability accounts at commercial banks. For instance, we find especially strong 

positive relationships between short-term loans and purchased funds financing, and between long-term 

loans and core deposit funding. These results are consistent with Song and Thakor (2007) which provides 

a theoretical basis for asset-liability matching at banking institutions. In their model, banks that offer 

liquidity services to depositors maximize their profits by making relationship loans, while banks making 

non-relationship loans or marketable “transactions” loans are better off using purchased fund financing—

thus, long-term assets and liabilities (relationship loans, core deposits) tend to appear together on the 

balance sheets of relationship lenders, while short-term assets and liabilities (transactions loans, 

purchased funds) gravitate toward the balance sheets of transactions lenders. 

The remainder of the paper proceeds as follows. In Section 2 we discuss some important 

background issues, including the finance literature on asset-liability independence, the incompleteness of 

financial markets, the asset-liabilities linkages that make financial institutions special, and how recent 

financial innovations and deregulations arguably make financial markets more complete and reduce assetliability linkages in all firms, but especially in financial intermediaries. In Section 3 we provide a basic 

outline of canonical correlation analysis, the statistical methodology we employ in this study to measure 

the strength of asset-liability linkages at commercial banks. In Section 4 we describe our data on U.S. 

commercial banks between 1990 and 2005. In Section 5 we present the basic results of our analysis, and 

in Section 6 we derive some additional results regarding banks that are heavy users of risk-mitigation 

techniques. Section 7 summarizes our findings and their implications for the theory of financial 

intermediation, the risk-return tradeoff in banking, and public policy toward banking institutions. 

2. Background

A number of theories have been advanced to explain why banks exist. In most of these theories, 

4
banks exist because they solve a host of problems that otherwise prevent the flow of funds from agents 

with excess liquidity (depositors) to agents in need of liquidity (borrowers). These problems arise 

because of informational asymmetries, contracting costs, and scale mismatches between liquidity 

suppliers and liquidity demanders. Intermediation-based theories of financial institutions see banks as the 

solution to these problems because: banks have a comparative advantage at gathering information on 

borrower creditworthiness; banks are better able than individual lenders to monitor borrowers; banks 

provide increased liquidity by pooling funds from many households and businesses and by issuing 

demandable deposits in exchange for these funds; banks diversify away idiosyncratic credit risk by 

holding portfolios of multiple loans; and banks are able to exploit inter-temporal production synergies 

that exist between deposit supply and credit demand.2

 

Banks earn a profit from the financial flows fundamental to the intermediation process (e.g., 

interest paid on deposits, interest received from loans and securities, and the resulting net interest 

margins) but the nature of these flows exposes the bank to risk. Some of these risks are associated solely 

or primarily with items on just one side of the balance sheet and are independent of items on the other 

side of the balance sheet, e.g., credit risk is associated primarily with loans, while market risk is 

associated primarily with investments in long-term fixed income securities. This independence suggests 

that a substantial amount of the risk inherent in banking is unrelated to the intermediation process. In 

contrast, interest rate risk is associated with the interaction of items on the right-hand side (e.g., the 

maturities of various loans and securities) and left-hand side (e.g., the maturities of various deposit 

accounts) of a bank’s balance sheet, and as such is a direct outgrowth of the intermediation process. 

Thus, the value of a traditional commercial banking company will depend systematically on its financing 

 

2

 Seminal theoretical studies in this area include Gurley and Shaw (1960), Pyle (1971), Benston and Smith (1976), 

Leland and Pyle (1977), Fama (1980), Diamond and Dybvig (1983), Diamond (1984), Boyd and Prescott (1986), 

James (1987), Gorton and Pennacchi (1990), and Kashyap, Rajan, and Stein (2002). See Saunders and Cornett 

(2006, chapter 1) and Freixas and Rochet (1999, chapter 2) for general discussions of why banks exist and 

overviews of the theoretical literature. 

5
decisions, even in a world without taxes or other frictions absent from the simplest Modigliani and Miller 

(1958) framework.3

 

The degree to which commercial banking companies rely on the traditional intermediation 

business model has declined over time. Two decades of innovations in information processing, 

communications technologies, and financial markets (e.g., credit bureaus, computers, the Internet, 

adjustable-rate loans, credit scoring, asset securitization, financial derivatives), plus a wave of industry 

deregulation that abolished barriers to diversification across geographic and product market boundaries, 

have allowed banks to (a) expand into non-intermediation activities, (b) alter the nature of their 

intermediation processes, and (c) adopt new methods of managing the risks inherent in intermediation. 

Collectively, these changes have reduced the degree of association between assets and liabilities that has 

traditionally been necessary for banks to operate profitably. In this paper, we employ canonical 

correlation analysis to document the increased independence of bank assets and bank liabilities over time, 

to demonstrate that the degree of asset-liability dependence has grown more similar across banks over 

time, and to test whether and how differences in bank size, business strategy, risk management practices, 

and financial performance may have influenced these changes. 

Commercial bank business models have evolved over the past two decades, and today banks 

generate an increased portion of their income from non-intermediation and/or non-interest activities. For 

example, between 1980 and 2001 non-interest income in the U.S. commercial banking system increased 

from 0.77% to 2.39% of aggregate banking industry assets, and increased from 20.31% to 42.20% of 

aggregate banking industry operating income (DeYoung and Rice 2004). This is not just a U.S. 

phenomenon: Kaufman and Mote (1994) found that non-interest income ratios increased in the banking 

sectors of virtually all developed countries between 1982 and 1990, while Choi, DeYoung, and Hasan 

 

3

 Imagine a bank with a $100 loan that matures in one year, that is funded by either (a) a $100 one-year CD or (b) a 

$100 six-month CD. The maturity-matched financing scheme (a) generates less interest rate risk than financing 

scheme (b), and hence results in higher bank value. (Note: With an upward-sloping yield curve, the cash outflows 

associated with short-run financing scheme (b) would be less than those associated with long-run financing scheme 

(a), and these savings could potentially offset some or all of the value-reducing effect of the interest rate risk. 

However, there is no guarantee that such conditions will obtain in credit markets; moreover, a downward sloping 

yield curve would exacerbate the value-reducing effect of interest rate risk in the short-run financing scheme.) 

6
(1997) show that non-interest income increased on average from 1.6% to 2.4% of assets at a sample of 41 

non-U.S. banking sectors between 1995 and 2002. On its face, the rapid growth in non-interest income at 

commercial banks suggests that intermediation activities have become a less important part of banking 

business strategies. (At least) two studies suggest that this would be a false conclusion. DeYoung and 

Rice (2004) showed that the correlation between return-on-equity and net interest margin in the U.S. 

banking system grew stronger between 1984 and 2001, and Boyd and Gertler (1994) showed that 

although the share of U.S. financial assets held by commercial banks was in decline, the amount of 

intermediation in which these banks participated was not. Both of these studies suggest a different, rather 

than declining, role for banks in financial intermediation which features off-balance sheet activities that 

generate fee income rather than, or in addition to, portfolio lending that generates interest income. 

If intermediation has indeed remained central to the profitability of commercial banks over the 

past two decades, there is no doubt that the manner in which banks intermediate has changed. Perhaps the 

most fundamental change in the intermediation process has been the securitization of consumer loans—

home mortgage loans in particular, but also credit cards, auto loans, and even more recently small 

business loans. Rather than holding these loans as on-balance-sheet investments, banks bundle the loans 

into loan pools, and sell these pools into an investment trust that is financed by the sale of securities (e.g., 

mortgage-backed securities). The security holders receive cash flows based on the interest generated by 

the pooled loans, as well as some protection from credit risk (the bank often takes a first-loss position). 

The bank earns fees when the loans are originated and fees for servicing the loans (or, alternatively, sells 

the servicing rights), but since the loans are not held on the balance sheet, the bank earns no interest 

income and economizes on equity capital. Securitized lending exhibits large scale economies, partly 

because banks use automated credit scoring models—a technology with a low ratio of variable costs to 

fixed costs—to evaluate loan applications. 

Loan securitization has led to a strategic dichotomy in the banking industry, with large banks and 

small banks having quite different approaches to intermediation (DeYoung, Hunter, and Udell 2004). 

Small community banks are more likely to evaluate credit applications based on “soft” information about 

7
the borrower that cannot be used in an automated underwriting model, hold the loan in its portfolio, and 

fund the loan with core deposits. This is a traditional, relationship-based approach to intermediation, 

which generates potential interest rate risk. Loans to small businesses are the quintessential example of 

the relationship loan, due primarily to the idiosyncratic nature of small businesses. In contrast, large retail 

banks have become more likely to evaluate consumer credit applications using automated credit scoring 

models that rely on “hard” quantitative information, treating the loans as financial commodities rather 

than customer relationships. Because consumer loan applications exist in large numbers and the 

applicants tend to be more homogeneous than commercial borrowers, credit scoring and securitization are 

almost exclusively applied to this lending sector. This transactions-based approach to intermediation 

generates little if any interest rate risk, because the assets are not on the bank’s books.4

 

Banks’ intermediation activities were also disrupted by the loss of commercial lending business 

to non-bank competitors (e.g., insurance companies, pension funds) and business borrowers’ increased 

access to financial markets (e.g., commercial paper, bonds) over the past two decades. The volume of 

commercial lending assets on banks’ balance sheets has declined, but banks have been able to retain some 

of the commercial lending cash flows by exploiting their comparative advantage in evaluating borrower 

creditworthiness. For a fee, commercial banks provide loan commitments and back-up credit lines to 

commercial firms—without these endorsements of creditworthiness, most firms would not be able to 

access credit inexpensively in financial markets. These credit references are also contingent liabilities for 

the banks, because firms are likely to draw down these lines of credit under adverse circumstances. A 

recent strand of the literature (Kashyap, Rajan, and Stein 2002; Gatev and Strahan 2005; Gatev, 

Schuerman, and Strahan 2006) points out that the liquidity risk created by credit commitments on the lefthand side of the balance sheet (in effect, banks have sold call options to their business customers) will 

tend to offset the liquidity risk created by transactions deposits on the right-hand side of the balance sheet 

(in effect, call options in the hands of depositors). This is because these two sets of call options tend to be 

 

4

 Under some recourse arrangements, the investors can put nonperforming loans back onto the bank’s balance sheet. 

In this eventuality, the primary risk facing the banks is credit risk, not interest rate risk. 

8
executed at different times: When market liquidity is tight, firms tend to draw down their available bank 

credit lines, and depositors tend to hold large balances. This literature provides yet another theory for 

why banks exist as intermediaries—holding both transactions deposits and unused loan commitments is a 

“natural hedge” that can reduce a bank’s liquidity risk, and by doing so reduces the bank’s need to hold 

otherwise unproductive cash balances. 

For banks with business strategies that generate fewer natural hedges, “maturity” or “duration 

matching” is a traditional way to mitigate interest rate risk.5

 But this is a potentially costly way to 

mitigate interest rate risk. Matching the durations of its existing loans can require a bank to purchase 

deposits in maturities that carry higher interest rates than the bank’s current deposits; similarly, matching 

the durations of its existing deposits can require a bank to forego some otherwise profitable lending 

opportunities. Duration matching can be less costly for banks with long-lasting relationships on both 

sides of the balance sheet—for example, traditional relationship banks use core deposits with long 

durations to fund repeat lending business—but many banks do not enjoy these types of natural strategic 

hedges against interest rate risk. The huge growth in the market for interest rate swaps (as well as other 

interest rate derivatives) over the past two decades has provided banks with an alternative approach for 

managing their interest rate risk, and as such has likely reduced the necessary link between assets and 

liabilities on banks’ balance sheets. These off-balance sheet risk-mitigation tools have been used mostly 

by larger banks, suggesting either that larger scale or a greater amount of financial expertise is needed to 

profitably deploy this risk-mitigation strategy, and/or that large banks simply practice business strategies 

with fewer natural interest-rate-risk hedges. 

We test whether changes in the intermediation environment at commercial banks over the past 

two decades (e.g., adjustable rate loans, interest rate derivatives) have reduced the degree of asset-liability 

linkage at commercial banks. We also examine whether differences across banks (e.g., bank size and 

 

5

 While the duration of a financial asset is shorter than the maturity of the asset, these two concepts are positively 

correlated by construction. Given that (a) we have little information about the rates and maturities of bank assets 

and liabilities, and (b) by necessity we must group assets and liabilities into very broadly defined buckets, the 

difference between these two concepts is immaterial for the purposes of this study. 

9
financial performance) influence asset-liability linkages. Our primary goal is to discern whether 

exogenous financial, regulatory, and technological changes that have arguably made markets more 

complete have weakened the relationships between assets and liabilities in commercial banks, and as such 

have moved these firms closer to a theoretical Modigliani-Miller (MM) world in which the financing and 

investment decisions are independent for value-maximizing firms. 

3. Canonical correlation analysis 

A canonical correlation is the maximum correlation between linear functions of two vectors of 

variables, where linear weights are selected that maximize the correlation. As such, canonical correlation 

is an especially appropriate tool for analyzing the inner workings of financial intermediaries like 

commercial banks that transform multiple types of liabilities with different characteristics (e.g., demand 

deposits, household checking and savings accounts, long-term certificates of deposit, purchased funds) 

into multiple types of assets with different characteristics (e.g., short-term loans, long-term loans, 

investment securities, cash and liquid reserves).6

 

Surprisingly, canonical correlation analysis has been applied only sparingly to describe assetliability relationships. Simonson, Stowe, and Watson (1983) used it to analyze a cross section of data for 

large U.S. commercial banks. Similarly, Obben and Shanmugam (1993) used canonical correlation 

analysis to analyze the incidence of maturity matching among Malaysian commercial banks, finance 

companies, and merchant banks. Prior to these two studies, Stowe, Watson, and Robertson (1980) 

applied the technique to non-financial firm balance sheet relationships. These studies have all been static 

in nature, and we are not aware of any studies using canonical correlation analysis to illustrate the 

evolution of asset-liability relationships across time. More recently, canonical correlation analysis has 

been used to study topics in finance other than asset-liability relationships. Duru and Iyengar (2001) used 

the technique to investigate the relationship between multiple CEO compensation measures (e.g., salary, 

bonus, present value of options grants) and multiple firm performance measures (e.g., return on equity, 

 

6

 Note that the results of canonical correlation analysis are unaffected by this inferred causation. The causation 

could just as well run in the opposite direction—banks having investment opportunities of various characteristics 

could then select liability funding with various characteristics. 

10
earnings growth, stock market returns). Hasbrouck and Seppi (2001) used canonical correlation analysis 

to examine the relationships between short-run (15-minute intervals) stock order flows and short-horizon 

stock returns (15-minute intervals) for the 30 stocks in the Dow Jones Industrial Average. 

The relationships between asset accounts and liability/capital accounts are not simple ones. 

(From this point forward, we use “liabilities” as a generic term to describe any of the accounts on the 

right-hand side of the balance sheet, including both liabilities and equity.) For example, the optimal 

balance of traditional home mortgage loans at a bank will depend not only on the liability account 

balances that fund those loans (say, long-term deposits and equity), but will also depend on the balances 

in other asset accounts with expected returns that co-vary with the expected returns of mortgage loans, as 

well as on the liability account balances that fund those other assets (say, checking accounts and 

purchased funds). Although canonical correlation analysis cannot directly consider return variances and 

co-variances, it considers them indirectly through the movements and co-movements in the relative levels 

of those balances.7

 More explicitly, canonical correlation analysis determines linear combinations of the 

various asset accounts that are most highly correlated with linear combinations of the various liability 

accounts. Moreover, because the complex relationships between and among asset and liability accounts 

are unlikely to be fully captured by a single set of linear functions, multiple canonical correlations are 

usually considered, based on multiple pairs of linear combinations that are orthogonal to each other. 

We make a brief presentation of the canonical correlation technique here; additional technical 

details are available in Appendix A. Let the asset variables be denoted X = [X1,X2,...,Xp] and the liability 

variables be Y = [Y1,Y2,...,Yq]. The X and Y variables are expressed as a proportion of total assets. 

From these variables we can construct linear combinations of X and Y: 

βββ XXXXBA ++++== β X pp ... 332211

' (1) 

YYYYYCL qq ...++++== γγγγ 332211

' (2) 

 

7

 We assume that there is some risk-based return maximization strategy in place that is generating these movements 

and co-movements in the relative levels of these asset balances. 

11
where B ́ = [β1,β2,...,βp] and C ́ = [γ1,γ2,...,γq] are vectors of scalars to be estimated. We refer to the 

scalars that comprise the vectors B ́ and C ́ as canonical coefficients, and we refer to the linear 

combinations A and L as canonical variables. The canonical coefficients are chosen to maximize the 

canonical correlation between the canonical variables A and L: 

( )(∑∑ ) = ∑

22

la

al

rAL (3) 

where a and l denote mean differences for the variables A and L, respectively. Importantly, because 

(assuming p≥q) there are up to p different ways to pair up each asset and liability variable, the 

maximization process generates p-1 separate canonical correlations, based on p-1 distinct and orthogonal 

linear combinations A and L.8

 

The size and strength of the canonical correlation forms the basis for identifying relationships 

between specific asset and liability accounts. For example, if we observe that actual core deposits 

(YCORE) are strongly correlated with the constructed canonical variable L, and we also observe that actual 

long term loans (XLTLOANS) are strongly correlated (in the same direction) with the constructed canonical 

variable A, then we can surmise that banks with high levels of core deposits will also tend to have large 

amounts of long term loans as long as the correlation rAL is strong. In other words, long term loans and 

core deposits share a common factor which is captured in rAL. This indirect relationship between YCORE

and XLTLOANS is illustrated in Figure 1, and depends entirely on the direction and strength of the 

maximized correlation between the two canonical variables A and L. 

The nature of the relationships between asset and liability accounts can be studied by examining 

more detailed information from the canonical loadings. Canonical loadings are the correlations between 

 

8

 The process generates p-1, rather than p, canonical correlations because one asset and one liability variable is 

dropped to avoid singularity in the maximization process. We use an F-test proposed by Bartlett (1947) to 

determine the statistical significance of the p-1 canonical correlations. 

12
the actual variables and their own canonical variables. For instance, a canonical loading of the variable 

X1 with the first canonical variable A1 is the simple correlation between X1 and A1: 

( ) ( ) XXXCorrAXCorr X pp x x 1, pxp

1

12,

1

211,

1

1

1

2

1

21

1

11 11 , = , ββ ... σβσββ ... +++=+++ σβ (4) 

 

where β1

1

, β2

1

, ..., βp

1

 are the first canonical coefficients for A1, σx,11 is standard deviation of X1, σx,12 is 

the correlation between X1 and X2, and so on. Similarly, canonical loadings can be derived for liability 

variables (e.g., Corr(Y1,L1)) or for higher order (p>1) canonical variables (e.g., Corr(X1,A3)). Calculating 

the canonical loadings allows us to implement the logic displayed in Figure 1. If the canonical correlation 

(3) between assets and liabilities is strong and the canonical loading (4) for asset i is strong and the 

canonical loading for liability k is strong, then we can surmise that a relationship exists between asset i

and liability k. The canonical loadings also prove useful for measuring the total amount of variance in the 

actual data accounted for by the canonical variables: 

 (5) ( ( )) ∑=

=

p

i

ji

jA p

AXCorr

R

1

2

2

,

,

where R2

A,j is the proportion of variance in the asset variables accounted for by the jth asset canonical 

variable (j=1,..., p). This measure indicates how well a canonical variable captures the total amount of 

variance in the X variables. For instance, if only one asset variable has high association with the asset 

canonical variable (i.e., a high canonical loading), the statistic R2

A,j will tend to be small. 

Note that the canonical correlation in (3) represents the variance shared by linear combinations of 

asset and liability variables, and not the shared variance of the original asset and liability variables. 

Hence, it is possible that a very large canonical correlation could be the result of a large correlation of just 

one asset variable with just one liability variable, while the other asset and liability variables are 

uninvolved in the canonical structure. In such a case, the canonical correlation would overstate the true 

13
relationship. The redundancy coefficient provides a summary measure of the average ability of asset 

(liability) variables taken as a set to explain variation in liability (asset) variables taken one at a time: 

 

. 2

,

2 2

,| = μ RR jAjjLA (6) 

The first term of the product, μj

2

, is the jth squared canonical correlation (or the jth eigenvalue) and 

measures the proportion of variance in jth asset canonical variable predictable from the jth liability 

canonical variable (see the Appendix for details). The second term, R2

A,j, is the proportion of asset 

variance accounted for by its jth canonical variable. The product of these two terms measures the 

proportion of asset variance explained by jth liability canonical variable. Summing the redundancy 

coefficients across all the canonical correlations provides an index, R2

A|L, of the proportion of variance of 

asset variables predictable from liability variables, or the redundancy in asset variables given liability 

variables. 

4. Data

We analyze asset-liability relationships and trends for FDIC-insured U.S. commercial banks 

between 1990 and 2005, using year-end data from the Reports of Condition and Income (call reports).9

 

We place a special emphasis on four separate cross sections of data in 1990, 1995, 2000, and 2005. 

Examining the data in five-year intervals allows sufficient time to pass between observations for assetliability relationships to react (or not react) to changes in financial markets, new risk mitigation tools, 

industry deregulation, etc. We begin our analysis in 1990 because changes in the call report during the 

mid- and late-1980s make it difficult to construct consistent definitions of asset and liability accounts 

before 1990. This starting date comes largely before the wide-spread adoption of financial innovations 

(interest rate derivatives, asset securitization, adjustable rate mortgages) and the onset of regulatory 

 

9

 Although it would have been interesting to include stock and mutual savings banks in our analysis, we are unable 

to do so because the financial data for these firms is formatted inconsistently with that of commercial banks during 

the first half of our data period. 

14
changes (FDICIA in 1991, Reigle-Neil in 1994, Gramm-Leach-Bliley in 1999) which likely have affected 

the nature of asset-liability relationships. We exclude banks less than 10 years old from the analysis 

because the balance sheets of young banks are known to be volatile (Brislin and Santomero, 1991). We 

also exclude credit card specialty lenders, as well as banks for which complete information was not 

available for the entire 1990 to 2005 sample period. 

We perform canonical correlation analysis on these data in each year from 1990 through 2005; 

each set of annual calculations is independent from the others. The models are estimated only for 

“survivor banks” that appear in the data every year during the sample period; this ensures that our 

findings will reflect the impact of changes in financial markets, information technology, and industry 

regulations on asset-liability dependence, while holding (as best possible) bank management and business 

strategy constant. Each of the survivor banks is assigned to one of four asset size categories, or quartiles, 

based on its average assets over the entire sample period; this ensures that our sub-sample canonical 

correlation measures will be based on the same number of banks, making comparisons across subsamples more valid. (Because the asset-size distribution of banks is skewed upward, we also construct a 

data sub-sample consisting of the largest ten percent (largest decile) of banks, and run selected tests on 

this data sub-sample.) Table 1 displays summary statistics for the variables we use to calculate the 

canonical correlations, arrayed separately for each of the four data cross sections and for four asset size 

quartiles. 

We subdivide bank assets into six accounts (cash, short-term securities, long-term securities, 

short-term loans, long-term loans, and other assets) and bank liabilities and equity into five accounts 

(demand deposits, purchased funds, core deposits, other liabilities, and equity). Each of these accounts is 

expressed as a percentage of total assets. Care was taken to use consistent definitions of each asset and 

liability account across time.10 A priori, there is no “right” way to subdivide the right-hand and left-hand 

sides of the balance sheet prior to applying canonical correlation analysis, and we make these choices 

 

10 The one small exception to this was “open account time deposits greater than $100,000,” which due to changes in 

the call reports are included in core deposits in 1990 and 1995, and in purchased funds in 2000 and 2005. 

15
based primarily on the maturity characteristics of the accounts: Cash, short-term securities, short-term 

loans, demand deposits, and purchased funds tend to have shorter maturities, while long-term securities, 

long-term loans, core deposits, and equity tend to have longer maturities. Exact definitions of the balance 

sheet items included in each of these accounts appear in the notes to Table 1. 

The individual accounts exhibit some trends over time, reflective of the changing nature of 

banking technologies and financial markets, as well as increasing competitive pressures in the 

consolidating industry. Both cash and short-term securities holdings declined on average for all size 

banks, the implication being that increased competition forced banks to economize on low-yielding 

assets, and/or that innovation in payments clearing or increasingly liquid markets for bank-owned 

securities reduced the size of precautionary balances. By-and-large, the data indicate a lengthening of 

loan maturities, as long-term loans increased as a percent of bank assets while short-term loans tended to 

decline. These shifts reflect multiple changes in the banking environment between 1990 and 2005, two of 

the more important being the decline in (mostly short-term) business lending as business borrowers 

increasingly accessed funding directly in capital markets, and the increased importance of (mostly longterm) home mortgage lending in the intermediation activities of commercial banks, either by originating 

and holding mortgage loans or by purchasing mortgage-backed securities. Historically, holding longer 

maturity mortgage loans (or securities backed by these mortgages) would have necessarily exposed banks 

to increased interest rate risk; however, this remains true only to the extent that these loans carry fixed 

interest rates, which today need not be the case due to the growth in adjustable rate mortgages. 

Trends on the right-hand side of the balance sheet illustrate ways in which small banks and large 

banks have grown less alike over time. At the three smallest quartiles of banks, core deposits declined 

while demand deposits (predominantly non-interest bearing commercial accounts) increased, emphasizing 

the continuing importance of small business customers at small banks, and perhaps indicating that small 

banks are having increased difficulty competing for core (mostly consumer) deposits against the large 

banks expanding into their local markets. These trends differ among the largest banks, however, with 

demand deposits falling but core deposits increasing or holding steady, patterns that are consistent with 

16
large banks’ increasing(decreasing) emphasis on consumer(business) banking during our sample period. 

Hence, the effective maturity of deposit funding has lengthened on average for the largest banks, but has 

gotten shorter on average for the smaller banks. Purchased funds financing increased for banks of all 

sizes, but especially for the smaller banks, additional evidence that small banks are losing core deposit 

funding to large banks and non-bank financial institutions. Finally, banks of all sizes increased their 

equity holdings as strong industry profits were retained and stricter government supervision (i.e., FDICIA 

in 1991) required them to hold higher levels of capital. 

Table 2 displays simple correlations between individual asset and liability accounts (i.e., a special 

case of canonical correlation), by asset size group in each of the four main years of our analysis. The 

table displays only “strong” asset-liability correlations, which we define in ad hoc fashion as correlations 

greater than 0.30 in absolute value. One pattern in these data is immediately apparent: strong assetliability correlations happen more often for large banks than at small banks. This implies that large banks 

are better able and/or more likely to practice on-balance sheet asset-liability management than are small 

banks. However, this result could also be caused by within-group heterogeneity among small banks that 

introduces noise into the correlation measures, or may indicate that the asset and liability categories that 

we impose on the data reflect large bank business models better than small bank business models. 

Looking more closely at Table 2 reveals economically sensible patterns in the pair-wise 

correlations. Excluding for the moment the “extra” data in the bottom panel of the table, we find that 11 

of the 32 strong correlations show a positive relationships between cash and demand deposits (i.e., banks 

with large amounts of transactions accounts need to hold higher balances of cash as a precaution against a 

large volume of payments presentments on any given day) while an additional 3 of the 32 show a negative 

correlation between cash and core deposits (banks with stable deposits face lower liquidity risk and hence 

can hold lower cash balances). Long-term loans are positively associated with core deposits in 7 of the 32 

strong correlations (banks match long-term credits with long-term deposits) and long-term securities are 

positively related to equity capital balances in 5 of the 32 (banks with large retained earnings “park” the 

funding in liquid but relatively high-yielding securities until profitable lending opportunities arise; 

17
alternatively, especially risk-averse banks both hold higher capital cushions and hold assets in safer 

investments). 

We now move from simple pair-wise correlation analysis, which completely ignores the 

movements and co-movements of other asset and liability accounts, to canonical correlation analysis, 

which considers simultaneously the economic complexities both within and across the two sides of the 

balance sheet. 

5. Main Results

Table 3 displays the canonical correlations (3), arrayed in twenty cells according to the five bank 

sizes and four main years in our data. We calculate five canonical correlations for each of the cells, the 

maximum allowable given the manner in which we group the asset and liability accounts.11 The asset and 

liability variables exhibit a relatively high degree of collective dependence. For example, the first 

canonical correlation in the table (for the smallest asset quartile group in 1990) is 0.42, which indicates 

that the first pair of canonical variables (A1 and L1) share 17.6% of their variance with each other; stated 

differently, the first factor extracted from the asset accounts data and the first factor extracted from the 

liability accounts data have a linear correlation of 0.42. The second canonical correlation is 0.19, 

indicating a common factor that accounts for 3.65% of the shared variance between the second pair of 

canonical variables (A2 and L2). Moving down each column, the canonical correlations tend to decline in 

explanatory power, as well as in statistical significance. In the first column, the first approximate F-value 

of 16.74 allows us to reject the null hypothesis that all five canonical correlations are zero; similarly, the 

second F-value of 5.75 rejects the null hypothesis that second, third, fourth, and fifth canonical 

correlations are zero. The third F-value is also statistically significant, but the fourth F-value is not, and 

as such we conclude that three or fewer canonical pairs are necessary to represent the asset-liability 

relationship. The asset and liability canonical variables are more strongly correlated—that is, the 

 

11 That is, p = 6 liability accounts, with one variable deleted to avoid perfect collinearity. 

18
numerical magnitudes tend to be bigger—for the larger banks, a result similar to the simple pair-wise 

correlations displayed above in Table 2. 

The statistics displayed in Table 3 represent relationships between linear combinations of asset 

variables and linear combinations of liability variables, and these canonical correlations may or may not 

indicate systematic relationships between or among the underlying asset and liability variables. To get at 

this question, we report information for the proportion of variance coefficients (5) and the redundancy 

coefficients (6) in Table 4. To reduce the amount of space necessary to display these diagnostics, each 

cell in the table displays a straight-line average based on the values of (5) or (6) from each of the four 

bank asset quartiles and four main years of our data. These averages are calculated separately for each of 

the five canonical loadings; the sixth column is the sum of the first five entries, and represents the total 

proportion of asset or liability variance explained by the canonical variables. 

By construction, the proportion of variance statistics (5) in the top half of the table must sum to 

100% across the five loadings. About 90 percent of the variation in the actual liabilities data is explained 

by the liability canonical variables in the first three loadings—in contrast, the variation in the actual assets 

data is explained by the asset canonical variables in a more uniform fashion in all five loadings. All else 

equal, this suggests that the relationships among the various asset accounts are more complex than the 

relationships among the various liability accounts. 

The redundancy coefficients (6) in the bottom half of the table sum to well less than 100% across 

the five loadings. The liability canonical variables explain only about 7% of the variation in the asset 

variables, while the asset canonical variables explain about 12% of the variation in the liability variables. 

Moreover, in both cases over 80 percent of the redundancy is accounted for in the first two loadings. We 

draw two informal inferences from these results: First, the calculations suggest that causation runs more 

strongly from assets to liabilities (i.e., banks seek funding and/or determine funding mix only after 

finding investment opportunities) than from liabilities to assets (i.e., banks are pools of deposits looking 

for lending opportunities). Second, the relatively small size of the redundancy coefficients, as well as the 

importance of the first two loadings in the calculation of these coefficients, suggests that the strong 

19
canonical correlations in Table 3 are driven by a relatively small number of relationships among 

individual asset and liability accounts. 

We look more closely at links between the individual asset and liability accounts in Table 5, 

which focuses on the individual asset-liability relationships in the canonical loadings (4). Given our 

results in Table 4, we limit our analysis here to the linkages suggested by the first loading (Table 5, panel 

A) and the second loading (Table 5, panel B). Correlations between individual actual asset accounts and 

their asset canonical variables appear on the left-hand side of the cells, while correlations between 

individual actual liability accounts and their liability canonical variables appear on the right-hand side of 

the cells. By the logic of Figure 1, finding simultaneous strong canonical loadings for asset and liability 

accounts implies a strong relationship between the underlying asset and liability variables, because the 

canonical correlations in both the first and second loadings are empirically large and statistically strong 

(see Table 3). As above, we use a 0.30 threshold to determine a “strong” relationship between the 

original variables and the canonical variables (Fornell and Larcker 1980). 

We find a limited number of strong and economically sensible relationships among the variables 

in Table 5. In panel A, the dominant relationship is between long-term loans and core deposits, which 

have strong canonical loadings with the same sign in all 20 of the cells, strong evidence that these two 

balance sheet accounts move up and down together. This is a plausible relationship: Banks with large 

amounts of core deposits are better able to hold large portions of their portfolios in long-term loans 

without incurring large amounts of interest rate risk. Panel A also contains similar evidence of a positive 

link between short-term loans and purchased funds: the canonical loadings for these two variables exceed 

0.30 and have the same signs in 19 of the 20 cells. This is also an economically sensible result: Because 

purchased funds can expose banks to severe interest rate risk, the most logical use for these funds is to 

finance short-run investments with relatively high yields (i.e., loans rather than cash or short-term 

securities). Importantly, we note that this relationship was not revealed by the simple pair-wise 

correlations in Table 2. Finally, the canonical loadings for core deposits and purchased funds exceed 0.30 

and have opposite signs in all 20 cells, consistent with (albeit merely suggestive evidence of) the 

20
conventional wisdom that banks turn to purchased funds financing in the absence of cheaper and more 

stable core deposit funding. All three of these results provided evidence consistent with the predictions of 

Song and Thakor (2007). 

We find a different set of strong and systematic linkages in Panel B—not surprising, because by 

definition the linear combinations (1) and (2) are orthogonal across loadings. The dominant relationship 

here is a positive association between long-term securities and equity capital, which appears in 10 of the 

20 cells, consistent with the findings pair-wise correlations in Table 2 as well as our suppositions about 

retained earnings and/or risk-averse bank management. The only other systematic finding is the positive 

association between cash holdings and demand deposits in 4 of the 20 cells, consistent with but less 

prevalent than the results of the simple correlation analysis in Table 2. 

Importantly, we have not found any evidence so far that the linkages between assets and liabilities 

have declined over time: such declines are necessary to support our conjectures about the increasing 

independence of bank assets and liabilities due to improvements in risk mitigation, more complete 

financial markets, etc. As explained above, however, the indirect logic displayed in Figure 1 (quantified 

by the results in Tables 3 and 5) can overstate the degree of correlation between the two vectors of 

variables under consideration. The redundancy coefficients (6) provide a more direct summary measure 

of asset-liability linkage that does not suffer from the same potential for overstatement. Figures 2 and 3 

plot the annual redundancy coefficients from 1990 through 2005 both for asset size quartiles (Panel A) 

and asset size deciles (Panel B).12 

Figure 2 displays the degree to which the liability canonical correlations explain the variation of 

the actual asset account data. There is little evidence in either panel of any systematic inter-temporal 

trends. Moreover, in Panel A the lines cross each other repeatedly and do not reflect the systematic sizebased patterns displayed in the data in Tables 2 and 3. The size-based ordering does appear in Panel B 

 

12 As is common practice, the redundancy measures plotted in Figures 2 and 3 are based on the summations over 

only the statistically significant j terms. 

21
(where we have averaged together for deciles 1 through 5, and also for deciles 5 through 9), but still there 

is little evidence of inter-temporal patterns in the data. 

The data provide a more systematic story in Figure 3, where the asset canonical correlations 

explain the variation of the actual liability account data (i.e., the converse of Figure 2). This is not 

surprising, given that the evidence in Table 4 that the liability data are more fully explained by asset 

canonical correlations than vice versa. First, the magnitudes of the redundancy coefficients are larger 

than in the previous figure, finishing in the 10% to 15% range as opposed to the 6% to 8% range shown in 

Figure 2. Second, both Panel A and B display a clear rank ordering by asset size, with asset-liability 

linkages stronger on average for larger banks and weaker on average for smaller banks. Third, consistent 

with our conjectures about the influence of new financial technologies on asset-liability linkages, there is 

a systematic decline in the redundancy coefficients across time for the larger banks. For example, the 

asset canonical variable explained a little over 20% of the variance in the liability accounts of the largest 

quartile of banks during the early 1990s, but no more than 15% by the early 2000s. In contrast, the data 

show a systematic increase in the redundancy coefficients across time for banks in the two smaller asset 

size quartiles. For example, this version of the redundancy coefficient increased from about 5% to 10% 

between 1990 and 2005 for banks in the smallest asset size quartile. Both Panels A and B show a clear 

and consistent convergence across time in the level of asset-liability linkage for banks of all sizes. By this 

measure, large and small commercial banks have become more alike over time. 

It is perhaps surprising that our measures of asset-liability linkage are systematically stronger at 

the larger banks than for the smaller banks, both in the early and later years of our sample period. A 

priori, one might have expected to find the strongest asset-liability relationships at the smallest banks—

that is, with less access to interest rate risk mitigation tools (e.g., derivatives hedges), small banks must 

manage interest rate risk on their balance sheets, which implies stronger rather than weaker correlations 

between the maturities and compositions of asset and liability accounts. One possible explanation for this 

unintuitive result is observable in the Table 1 summary statistics: Smaller banks have traditionally held 

more equity capital than larger banks (for example, in 1990 the equity-to-assets ratio for the small Group 

22
1 banks averaged about 9%, compared to just 6% to 8% for banks in the larger groups), suggesting that 

small banks practiced a strategy of absorbing rather than hedging interest rate risk. This extra equity 

cushion may have allowed them to operate with a greater than average amount of maturity mismatches on 

their balance sheets. This explanation is also consistent with the convergence of the redundancy 

coefficients over time: By the end of our sample, the smallest banks no longer held larger equity ratios 

than the larger banks, with equity/assets averaging about 11% in 2005 for the banks in Group 1, compared 

to between 10% and 12% on average for banks in the larger groups. 

Differences in operating scale and business environment provide another likely explanation for 

the relatively low redundancy coefficients for small banks. If profitable lending opportunities present 

themselves to at banks with some randomness, then small banks—which do a small number of deals in 

any given time period—will naturally have more difficulty managing the composition of their assets. 

Combine this with the fact that small banks have historically been substantially more dependent on core 

deposit funding than their large bank counterparts (e.g., as shown in Table 1, in 1990 core deposits 

provided nearly 70 percent of total financing for small banks). If loan balances change frequently and 

with some randomness, but deposit balances are stable and change slowly (a characteristic of core 

deposits), then measures of asset-liability relationships will necessarily be weak. 

The convergence of strength of asset-liability linkages for banks of all sizes is illuminating. The 

obvious inference to be drawn from the downward drift in the redundancy coefficients for the larger 

banks is that the compositions of assets and liabilities at these banks have grown more independent over 

time. This could indicate that larger banks have been more active in adopting interest rate risk mitigation 

tools such as derivative hedges, adjustable rate consumer loans, and asset securitization. Also, large 

banks have accounted for the bulk of the geographic expansion as the banking industry has consolidated, 

and have also expanded more aggressively than small banks into non-interest-based (off-balance sheet) 

financial services—both of which may have resulted in greater diversification for larger banks and may 

have allowed them to accept more risk from mismatched assets and liabilities. 

23
The upward drift in the redundancy coefficients for the smaller banks indicates that the 

compositions of assets and liabilities at these banks have grown less independent over time. Small banks 

are not intensive users of interest rate derivatives, but like their larger peers they did increase their use of 

adjustable rate loans over the sample period. This should weaken (rather than strengthen) the measured 

linkages between our long-run and short-run asset and liability categories. The quality of management 

(and hence better ALM) at small banks likely increased during our sample period—but this is unlikely to 

be driving our results, because our survivor-only sampling method should substantially control for the 

exit of poorly managed banks between 1990 and 2005. The more likely explanation is the tripling in the 

real size of small banks over time (see Table 3), a byproduct of the industry consolidation among banks of 

all sizes during our sample period. As these small banks got larger, constraints on ALM due to 

idiosyncratic loans, granularity in asset growth, and dependence on core deposit funding to which we 

alluded above would have naturally lessened, resulting in the stronger asset-liability linkages we observe 

for these banks in Figure 2. 

Rapid growth—especially growth by acquisition, which combines two different balance sheets—

should make ALM more difficult in the short-run, just as rapid growth hampers most operational tasks in 

the short-run. Since our sample includes only those banks that survived the entire sample period (i.e., 

banks that were acquirers during the sample period rather than targets), the data in displayed in Tables 3 

and 4 and in Figures 2 and 3 are likely to understate the degree to which bank assets and liabilities are 

related to each other in equilibrium. Apart from these transitory effects, our results suggest that asset 

growth is related to higher canonical correlations in equilibrium, because the banks that have grown the 

most are disproportionately represented in the higher asset-size quartiles. Finally, the inter-termporal 

convergence of the results for these asset-size quartiles suggests that the influence of growth on our 

results has diminished over time. 

6. Sub-sample analysis

Our analysis above indicates that the strength of asset-liability relationships, while converging 

over time, still varied substantially across different size banks at the end of our sample period. In this 

24
section we explore some of the possible reasons for this. For example, can derivatives securities (a 

predominantly large bank activity) mitigate interest rate risk enough to materially weaken asset-liability 

correlations? Similarly, are differences in product mix or financial condition across banks associated with 

stronger or weaker asset-liability relationships? We perform these analyses using data from 2005, when 

our measured asset-liability correlations were much more similar across banks of different sizes. 

In Table 6 we test whether actively hedging against interest rate risk allowed banks to operate 

with greater asset-liability freedom. Panel A displays redundancy coefficients for the group of 91 banks 

from our sample that reported positive amounts of “total gross notional amount of interest rate swaps held 

for purposes other than trading where the bank has agreed to pay fixed rate” in 2005; we calculated the 

redundancy coefficients separately for banks above and below the median. Panel B displays redundancy 

coefficients for the entire sample of banks for “total loans with remaining maturity or next repricing 

frequency of 1 year or less” as a percentage of total bank assets, again calculated separately for banks 

above and below the median. In both panels, the asset canonical variables have greater explanatory 

power than the liabilities canonical variables, and hence we will refer to these data in our discussion here. 

We find suggestive evidence in both Panel A and Panel B that interest rate derivatives and adjustable rate 

loans allow banks to relax their on-balance sheet asset-liability management. For example, the 

redundancy coefficient (variance of liabilities variables explained by assets canonical variable) for more 

intensive users of interest rate swaps to hedge against exposure to fixed interest rate loans is just 49.60, 

compared to 56.70 for less intensive user of interest rate swaps. Similarly, redundancy coefficients are 

lower for intensive users of adjustable rate loans (9.05) than for largely fixed-rate lenders (13.76).13 

Banks recognized by regulators as being well-managed—and especially banks recognized as 

being well-positioned against market risk—should feel less regulatory pressure to operate with tight assetliability linkages. In Table 6, panels C and D display redundancy coefficients separately calculated for 

 

13 To control for the effects of asset size on the full-sample results in Panels B, C, and D, we first divided each of the 

four asset size groups into top and bottom halves in terms of adjustable rate lending, then aggregated the top and 

bottom halves across bank size groups, and finally calculated the redundancy coefficients separately for these two 

resulting asset-stratified sub-samples. 

25
sub-samples of banks with strong, satisfactory, and weak regulatory safety and soundness ratings in 2005. 

The overall safety and soundness rating—known as a “CAMELS” rating for Capital Adequacy, Asset 

Quality, Management Quality, Earnings Quality, Liquidity, and Sensitivity to Market Risk—bear this out. 

The redundancy coefficients in Panel C are lowest (11.36) for banks judged to be the very safest (1-rated), 

and highest (12.63) for the banks judged to have substantial risk (3-rated or worse). Not surprisingly, this 

discrepancy is larger in Panel D where the Sensitivity to Market Risk component of the CAMELS ratings 

was used to construct the sub-samples; ranging from 12.21 for the 1-rated banks to 19.22 for the 3-, 4-, 

and 5-rated banks.14 

We performed additional tests (not shown) similar to those shown in Table 6 in which the subsamples were defined by non-interest income levels, reasoning that asset-liability management may be 

less important for banks that earn large portions of their incomes from non-interest sources. However, we 

found virtually no difference in redundancy coefficients between the high non-interest and low noninterest sub-samples.15 We can think of two mutually exclusive explanations for this non-result. On-theone-hand, much non-interest income derives from activities related to balance sheet accounts (e.g., fees 

charged to depositors, fees from contingent lines of credit, fees associated with loan origination and 

securitization), and as such the generation of this non-interest income need not affect existing assetliability linkages. Similarly, some non-interest income, while wholly unrelated to balance sheet activities, 

can still be quite sensitive to changes in interest rates (e.g., brokerage services, asset management 

services), so that an increase in these activities will not weaken, and may actually re-enforce, existing 

asset-liability linkages (DeYoung and Roland 2001). On-the-other-hand, non-interest income may 

generate a set of risks that are orthogonal to interest rate risk and ALM, in which case we would indeed 

expect them to have no impact on our measures of asset-liability linkages. Although additional tests on 

 

14 This result is consistent with DeYoung, Hughes, and Moon (2001), who found that the national bank regulator 

(the Office of the Comptroller of the Currency) gave worse CAMEL ratings to risky banks in general, but did not 

give worse CAMEL ratings to risky banks that were efficiently run. 

15 The redundancy coefficients for banks with above median non-interest income were 6.12 (variance of asset 

variables explained by liabilities canonical variable) and 13.41 (variance of liabilities variables explained by assets 

canonical variable), compared to 6.04 and 10.66 for banks with below median amounts of non-interest income. 

26
individual fee-based product lines may yield less ambiguous results, the availability of such data is sparse 

in commercial bank financial reports. 

7. Conclusions

Unlike most commercial firms, banking companies have typically profited by managing their 

investment decisions together with their financing decisions, trading off expected profits from 

mismatches in the maturity of assets and liabilities (e.g., lending long and borrowing short) against 

increased interest rate risk. During the late 1980s, this formula resulted in mass insolvencies of U.S. thrift 

institutions, due to the inability of these lenders to effectively mitigate the interest rate risk. Since that 

time, however, deregulation has allowed banks to diversify risk by expanding into new products and new 

geographic markets, innovations in risk management have allowed banks to better mitigate interest rate 

risk, and more highly developed financial markets have allowed shareholders to better diversify their 

personal portfolios. In this paper, we find broad evidence that these developments have permitted banks 

to operate with fewer balance sheet constraints. 

We use canonical correlation analysis to measure the relationships among and between asset and 

liability accounts at U.S. commercial banks in 1990, 1995, 2000, and 2005. We find strong and 

substantial evidence that bank assets and bank liabilities have indeed become more independent over time 

for large banks (but not for small banks). While there are many reasons that this may have happened, we 

show that at least some portion of this increased independence is driven by intensive use of riskmitigation tools such as interest rate swaps and adjustable rate loans. We also find that banks with strong 

regulatory safety and soundness ratings have weaker asset-liability linkages, consistent with the idea that 

bank supervisors give well-run banks more risk-taking leeway (DeYoung, Hughes, and Moon 2001). 

Perhaps surprisingly, we find that bank size is positively related to asset-liability dependence in every 

year of our analysis. This may reflect the existence of scale economies in traditional asset-liability 

management—in particular, duration matching could be more difficult at small banks, where just a few 

new loan accounts could upset the duration match, and a reliance on stable core deposit funding could 

make fast adjustments difficult. This interpretation is consistent with the large equity cushions 

27
historically held by small banks, perhaps as an offset to their inability to effectively practice ALM. 

Regardless, we find that asset-liability linkages have tended to converge over time for banks of all sizes, 

growing weaker for larger banks, and growing stronger for smaller banks. We hypothesize that the 

increased size of small banks over time, and thus increased diversity of their loan portfolios, may simply 

make ALM more efficient. 

One inference from these results is that large banks have moved closer to an abstract Modigliani 

and Miller (1958) world in which investment and financing decisions are more independent and thus 

more efficient, and that there is less need for banks to accept interest rate risk to earn profits. In other 

words, deregulation and financial innovation have made banking markets, and the markets to which banks 

have access, more complete. (See Appendix B for a brief discussion.) 

Our results also suggest that banks have become better able to accept and manage interest rate 

risk without constraining the composition of their balance sheets; stated differently, our results suggest 

that banks do not need to accept as much interest rate risk as in the past in order to earn profits. However, 

this does not mean that banks are taking less risk. A number of previous studies of bank risk-taking 

indicate that banks tend to “spend” risk reductions in one area on increased risk-taking in other areas 

(Demsetz and Strahan 1997, Hughes, Lang, Mester, and Moon 1999, Schrand and Unal, 1998), and the 

reduction in asset-liability linkages that we find here may be further evidence of such behavior. 

In addition, our findings highlight the challenges facing researchers estimating cost, profit, and 

production functions for commercial banks. Such studies typically assume that banks of all sizes use the 

same production technology, and rely on flexible functional forms to fit this technology to the data. Our 

results suggest that the relationships between liabilities (the primary inputs in such models) and assets 

(the primary outputs in such models) have historically been quite different across different sized banks, 

perhaps too different to be captured by a single, albeit flexible, parametric form. This could help explain 

why scale economies and scope economies at banking companies have been so difficult to measure, and 

why the resulting point estimates are often statistically weak or economically nonsensical. On the bright 

28
side, we find that these relationships have been converging over time for different sized banks, so perhaps 

future estimates of bank cost and profit functions using such techniques will deliver more accurate results. 

We stress that our findings are generated using a statistical approach, canonical correlation 

analysis, that has been used only occasionally in financial institution research. While we argue above that 

this technique is completely appropriate for a first examination of these phenomena, we also stress that 

this technique—at least as it is employed here—can generate only broad suggestive evidence at the 

industry or industry subsample levels. As such, our findings here should be interpreted with some degree 

of caution. Further investigation into asset-liability linkages needs to generate bank-level evidence. One 

potential approach would be to apply canonical correlation analysis to time-series data at the bank level; 

such an approach would generate bank-specific estimates of canonical correlations, redundancy 

coefficients, etc. which could then be regressed on bank-specific arguments to test a variety of 

hypotheses. 

29
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32
Appendix A: Details of Canonical Correlation Analysis 

The reader may be interested in a more explicit presentation of the maximization process in 

canonical correlation analysis. Given observations of the data X and Y, we solve for the vectors of 

canonical coefficients B ́ and C ́ as follows. In equation (3), we make the substitutions Σal = B’SxyC, Σa

2 

= B’SxxB, and Σl

2 

= C’SyyC, resulting in: 

( )( CSCBSB )

CSB

r

xx yy

xy

AL ' '

'

= (A1) 

where Sxx and Syy are the within-set variance-covariance matrices for assets and liabilities, respectively, 

and Sxy is the between-sets covariance matrix for assets and liabilities. Since rAL is invariant to the scaling 

of B and C, we constrain the linear combinations A and L to have zero means, E(A)=E(L)=0, and unit 

variances, B ́SxxB = C ́SyyC = 1. These constraints normalize the denominator in (3 ́) to 1.0, while 

retaining in the numerator the information in which we are most interested, the asset-liability variancecovariance matrix Sxy. Maximizing (3 ́) subject to these constraints is equivalent to solving the 

Lagrangian: 

( ) ( 1) 21

2

' ' '

xy −= xx −− yyCSCBSBCSBL − λ μ (A2) 

Setting equal the expressions for λ and μ derived from the first order conditions of (4) and rearranging 

terms gives us the following matrix equations: 

( ) 0 11 2 =− −−

yxyyxyxx μ BISSSS (A3) 

( ) 0 11 2 =− −−

xyxxyxyy μ CISSSS (A4) 

33
where I is the identity matrix. The matrix equations (5) and (6) can be rewritten as systems of p linear 

equations in p vectors of unknown coefficients Bi and Ci (i = 1,2,...,p). For instance, the matrix equation 

(5) can be written as: 

( )

( )

( ) ⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

⎡

=

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎢

⎣

⎡

−

−

−

0

.

.

.

0

0

.

.

. .

1...

.

.

.

1 ...

1 ...

2

1

2

1 2 3

23 2

2

21

12 13 1

2

pi

i

i

p p p i

i p

p

r rr

r r r

rr r i

β

β

β

μ

μ

μ

. 

We then solve for the systems (5) and (6) for the p sets of canonical coefficients B ́ = [β1,β2,...,βp] and C ́ 

= [γ1,γ2,...,γq]. These systems of linear equations will have non-trivial solutions only if their determinants 

are zero: 

0 11 2 =− −− ISSSS yxyyxyxx μ (A5) 

0 11 2 =− −− ISSSS xyxxyxyy μ (A6) 

Equations (7) and (8) are called characteristic equations (every square matrix has associated with it a 

characteristic equation). The characteristic equation is formed by subtracting some value μ

2

 from each of 

the diagonal elements of the matrix. The values of μ

2

, which are the roots of the characteristic equations, 

are chosen so that the determinant of the resulting matrix is equal to zero (i.e., the matrix is singular). 

Normally, for a matrix of order p, there are up to p different values for μ

2

 that will satisfy the 

characteristic equation. In our case, there are p-1 (or q-1) different values for μ

2

. This is because the 

34
asset and liability variables sum to one, and Sxx and Syy are singular. To avoid the singularity, one 

variable from each set is eliminated. The largest root of the characteristic equation, μ1

2

, is also the first 

eigenvalue, and B1 and C1 are its corresponding eigenvectors. More generally, for each μi

2

, there is 

corresponding vector of solutions Bi and Ci, which constitute the weights for the linear combinations: 

ii XBA

' = (A7) 

ii

YCL

' = (A8) 

 

where both Bi and X are px1 vectors and both Ci and Y are qx1 vectors. There are p canonical variable 

pairs, and the corresponding p correlations Corr(Ap,Lp) are all maxima, subject to the conditions that the 

Ap are uncorrelated with A1,A2,...,Ap-1 and the Lp are uncorrelated with L1,L2,...,Lp-1 (that is, the p 

canonical variable pairs are linear functions selected subject to the restrictions of orthogonality). Finally, 

the correlations of the canonical variable pairs are such that Corr(A1,L1) > Corr(A2,L2) > ... > 

Corr(Ap,Lp). 

Canonical correlation analysis is directionless and symmetric. The analysis is invariant to 

whether causation runs from assets-to-liabilities (i.e., banks with pre-existing investment opportunities 

looking for financing) or from liabilities-to-assets (i.e., banks with core deposit customers looking for 

investment opportunities). The analysis presumes that banks determine the optimal balances of asset 

(liability) accounts jointly with the balances of other asset (liability) accounts as well as with liability 

(asset) accounts, and it measures the resulting co-variations among these accounts. This approach 

contrasts with multiple-output production (or cost or profit) function analysis of banks, which assigns 

certain balance sheet accounts to be inputs and other balance sheet accounts to be outputs.16 

 

16 The typical bank production/cost/profit function approach assumes an intermediation framework that constrains 

all deposit accounts to be inputs and all asset accounts to be outputs. 

35
Appendix B: Modigliani and Miller and Banks 

Under strong assumptions about transactions costs, information symmetry, bankruptcy costs, and 

the tax code, modern finance theory postulates that a firm’s financial structure does not influence the 

value of its assets (Modigliani and Miller, 1958). However, because these assumptions hold imperfectly 

in real markets, a firm’s value can indeed be a function of its balance sheet structure. The most familiar 

theoretical treatment of “real world” considerations posits an optimal financial structure that balances the 

tax advantages of debt against the probability of costly bankruptcy, but additional temporal considerations 

such as personal income taxes and managerial agency costs have also been used to motivate theoretical 

value-maximizing tradeoffs between debt and equity financing (Miller 1977, Jensen and Meckling 1976). 

There is no unifying theory of corporate financial structure, and much of the recent empirical research 

attributes differences in debt-equity mix to industry-specific factors such as competitive rivalries and 

production technologies.17 

The debt-equity choices of commercial banking companies are influenced by two industryspecific factors: Under-priced deposit insurance creates strong financial incentives for banks to use debt 

(deposit) financing, and in response to these incentives government regulators impose explicit limits on 

debt financing in the form of minimum capital ratios. In recent years, most commercial banking 

companies have used less than the maximum amount of financial leverage permitted by regulators, which 

suggests that banks target an optimal debt-equity mix that balances the benefits (e.g., interest 

deductibility, subsidized interest rates, agency considerations) and the costs (e.g., costs of insolvency, 

regulatory pressures) of debt finance.18 Moreover, the value of banking companies depends not only on 

their debt-equity financing choices, but also on their choices of debt maturity structure. For financial 

intermediaries, an important profit driver is the maturity mismatches between assets and liabilities—for 

 

17 Other important theoretical explanations of firms’ financial structure decisions include the “pecking order” and 

“signaling” hypotheses (Donaldson 1961, Myers 1984). A full review of the theoretical and empirical literature on 

optimal financial structure is beyond the scope of this paper. Some recent empirical investigations include Frank 

and Goyal (2001), Fama and French (2002), and MacKay and Phillips (2002). 18 Berger, DeYoung, Flannery, Lee, and Oztekin (2008) show that the vast majority of publicly traded U.S. bank 

holding companies hold equity capital ratios that are hundreds of basis points in excess of levels required to be 

“adequately capitalized” or “well-capitalized” by regulatory standards. 

36
example, borrowing short for which interest rates paid are typically low, and lending long for which 

interest rates received are typically high. Thus, when choosing the optimal amount of maturity mismatch 

in its debt structure, banks must perform a second balancing act, weighing the benefits of wider profit 

margins against the interest rate risk generated as these mismatches increase (e.g., increased probability of 

insolvency and the attendant costs of regulatory intervention). 

In a strict Modigliani-Miller (MM) world, a bank’s value would be invariant to its debt maturity 

structure: Investors in a bank that uses a high proportion of short-maturity debt (e.g., borrowing short and 

lending long) would be able to undo the interest rate risk associated with this debt structure by borrowing 

long-term and using the proceeds to lend short. However, this is an unprofitable maneuver outside the 

strict assumptions of MM, because investors do not have access to the same interest rates as banks, and 

under normal market conditions would be borrowing at long rates (say, mortgaging their homes) that 

exceed their lending rates (say, making bank deposits) after taxes. 

37
Table 1 

This table displays the mean values for asset and liability/equity account items. All variables are expressed as a percentage of 

total assets. Asset size groups are in 2005 dollars. Cash balances include cash at the bank, deposits at other banks, and reserves 

at the Federal Reserve. Short-term securities include all investment securities with maturities of less than one year. Long-term 

securities include all investment securities with maturities of more than one year. Short-term loans include all loans with 

maturities of less than one year and federal funds sold and securities purchased under agreements to resell. Long-term loans are 

obtained by subtracting short-term loans from the sum of total loans and leases and federal funds sold and securities purchased

under agreements to resell. Other assets include all other assets not described. Equity includes all common stock, perpetual 

preferred stock, surplus, retained earnings, other equity capital, and subordinated notes and debentures. Demand deposits include 

all demand deposit accounts. Core deposits include NOW accounts, money market deposit accounts, savings deposits, time 

certificates of deposits in amounts less than $100,000, fixed rate time certificates of deposits in amounts of $100,000 or more

with a remaining maturity of over 1 year, time deposit open accounts in amounts greater than $100,000 with a remaining maturity

of over 1 year, demand notes issued to the U.S. Treasury, and other borrowed money such as Federal Home Loan Bank advances. 

Purchased funds include fixed rate time certificates of deposits in amounts of $100,000 or more with a remaining maturity of 12 

months or less, floating rate time certificates of deposits in amounts of $100,000 or more with a repricing frequency of 12 months 

or less, and federal funds purchased. Other liabilities include all other liabilities not described. All variables are based on yearend data from the Reports of Income and Condition (call reports). 

1990 1995 2000 2005 

Group 1 – Bottom Quartile (N = 1315) 

Assets (in $1000s) 11,729 15,546 22,654 33,569

Asset accounts 

Cash balances 8.24 6.11 5.67 6.23

Short term securities 12.16 9.32 5.43 5.02

Long term securities 24.53 25.05 23.50 20.90

Short term loans 35.14 35.64 33.34 33.73

Long term loans 17.19 21.45 29.23 30.77

Other assets 2.74 2.43 2.82 3.35

Liability/Equity accounts 

Equity 10.15 11.39 11.53 11.56

Demand deposits 12.17 12.89 13.33 15.22

Core deposits 69.05 67.45 64.16 62.52

Purchased funds 6.74 6.71 9.82 10.10

Other liabilities 1.89 1.55 1.16 0.59

Group 2 – Second Quartile (N = 1316) 

Assets (in $1000s) 23,472 33,102 50,858 78,544

Asset accounts 

Cash balances 7.13 5.14 4.71 4.87

Short term securities 10.99 7.66 4.24 4.22

Long term securities 24.48 26.43 24.29 21.94

Short term loans 35.37 35.01 31.47 32.51

Long term loans 19.08 23.08 32.06 32.52

Other assets 2.95 2.67 3.23 3.93

Liability/Equity accounts 

Equity 9.45 10.74 10.75 10.77

Demand deposits 11.20 12.22 12.45 14.44

Core deposits 69.63 68.05 65.02 63.56

Purchased funds 7.90 7.44 10.62 10.57

Other liabilities 1.82 1.56 1.16 0.65

38
Table 1 (continued) 

1990 1995 2000 2005 

Group 3 – Third Quartile (N = 1316)

Asset (in $1000s) 41,617 62,205 101,145 163,801

Asset accounts 

Cash balances 6.08 4.68 4.21 4.19

Short term securities 10.34 6.98 3.66 3.72

Long term securities 24.19 26.48 23.42 21.18

Short term loans 36.79 35.82 31.81 33.58

Long term loans 19.56 23.32 33.57 33.14

Other assets 3.04 2.72 3.33 4.18

Liability/Equity accounts 

Equity 9.24 10.52 10.38 10.44

Demand deposits 11.43 12.48 12.60 14.12

Core deposits 68.49 67.40 64.37 63.47

Purchased funds 9.09 8.10 11.59 11.31

Other liabilities 1.75 1.50 1.07 0.65

Group 4 – Top Quartile (N = 1316) 

Asset (in $1000s) 241,569 431,672 1,013,934 1,956,61

3

Asset accounts 

Cash balances 6.39 5.04 4.36 3.93

Short term securities 8.44 6.12 3.21 3.10

Long term securities 20.44 23.76 21.69 20.26

Short term loans 39.26 36.41 32.33 35.02

Long term loans 22.24 25.76 34.96 32.87

Other assets 3.23 2.90 3.45 4.82

Liability/Equity accounts 

Equity 8.37 9.67 9.52 9.99

Demand deposits 13.00 13.91 11.68 10.04

Core deposits 65.20 65.18 63.92 65.89

Purchased funds 11.36 9.39 13.45 12.93

Other liabilities 2.07 1.85 1.43 1.16

Extra Group – Top Decile (N = 526) 

Asset (in $1000s) 

491,476 906,006 2,220,178 

4,331,55

5

Asset accounts 

Cash balances 7.31 5.63 4.49 3.68

Short term securities 7.79 5.81 3.19 3.09

Long term securities 18.59 22.98 20.60 19.84

Short term loans 40.95 37.48 33.96 36.20

Long term loans 22.00 25.07 34.14 31.81

Other assets 3.36 3.04 3.62 5.38

Liability/Equity accounts 

Equity 8.02 9.20 9.29 10.11

Demand deposits 13.69 14.55 10.42 8.31

Core deposits 13.08 10.98 15.13 14.08

Purchased funds 62.64 62.80 63.15 65.68

39
Other liabilities 2.58 2.47 2.01 1.83

40
Table 2 

“Pair-wise” or “simple” correlations between asset accounts and liability accounts that exceed 0.30 in 

absolute value. Asset size groups are defined in terms of 2005 dollars. 

1990 1995 2000 2005

Group 1 – Bottom Quartile

Cash 0.34 DD 

Group 2 – Second Quartile

Other asset -0.31 Equity Cash 0.36 DD Cash 0.37 DD Other asset 0.46 Other liab 

LT secs 0.33 Equity LT secs 0.34 Equity LT loans 0.39 Core 

Cash 0.32 DD 

Group 3 – Third Quartile

Cash 0.34 DD Cash 0.46 DD Cash 0.45 DD Cash 0.37 DD 

LT secs 0.34 Equity LT secs 0.32 Equity LT secs 0.34 Equity LT loans 0.32 Core 

LT loans 0.32 Core LT loans 0.33 Core 

Group 4 – Top Quartile

Cash 0.47 Other liab Cash -0.45 Core Cash 0.42 DD Other asset 0.69 Equity 

Cash -0.42 Core Cash 0.42 DD Other asset 0.35 Equity LT loans 0.32 Core 

Cash 0.32 DD Cash 0.41 Other liab Cash -0.30 Core 

LT loans 0.37 Core LT loans 0.30 Core 

Extra Group – Top Decile

Cash 0.58 Other liab Cash 0.52 Other liab Cash 0.38 DD Other asset 0.67 Equity 

Cash -0.49 Core Cash -0.50 Core LT loans 0.36 Core Cash 0.46 Other liab 

LT loans 0.39 Core Cash 0.45 DD Cash -0.34 Core LT loans 0.38 Core 

LT loans 0.33 Core Cash -0.30 Core 

41
Table 3 

This table displays the 1st through the 5th canonical correlations for asset size groups of U.S. commercial 

banks in 1990, 1995, 2000, and 2005. The F-statistics (Rao’s F-ratio approximation) tests whether there 

is any association between the p pairs of canonical variables. 

1990 1995 2000 2005 

Loadings 

Canonical 

Correlation F-statistic 

Canonical 

Correlation F-statistic 

Canonical 

Correlation F-statistic 

Canonical 

Correlation F-statistic 

Group 1 – Bottom Quartile 

1 0.42 16.74*** 0.39 20.58*** 0.40 24.57*** 0.39 17.24*** 

2 0.19 5.75*** 0.32 15.43*** 0.36 21.05*** 0.27 12.63*** 

3 0.11 3.09*** 0.17 6.95*** 0.21 10.30*** 0.22 10.96*** 

4 0.05 1.86 0.04 1.08 0.03 0.52 0.15 7.91*** 

5 0.00 . 0.00 . 0.00 . 0.05 3.41* 

Group 2 – Second Quartile

1 0.49 23.47*** 0.46 29.15*** 0.44 28.72*** 0.52 33.06*** 

2 0.22 6.63*** 0.37 19.99*** 0.39 22.56*** 0.40 23.48*** 

3 0.11 2.67** 0.17 7.17*** 0.18 8.24*** 0.26 14.28*** 

4 0.02 0.41 0.07 3.28** 0.07 2.84* 0.15 7.98*** 

5 0.00 . 0.00 . 0.00 . 0.00 0.01 

Group 3 – Third Quartile

1 0.50 28.02*** 0.52 38.60*** 0.49 37.40*** 0.43 23.38*** 

2 0.27 12.23*** 0.41 26.24*** 0.42 29.26*** 0.29 18.68*** 

3 0.18 8.15*** 0.20 11.24*** 0.22 12.65*** 0.28 19.78*** 

4 0.05 1.80 0.11 7.59*** 0.08 4.60** 0.22 17.31*** 

5 0.00 . 0.00 . 0.00 . 0.03 1.43 

Group 4 – Top Quartile

1 0.61 42.69*** 0.64 49.78*** 0.49 38.71*** 0.72 72.38*** 

2 0.26 14.01*** 0.34 18.86*** 0.44 31.73*** 0.38 26.78*** 

3 0.22 12.73*** 0.20 10.74*** 0.23 12.35*** 0.28 18.26*** 

4 0.08 4.55** 0.09 4.89*** 0.06 2.14 0.06 2.04 

5 0.00 . 0.00 . 0.00 . 0.00 . 

Extra Group – Top Decile 

1 0.69 23.69*** 0.69 24.40*** 0.52 12.05*** 0.72 38.46*** 

2 0.31 7.45*** 0.36 7.71*** 0.31 5.66*** 0.57 23.62*** 

3 0.23 5.88*** 0.18 3.19*** 0.16 2.39** 0.30 9.32*** 

4 0.10 2.74* 0.07 1.35 0.01 0.04 0.10 2.81* 

5 0.00 . 0.00 . 0.00 . 0.00 . 

42
Table 4 

This table displays the average proportion of the variance in asset and liability variables explained by the 

canonical variables, for each of the five canonical loadings. The averages are un-weighted means across 

20 separate calculations (5 size groups by 4 time periods). 

1st

loading 

2nd

loading 

3rd

loading 

4th

loading 

5th

loading total 

Proportion of variance (5):

Asset variables variance Assets canonical variable 17.76 19.48 26.65 20.00 16.12 100.00 

Liabilities variables variance 

explained 

by: Liabilities canonical variable 30.07 28.27 32.08 8.92 0.66 100.00 

Redundancy coefficient (6):

Assets variables variance Liabilities canonical variable 3.88 2.19 1.23 0.15 0.01 7.46 

Liabilities variables variance 

explained 

by: Assets canonical variable 7.57 2.96 1.46 0.08 0.00 12.07 

 

 

43
44

Table 5a (Varimax Rotated)

Correlations from the first canonical loadings. The left-hand part of each cell displays correlations between actual assassets canonical variable. The right-hand part of each cell displays correlations between actual liabilities account data and variable. The correlations are ranked in order of declining absolute value, up to the fourth largest correlation. 

1990 1995 2000 

Group 1 – Bottom Quartile

LT loans 

0.95 PF -0.90 LT loans 0.92 PF -0.93 LT loans 0.94 PF -0.84 LT loans 

LT Secs -0.45 Core 0.71 ST 

loans 

-0.66 Core 0.70 ST 

loans 

-0.66 Core 0.77 ST loans 

ST loans 

-0.27 Equit

y 

-0.27 Cash 0.13 Equity -0.16 LT Secs -0.24 Equity -0.30 LT Secs 

Other -0.13 DD -0.14 LT Secs -0.11 DD -0.12 Other -0.15 Other 0.13 ST Secs ST Secs 

-0.10 Other -0.03 Other -0.11 Other -0.03 Cash 0.03 DD -0.09 Other 

Cash 0.04 ST Secs -0.06 ST Secs 0.01 Cash 

Group 2 – Second Quartile 

LT loans 

0.96 PF -0.91 LT loans 0.95 PF -0.95 ST 

loans 

0.86 PF 0.92 LT loans 

ST loans 

-0.52 Core 0.87 ST 

loans 

-0.59 Core 0.76 LT loans -0.86 Core -0.81 ST loans 

LT Secs -0.22 DD -0.23 LT Secs -0.24 Other 0.13 ST Secs -0.09 DD 0.13 LT Secs Other -0.21 Equit

y 

-0.21 Other -0.17 DD -0.12 LT Secs 0.06 Equity 0.03 ST Secs 

ST Secs 

-0.18 Other -0.06 Cash 0.08 Equity -0.10 Cash -0.06 Other -0.01 Other 

Cash 0.09 ST Secs 0.02 Other 0.03 Cash 

Group 3 – Third Quartile 

LT loans 

-0.91 PF 0.98 LT loans 0.96 PF -0.97 LT loans 0.93 PF -0.91 LT loans 

ST loans 

0.74 Core -0.84 ST 

loans 

-0.64 Core 0.78 ST 

loans 

-0.73 Core 0.83 ST loans 

Other 0.02 DD 0.21 LT Secs -0.21 DD -0.17 LT Secs -0.24 DD -0.19 LT Secs LT Secs 0.01 Equit

y 

0.11 ST Secs 0.02 Equity -0.12 ST Secs 0.08 Equity -0.10 ST Secs 

Cash 0.01 Other 0.05 Other 0.02 Other -0.01 Other -0.06 Other 0.07 Other ST Secs 

-0.01 Cash 0.00 Cash 0.01 Cash 

Group 4 – Top Quartile 
LT 

loans 

-0.90 PF 0.98 LT loans 0.97 PF -0.98 LT loans 0.97 PF -0.96 LT loans 

ST loans 

0.78 Core -0.79 ST 

loans 

-0.62 Core 0.77 ST 

loans 

-0.58 Core 0.82 ST loans 

Cash 0.10 DD 0.18 LT Secs -0.19 DD -0.13 LT Secs -0.34 Other -0.21 LT Secs ST Secs 

-0.06 Equit

y 

0.04 ST Secs -0.09 Other -0.11 Cash -0.09 Equity -0.11 ST Secs 

LT Secs -0.04 Other 0.00 Cash -0.06 Equity -0.02 ST Secs -0.06 DD 0.01 Other Other -0.01 Other 0.01 Other 0.05 Cash 

45
46

Table 5b (Varimax Rotated)

The Second canonical loadings. The left-hand part of each cell displays correlations between actual asset account data variable. The right-hand part of each cell displays correlations between actual liabilities account data and the liabilities correlations are ranked in order of declining absolute value, up to the fourth largest correlation. 

1990 1995 2000 

Group 1 – Bottom Quartile

Cash 0.92 DD 0.93 LT Secs 0.96 Other 0.84 LT Secs 0.93 Other 0.85 Cash LT Secs -0.54 Core -0.66 ST loans -0.64 Equity 0.52 ST loans -0.71 Equity 0.44 ST 

loans 

ST loans 0.13 Other 0.30 LT loans -0.24 Core -0.30 ST Secs -0.11 Core -0.22 LT 

loans 

LT loans -0.12 PF -0.11 ST Secs -0.10 PF -0.14 LT loans -0.11 PF -0.18 LT 

Secs 

ST Secs 0.04 Equity 0.10 Cash -0.08 DD -0.06 Cash -0.06 DD -0.02 ST 

Secs 

Other -0.02 Other 0.06 Other 0.04 Other 

Group 2 – Second Quartile 

LT Secs -0.86 Other 0.91 LT Secs 0.95 Equity 0.85 LT Secs 0.98 Equity 0.88 Cash ST loans 0.64 Equity -0.30 ST loans -0.75 Other 0.34 ST loans -0.50 Core -0.32 LT 

loans 

LT loans 0.17 Core -0.25 Other -0.29 Core -0.29 LT loans -0.45 PF -0.06 LT 

Secs 

Cash -0.17 DD 0.25 LT loans -0.19 PF -0.12 Other -0.12 DD -0.03 ST 

loans 

ST Secs 0.13 PF -0.05 ST Secs 0.12 DD -0.11 ST Secs 0.07 Other 0.00 ST 

Secs 

Other -0.09 Cash -0.06 Cash -0.07 Other 

Group 3 – Third Quartile 

LT Secs 0.98 Equity 0.94 LT Secs 0.96 Equity 0.82 LT Secs 0.96 Equity 0.83 Cash ST loans -0.59 Other 0.26 ST loans -0.75 Other 0.43 ST loans -0.68 Core -0.28 ST 

Secs 

LT loans -0.36 PF -0.16 Other -0.20 Core -0.25 LT loans -0.23 DD -0.09 LT 

loans 

Other -0.25 DD -0.11 LT loans -0.18 DD -0.15 Other -0.11 Other 0.07 LT 

Secs 

ST Secs 0.18 Core -0.20 ST Secs 0.13 PF -0.10 ST Secs 0.09 PF 0.01 ST 

loans 

Cash -0.04 Cash -0.08 Cash -0.04 Other 

Group 4 – Top Quartile 

LT Secs 0.99 Equity 0.96 LT Secs 0.94 Equity 0.96 LT Secs -0.93 Other 0.90 ST 
Secs 

ST loans -0.54 PF -0.14 ST loans -0.78 DD -0.36 ST loans 0.78 Equity -0.21 Cash LT loans -0.34 Core -0.09 ST Secs 0.22 Other 0.17 Other 0.20 DD -0.17 Other ST Secs 0.19 Other -0.07 Cash -0.14 PF -0.09 Cash 0.14 Core -0.09 ST 

loans 

Other -0.10 DD -0.04 LT loans -0.12 Core -0.05 LT loans -0.04 PF -0.03 LT 

Secs 

Cash -0.07 Other 0.00 ST Secs 0.00 LT 

loans 

47
Table 6 

Redundancy Coefficients: Interest Rate Hedging and Regulatory Ratings. 

Panel A displays separate results for high and low halves of banks that reported non-zero values for 

“Total gross notional amount of interest rate swaps held for purposes other than trading where the bank 

has agreed to pay fixed rate” in 2005. Panel B displays results for the aggregated high and low halves of 

the sample bank in 2005, stratified across the five size groups, for “Total loans with remaining maturity or 

next repricing frequency of 1 year or less” as a percentage of total bank assets. Panels C and D display 

separate results for banks with strong (1-rated), good (2-rated), and poor (3-, 4-, or 5-rated) regulatory 

safety and soundness ratings in 2005. 

A. Interest Rate Swaps, Bank Pays Fixed Rate. 

Top 50% (46) 

Asset variables variance Liabilities canonical variable 30.36 

Liabilities variables variance 

Explained 

by Assets canonical variable 49.60 

Bottom 50% (45) 

Asset variables variance Liabilities canonical variable 27.67 

Liabilities variables variance 

Explained 

by Assets canonical variable 56.70 

B. Adjustable Rate Loans, Repricing in One Year or Less. 

Top 50% (2632) 

Asset variables variance Liabilities canonical variable 4.88 

Liabilities variables variance 

Explained 

by Assets canonical variable 9.05 

Bottom 50% (2631) 

Asset variables variance Liabilities canonical variable 7.77 

Liabilities variables variance 

Explained 

by Assets canonical variable 13.76 

C. Composite CAMELS Rating 

Composite CAMELS = 1 (2,196) 

Asset variables variance Liabilities canonical variable 5.27 

Liabilities variables variance 

Explained 

by Assets canonical variable 11.36 

Composite CAMELS = 2 (2,840) 

Asset variables variance Liabilities canonical variable 5.84 

Liabilities variables variance 

Explained 

by Assets canonical variable 11.65 

Composite CAMELS = 3, 4, or 5 (227) 

Asset variables variance Liabilities canonical variable 5.29 

Liabilities variables variance 

Explained 

by Assets canonical variable 12.63 

D. Component Market Sensitivity Rating 

Market Sensitivity Component = 1 (2,157) 

Asset variables variance Liabilities canonical variable 5.45 

Liabilities variables variance 

Explained 

by Assets canonical variable 12.21 

Market Sensitivity Component =2 (2,917) 

Asset variables variance Liabilities canonical variable 6.28 

Liabilities variables variance 

Explained 

by Assets canonical variable 11.41 

Market Sensitivity Component = 3, 4, or 5 (189) 

Asset variables variance Liabilities canonical variable 10.75 

Liabilities variables variance 

Explained 

by Assets canonical variable 19.22 

48
Figure 1 

[A = β ́X] [L = γ ́Y]

[Xlong loans] [ core deps Y ]

1

The following three conditions:

1. A strong canonical correlation between Assets and Liabilities (equation 3, Table 3).

2. A strong canonical loading between Long-term Loans and Assets (equation 4, Table 5).

3. A strong canonical loading between Core Deposits and Liabilities (equation 4, Table 5).

Imply the following fourth condition:

4. There is a strong relationship between Long-term Loans and Core Deposits, after considering 

the correlations among all of the other asset and liability accounts.

2 3

4

49
Figure 2 

Redundancy Coefficients, 1990-2005 

Liabilities explaining Assets 

Panel A: Size Quartiles 

Asset variance explained by Liability

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Year

%

First Quartile

Second Quartile

Third Quartile

Fourth Quartile

Panel B: Size Deciles 

Asset variance explained by liability

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Year

(%)

10th decile

6th-9th deciles

1st-5th deciles

50
Figure 3 

Redundancy Coefficients, 1990-2005 

Assets explaining Liabilities 

Panel A: Size Quartiles 

Liability variance explained by Asset

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Year

%

First Quartile

Second Quartile

Third Quartile

Fourth Quartile

Panel B: Size Deciles 

 

Liability variance explained by asset

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

Year

(%)

10th decile

6th-9th deciles

1st-5th deciles

51