Journal of Monetary Economics 31 (1993) 47-67. North-Holland

Size and performance of banking firms

Testing the predictions of theory

John H. Boyd and David E. Runkle

In recent years, two important hteratures on the theory of bankmg firms have developed. One exammes the economic functtons of banks m environments m which agents are asymmetrically mformed Another considers the mcenttve effects (moral hazard) resultmg from deposit msurance Both theortes make predtcttons about the relation between bankmg firm stze and performance. An emptrtcal analysis of large bank holdmg companies investigates measures of market valuation and rusk of fadure. Limited support is provided for either set of theoretical predictions.

1. Introduction

In recent years, two important literatures on the theory of the banking firm have developed. Both predict relationships between the size of banking firms and their performance. This study tests predictions of the theories.

One substantial literature deals with deposit insurance and the effect that it has on bank decisions. A fundamental finding is that the U.S. system of deposit insurance produces an incentive for insured banking firms to take risk. Theoret- ically, in fact, this distortion pushes them to corner solutions taking as much risk as they can (for example, through the use of financial leverage). With this approach banks are viewed. essentially, as portfolios of risky claims. Their production technologies are unimportant, and size plays no role in the theory. If regulatory treatment were the same for insured banks of all sizes, this theory would predict no relationship between size and performance.

Correspondencr to. John H. Boyd. Research Department, Federal Reserve Bank of Mmneapohs, P 0. Box 291, Minneapohs, MN 55480-0291. USA.

*Thanks are due to V.V. Chari, Stan Graham, Raw Jagannathan. Jim OBrien. and Arthur Rolmck for help with earlier drafts The vtews expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Mmneapolis or the Federal Reserve System.

0304-3932~93,$05.00 m(_ 1993-Elsevter Sctence Pubhshers B.V. All rtghts reserved

In practice, though, regulatory treatment of banking firms has not been symmetric by size. Large-bank failures are supposedly more feared than small- bank failures, since the former are viewed as more likely to result in macroeco- nomic externalities. Under the policy of too big to fail. all liabilities of very large banks ~ whether formally insured or not - have been de,fucto guaranteed. They have not been permitted to fail in the sense of defaulting on debt, because all creditors were made well by the government. As a result, the total package of government insurance. formal and informal. should have been more valuable for large banking firms than for the rest of the industry, cetrris parihus. More precisely. accordmg to the theory. either large banking firms receive a greater net subsidy from government insurance than do others. or they are less risky, or both.

Another recent literature deals with the economic role of banking firms (generally, financial intermediaries) in environments in which agents are asym- metrically informed. This modern intermediation theory predicts that large intermediary firms will be less likely to fail than small ones, and because of that fact, more cost-efficient. Importantly, modern intermediation theory predicts efficiency gains related to size, whereas deposit insurance theory predicts size- related subsidies and distortions.

The empirical tests to be presented cannot clearly differentlate between a competitive advantage due to technical efficiency (predicted by modern inter- mediation theory) and one due to a high subsidy rate (predicted by deposit insurance theory). Thus, the two sets of theoretical predictions intersect and there is not a clean test of the one theory against the other. However, we can and do test the joint predictions of both theories, as will be made precise in what follows.

As it turns out, the data provide only limited support for either theory. Our results do suggest an inverse relationship between size and the volatility of asset returns. consistent with the predictions of modern intermediation theory. How- ever. we find no evidence that large banking firms are less likely to fail than smaller ones. In fact. es posf evidence shows that in recent years the large banking firms have failed somewhat more often. How can that be, if size confers a diversification advantage? The apparent answer is that there is an inverse relationship between size and two other variables: the rate of return on assets and the ratio of equity to assets. In other words, larger banking firms are systematically less profitable in terms of asset returns and systematically more

The Federal Deposit Insurance Corporation Improvement Act of 1991 Includes prowsIons Intended to hmlt the pohcy of too big to fad to only sltuatlons m which the stabihty of the bankmg system IS truly threatened To mtoke this pohcy now ~111 reqtnre a two-thirds vote by both the Federal Reserve and the FDIC boards and the agreement of the Treasury Secretary. It is too soon to say what the effect of this change wll be In any case. the law was passed well after the end of the sample period employed m this study and could not affect our findings. (See also footnote Il.)

highly levered. Their greater use of leverage is consistent with one prediction of deposit insurance theory, a nonmarket distortion. Finally, we find no evidence of a positive relationship between size and market valuation as represented by Tobins 4. Such a relationship is predicted by both theories, due to either cost efficiencies (modern intermediation theory) or a size-related subsidy (deposit insurance theory). In fact, during the second half of the sample period, 1981-90, size and Tobins y are significantly inversely correlated.

The empirical tests employ data for 1 22 banking holding companies over the period 1971.-90. The sample is restricted to firms that are large by industry standards, those whose shares are listed and actively traded. This is not a repre- sentative sample, and admittedly our findings could be different for small banking firms.

The rest of the study proceeds as follows. Section 2 discusses the two theory literatures. Section 3 examines the relation between this study and the literature on economies of scale in banking. Section 4 considers issues in measurement, explains the performance and risk indicators used, and describes a conjectured industry equilibrium. Section 5 presents the empirical results. Section 6 con- siders whether our results may be influenced by systematic differences in market power among sample firms. Section 7 concludes.

2. Theory

There is a large literature examining the incentive effects of fixed premium deposit insurance, the kind offered by the FDIC. Studies on this topic, which we call ~~~~~s~~ iil~~~un~~ theor): include, for example, Merton ( 19771, Kareken and Wallace (19781, Sharpe (19781, Flannery (1989). and Ghan, Greenbaum, and Thakor (1992). A basic conclusion of deposit insurance theory is that as an insured bank increases its risk of failure without limit, there is an ever-larger expected-value wealth transfer from the FDIC to bank owners. A straight- forward implication is that regulation of banks risk-taking, including their leverage ratios, is essential, so as to bound the expected losses of the FDIC2

It is also easy to show that under the too big to fail policy, the net deposit insurance subsidy per dollar of assets is greater for too big . . . banking firms

Flannerys (1989) model exhtbtts decreasmg returns to rusk-takmg, due to regulatory feedback m the form of capital reqmrements. ln thts particular model, the incentive to mcrease the risk of farlure may be hmtted. depending on parameter values There IS also some evidence that banks with high charter values (for example. because of then ability to earn monopoly rents) may be relatively less willing to take risks so as to exploit the deposit insurance subsrdy [Keeley (199O)J Benveniste, Boyd, and Greenbaum (1989) argue that thts constramt on moral hazard may have been what kept the FDIC intact unttl the late 1970s. when mcreased competitton substanttally reduced charter values.

than it is for others. For brevity, we do not include a formal proof, but the logic is simple: too big . . . banking firms receive free insurance on their (technically) uninsured deposits and other liabilities. Other banking firms dont. This asym- metric treatment is defended on the grounds that banking authorities fear the possible macroeconomic consequences of permitting a large banking firm to default on its liabilities. OHara and Shaw (1990) find that public announcement of commitment to such a policy has had a favorable effect on the share prices of the too big . banks.

Ceteris might not be pwibus with respect to regulation of very large banking firms. The authorities have repeatedly stated that they are especially concerned about disruptions of the largest banks, since these may result in systemic effects (negative externalities). In fact, such concerns are the rrrison d&re of the too big to fail policy. Based on these statements, one might logically expect regulators to be more conservative in setting risk constraints on large banking firms ~ for example, by requiring less risky asset holdings and less financial leverage. Then if the true equilibrium were one in which all firms are at regulatory corner solutions as predicted by the deposit insurance theory, empirical tests would reveal an inverse relationship between size and failure risk. Such regulatory risk constraints would also reduce the subsidy component in deposit insurance so that the net effect of differential treatment by size would be unclear. Even so, deposit insurance theory does make a testable prediction:

Prediction 1. Either large (too big to fail) banking firms are less likely to fail than small ones, or they are more highly subsidized per dollar of assets by government insurance, or both.

Obviously, Prediction 1 does not preclude the possibility that large banking firms will be less likely to fail than small ones urrd less subsidized. The conjecture about regulatory risk constraints is also testable.

Co?qecture. As a result of differential regulation, large banking firms will be less likely to fail than smaller banking firms.

7 7 Moderri intertmhltiorl theor!. _.a.

Another large literature has examined the economic role of banks (more generally, financial intermediaries) in environments in which borrowers and lenders are asymmetrically informed. This literature includes studi:s by Diamond (1984) Ramakrishnan and Thakor (1984), Boyd and Prescott (1986). Williamson ( 1986). and Allen (1990), to name a few. We shall refer to it as modern intermediation theory. Prior to the development of such theory, there was no satisfactory explanation for the existence of banks; in the widely studied Arrow-Debreu paradigm. for example. there is no reason for them.

J.H. Boyd and D.E. Runkle. Size and performance of banking firms 51

This body of theory predicts economies of scale in intermediation, quite apart from any production efficiency gains (such as those due to large-scale com- puters). Here the advantage of size is that it means an intermediary can contract with a large number of borrowers and lenders. Large numbers are assumed to result in diversification, and that has been shown to be valuable even in environments with all agents risk-neutral. 3 Specifically, diversification is valu- able because it reduces the cost of contracting among asymmetrically informed agents. In many of these models it is assumed that borrowers, but not lenders, costlessly observe investment return realizations. Uncertainty about return realizations is undesirable, and bad (failure) realizations trigger costly informa- tion production. However, if a large number of investments is made by a single intermediary, pooled risk is reduced or eliminated, and so is the frequency of costly failure states. What is predicted, then, is an inverse relationship between size and the probability of failure.4

In addition, diversification reduces the ex ante expected cost of overcoming information asymmetries. This results in cost savings which are realized whether or not failure actually occurs. The precise link between diversification and intermediation costs is to some extent model-specific. In Diamond (1984), for example, contracting with many agents reduces the ex ante expected cost of state verification. In Boyd and Prescott (1986) intermediaries produce information about the return distributions of investment projects before funding (some of) them. In that environment, large scale not only reduces contracting costs, it also permits intermediaries to fund the most profitable investments. However, the finding that large intermediaries are more efficient than small ones - even abstracting from risk aversion - is quite general. At least one textbook now discusses this relationship in some detail [Greenbaum and Thakor (1991, ch. 3)]. To summarize, modern intermediation theory makes two related predictions about scale effects in banking firms:

Prediction 2. Large banking firms will be less likely to fail and more cost- efficient than small banking firms.

3Not surprtsingly, dtversification IS even more valuable when agents are risk-averse This issue is explored in Diamond (1984).

40ne deficiency of modern intermediatton theory will become apparent when our empirtcal results are presented. The theory has not yet paid adequate attention to a choice variable which partially determines the probability of failure: the ratio of equity to assets. In Boyd and Prescott (1986), for example, the efficient arrangement is one in which both debt and equity claims are issued by intermedtartes. While a umque equity/asset is required for effictency in that environment, it is exogenously determined. A study by Bernanke and Gertler (1989) treats the financial leverage decision of financial Intermediaries in a more serrous way. There, however, it is optimal to go to corner solutions at which intermediary owners invest their entire endowment in the intermediary. There are no outside eqmty investors.

52 J.H. Boyd and D.E. Runkle, Sm and performance of bankmg firtm

3. The relation of our work to the economies of scale literature

There have been a number of studies using econometric methods to test for the existence of economies of scale in banks. The consensus seems to be that there are significant scale economies up to a rather modest size, say $100 million in total deposits. For larger-size banking firms, there is some disagreement: some researchers find evidence of (slight) economies, others find evidence of (slight) diseconomies5

Our study is different than most of the existing literature, however, in several fundamental ways. The performance measures employed in the litera- ture are generally based on accounting costs or profitability. Here market (stock price) data will be used to indicate performance. Moreover, based on the predictions of theory, we investigate the relationship between scale and risk of failure. This link has received little attention previously. With few exceptions, existing studies have investigated banks, whereas this one investigates bank holding companies (BHCs). The holding company is a common organizational form in U.S. banking, and virtually all large firms in the industry employ it. Many small ones do too. In a bank holding company, a parent corporation controls one or more banking subsidiaries and often nonbank financial subsidiaries as well. This structure provides opportunities for diversification not available to an individual bank. When risk measures are investigated as they are here, the BHC is clearly the appropriate organizational entity to consider.6

The trend in empirical investigations of economies of scale in banking seems to be to more and more complex econometrics. Our work, on the other hand, relies on rather straightforward univariate procedures, but is related directly to the predictions of theory. Our approach has the obvious advantage of ease of interpretation, and it avoids a myriad of measurement problems with accounting data. As we see it, if the scale effects predicted by theory are large enough to be of much interest. they should be clearly reflected in market valuation.

See Clark (1988) or Humphrey (1990) for useful revtews of thts hterature.

bA bank holdmg company is defined as an orgamzatton (parent company) whtch holds a controlling share of equity in one or more commercial banks. Often multiple banks are held as well as nonbank financial subsidiartes. Each firm in a bank holding company is a separate legal enttty. However, the enttre orgamzatton ts regulated by the Federal Reserve System under author- ity of the Bank Holdmg Company Act of 1956 and subsequent amendments. A ttme-honored Fed position is that holding companies should provide valuable diverstfication. and that the nonbank affiliates and the parent company should be a source of strength to commercial bankmg affili- ates. With that objective. there are a number of regulations which make tt caster for funds to flow from nonbank affiliates to banks than in the other directton. However, funds do flow in both directions and, of course, all affiliates take their orders from the same parent. For our pur- poses, tt seems reasonable and approprtate to treat bank holding companies as consolidated organizattons.

J.H. Bo_vd and D.E. Runkle, See and pe$ormance of bankmgjrtns 53

4. Measuring performance: Market valuation and risk of failure

Let it = profits, A = assets, E = equity, k = - E/A, and i = 5/A, where a tilde denotes a random variable. The performance of BHC i, relative to other BHCs, is reflected in its return distribution b(?)[. In our empirical tests, 4(f) is represented by sample estimates of its first and second moments, R and S, respectively. For purposes of comparison across firms, these two statistics must be combined into a single performance indicator. That is done here by using Tobins q, the ratio of the market value of assets to their replacement cost. Market investors have preferences not just toward mean returns but also toward risk, and Tobins q will reflect the assessment of all relevant moments of #J(?). with market weights.

Define failure as a realization of it in which losses exceed equity. The probability of failure is then

p(E< -E)=p(r

54 J.H Boyd und D.E Runkle. SIZ and performunce of bankmg firms

In summary, the empirical performance indicator is Tobins 4 and the risk indicator is the Z-score. We also examine sample estimates of R, S, and K, the underlying parameters which determine q and z.

4.1. A corljecturecl inhstry equilihriw?l

Eq. (4) indicates the dependence of q on 4(3, and sets out the arguments which determine @(?) in a conjectured industry equilibrium,

T(A) is included to represent scale effects, and modern intermediation theory predicts T > 0, for all A. S(A) is included to reflect the net rate of subsidy in government insurance. With the policy of too big to fail, the deposit insurance theory predicts S 2 0, for all A. with strict inequality over some size range as a BHC approaches too big . . status. For small BHCs and for very large ones which already receive the maximum subsidy, S = 0.

If T and S were the only arguments in (4), the unique equilibrium would be one with a single large BHC. What we actually observe, however, is great variation in BHC size. One possible explanation is, simply, that both theories are wrong and that T = S = 0, for many levels of A. Yet, other explanations are possible. Besides great variation in size, the data suggest a consistent relationship between population concentration and BHC size. For example, virtually all large BHCs are located in major population centers such as New York and Chicago. Small towns and cities have small BHCs. In other words, we observe limited geographic markets. In the U.S.. that is largely attributable to the fact that interstate banking has been prohibited or at least greatly restricted by legislation and regulation. Intrastate branching is also restricted in many states. The argument A4 is included in (4) to stylistically represent the effect of market size, and C, is the number of potential customers in the market of BHC i. Over some range of A. M > 0 as assets are expanded to meet the intermediation needs of agents in that market. Eventually, given a fixed market size, however, the cost of further asset expansion exceeds the benefit and M < 0. Note that this structure results in a distribution of BHC sizes even if T = S = 0, for all A.

Finally, .R is included in (4) to represent market power, the ability to earn rents. .3 depends on a number of arguments, for example the size distribution of BHCs in the market. Our empirical tests will not attempt to directly control for differences in 3 across BHCs. However, we recognize A as an argument in (4) and defer this issue. If BHCs maximize shareholder wealth, as we assume, each will choose A so as to maximize q. The distribution of Cs will induce a distribution on A, and if T > 0 or S > 0, there will be a positive cross-section relationship between A and q in equilibrium. Of course, if neither

J.H. Boyd and D.E Runkle. Size and performance sf banking firms 55

theory is correct and T = S = 0, for all A, then A and q will be unrelated (assuming, further, that size and & are unrelated).

4.2. Market data estinutes

With banking firms, accounting profitability measures are notoriously poor since gains and losses need not be realized in a timely manner. Loan losses, in particular, may not show up in the accounting data for years. For that reason, we use market-based estimates of rates of return. In so doing. we take advantage of the fact that most measurement error in bank accounting data is in the assets. Bank liabilities are relatively homogeneous and short-term. except for small amounts of subordinated debt. Thus, for liabilities, book values should be reasonable proxies for replacement cost. Our estimate of the market value of total assets A is

Am = Em + LB,

where Em = market value of equity (average price per share times average number of shares outstanding) and LB = accounting (book) value of total liabilities. Profits are estimated as

7rrn = NV, - P,- 1 + D,)/P,- 1)

where P = price per share of common stock, D = dividends per share, t = time period, and N = average number of shares outstanding. Our estimate of the rate of return on assets is simply R = nm/Am.

The Z-score estimates depend critically upon the volatility of returns. For these estimates, market return measures are also employed, since it seems sure that BHCs accounting profits are highly smoothed. Finally, Tobins q is estimated by Am/(LB + EB), where EB is the accounting value of equity. Any attempt to measure Tobins q is subject to measurement error because of difficulties in evaluating both the total market value of the firms assets and the

The assumed mdustry structure IS obvtously very sample. But It is consistent with some stylized facts m that tt results m an equthbrmm distrtbutton of BHC stzes. depending on srze of market. Of course, if T > 0 and S > 0, thts structure predtcts there will be one BHC per geographrc market, which is inconsistent with the facts. However. the observed structure of the Industry may be significantly influenced by anti-trust policies.

For each firm m the sample we computed the standard deviation of the rate of return on equtty with both accounting and market data. The mean (median) standard deviation of the rate of return on equity for all firms was 0.051 (0.035) wtth accountmg data and 0.289 (0.278) wtth market data. Clearly, market returns are much more volattle than accounting returns. Z-scores estimated with the accounting data are implausible, predicting farlure rates of essenttally zero. This is entirely attrib- utable to the low standard deviations with the accounting data. Simtlar evtdence of smoothing accounting profits has been reported elsewhere [e g.. Greenawalt and Sinkey (1988)].

replacement cost of those assets. However, these problems are likely to be less severe for banks than for manufacturing firms for two reasons. First, banks issue little long-term debt. The overwhelming majority of their liabilities are short- term deposits. For such deposits, book value is a close approximation to market value. Therefore, for banks, the sum of the market value of equity and the book value of liabilities is likely to be a good approximation to the market value of total assets. Second, relatively few bank assets are plant and equipment. There- fore, the major deviation of asset book value from replacement cost is likely to occur in the loan and bond portfolios. To the extent that asset values (especially loan values) are inaccurate at any date, this will be reflected in sample estimates of Tobins q. Note, however, that generally accepted accounting procedures can only drfer capital gains and losses; they cannot make them vanish. Eventually, these must be realized. and when that occurs, accounting asset values are adjusted accordingly. Here we investigate relative values of q over a long (20-year) period. This surely helps to reduce, if not totally eliminate, measure- ment error from this source. Measurement errors are potentially much more severe in estimating the risk indicators S and Z-score. Estimates of those statistics, however, rely strictly on market data.

4.3. Sample bank lzolditzy companies

The annual data in this study include the years 1971-90 and come from Standard and Poors COMPUSTAT. This source provides both accounting data and stock prices for publicly traded firms. We do not include all the BHCs that are in the COMPUSTAT data base. For one thing, not all BHCs have data in all sample periods, and we require that sample firms have a minimum of five consecutive years. In addition, we exclude the smallest BHCs in the COM- PUSTAT data base. those with average total assets below $1 billion. BHCs in this size range typically are not publicly traded, and the COMPUSTAT BHCs in this size range are too few to provide reliable statistics. Finally, for those BHCs that would have failed except for government assistance, we eliminated all data from the first year of such assistance and thereafter. We justify this action on the grounds that we are interested in market behavior. There are nine such firms in the sample, including some very large ones. These are too big to fail BHCs which actually did fail in the sense of eq. (1)

The so-called survivor bias is a widely recogmzed problem with the COMPUSTAT data set. Firms which are acquired. fail, or have their securities dehsted are dropped from COMPUSTAT. At any pomt m time. therefore. the firms mcluded m this data set are not necessarily representative of their Industry, but are the survtvors. Admittedly, that is true of our sample, but the special regulatory treatment afforded to bankmg firms helps to attenuate the problem The FDIC has almost never liquidated banks or BHCs as large as those in our sample. Instead, it infuses them wtth new capital and reorgamzes them. When the reorgamration mvolves an acqutsition by a stronger firm. the failing bank loses its identity and will subsequently be removed from COMPUSTAT. Often.

Table

1

Perf

orm

ance

and r

isk

chara

cteri

stic

s of

sam

ple

bank

hold

ing c

om

panie

s, sam

ple

means (m

edta

ns i

n p

are

nth

ese

s).

-_

__-

--

_-.

_. .

._

Vari

able

1.

Num

ber

of

firm

s

2.

Ass

ets

($ b

k),

A

3.

Tobm

s 9

4.

Z-s

core

, (R

+ K

)/S

5. S

tandard

devt

att

on of R

, S

6 Equtt

yiass

ets

, -K

7.

Retu

rn o

n a

ssets

, R

8.

Retu

rn o

n e

qutt

y, R

,

All

firm

s __

_-.

122

9.7

3

(3.8

6)

I .ooz

11

.QW

4.3

1

(3.9

9)

0.0

17

(0.0

16)

0.0

61

(0.0

60)

0.0

055

(0.0

047)

0.1

37

(0.1

39)

-

1971-9

0

(full

sam

ple

peri

od)

-..

Siz

e c

lass

(ave

rage to

tal

ass

ets

) --

___-

--

-...

-..-

__

_~

-_._

__._

____

(I)

$1 b

il-

(II)

$2 5

bil-

(I

II)

$4 b

il.-

(IV

) O

ver

$2.5

btl

. $4 b

il.

$8 b

tl.

$8 b

il.

24

38

27

33

1.9

8

3.1

6

5.6

1

26.3

(1

.991

(3.1

3)

(5 3

7)

(15.2

)

1.0

04

1.0

06

0.9

95

1.0

03

(1.0

01)

(1.0

03)

(0.9

93)

tt.O

W

4.0

5

4.6

1

4.4

4

3.9

9

(4.2

1)

(4.1

9)

(3.9

6)

(3.7

8)

0.0

19

0.0

19

0.0

15

0.0

16

(0.0

17)

(0.0

17)

(0.0

15)

(0.0

13)

0.0

66

0.0

7 1

0.0

53

0.0

52

(0.0

63)

(0.0

67)

(0.0

52)

(0.0

45)

0.0

056

0.0

072

0.0

037

0.0

039

(0.0

057)

(0.0

059)

(0.0

039)

(0.0

030)

0.1

40

0.1

48

0.1

28

0.1

29

(0.1

36)

(0.1

49)

(0.1

32)

(0.1

32)

Sig

mfica

nce

1eveP

0.0

14

0.2

82

0.0

54

O.O

OO

0.0

09

0.6

03

-~ 19

81-9

0

(seco

nd h

alf)

~__

__ All

firm

s -.

.--.

-___

122

13.9

3

(5.3

1)

1.0

05

(1,0

01)

4.9

0

(4.5

2)

0.0

16

(0.0

15)

(~~

~

0.0

065

(0.0

064)

0.1

51

(0.1

62)

Cro

ss-s

ect

ion a

vera

ges (

media

ns)

of

tndiv

ldual

firm

s s

tati

sttc

s.

bSig

nific

ance

level f

rom

xi

test

. Test

is a

gain

st n

ull

hyp

oth

esi

s of

no s

ignific

ant

diffe

rence

in g

roup m

eans.

58 J.H. Boyd and D.E. Runkle. Si:e and performance qf hankmgjirms

After deletions, 122 BHCs remain. This is a small sample for an industry that includes thousands of firms, and it does not include any firms with total assets of less than $1 billion. Admittedly, findings could be different if these smaller firms were included. Fortunately there are still great differences in the sizes of firms included: the largest sample BHC has total assets about 100 times greater than the smallest. Table 1 shows the distribution of sample firms, grouped into four size classes. The largest size category (IV) includes 33 firms with average assets of $26.3 billion. These are some of the largest BHCs in the United States, and presumably most of them have been viewed as too big to fail by the authorities. At the other extreme, the smallest size category (I) includes 24 firms with average assets of about $2 billion. Based on official statements, these BHCs are not in the too big to fail category.

Also shown in table 1 are performance and risk statistics for the sample firms, grouped in several ways. The first column shows sample means and medians for all firms in the entire 20-year period, 1971-90, followed by a breakdown by size class. The last column shows sample statistics for all firms in the second half, 1981-90.

5. Size and performance, size and risk

Table 2 shows the results of tests in which the performance and risk indicators are regressed on BHC size, represented by In(A), the natural logarithm of total assets. Both cross-section and panel results are displayed. However, the statistics S and Z-score can only be obtained intertemporarily. This is done once for each firm, using the full sample period or whatever smaller number of observations is available. Then the individual firm statistics are regressed against In(A) in cross-section. Panel data tests include dummy variables for time periods, but for brevity those coefficients and t-statistics are not reported. In the panel data tests, t-statistics are adjusted to account for random firm-specific effects. Cross- section regressions employ a correction for conditional heteroskedasticity using Whites (1980) method.

however, the restructured firm maintams its identity, wrth new owners and managers. In fact, nine such BHCs are included m the sample employed here. As dtscussed above, we drop all data points for these firms from the date of government assistance onward (smce we are Interested in market behavior). This regulatory treatment of large BHCs is extraordmary. and it reduces the survivor btas compared with almost any other Industry

It ts not enttrely clear how large a BHC must be before it ts constdered too big to fall by the authorities, Since the pohcy has been Implemented by admnustrative deciston, no formal guidelines are avatlable. In September 1984. the Comptroller of the Currency dtd testify before Congress that 11 BHCs (roughly the 11 largest) were too big to fad. However, banking firms considerably smaller than that have recetved government assistance, and tt seems clear that the policy may apply to smaller firms under some circumstances.

J.H. Boyd and D.E. Runkle, Size and performance qf banking firms 59

Table 2

Performance and risk measures regressed on BHC size. annual data, 1971-90, 122 firms.

Dependent variable

1.

2.

3.

4.

5.

6.

Slope coefficient of size. In(A) t-statistic

Sample Type of sizeb regression

Tobins 4 - 0.0012 1.07 122 - 0.0004 0.36 2029

Z-score, (R + K)$

Standard deviation of R. S

Equity/assets, -K

- 0.0904 0.77 122 n,a n/a n/a

~ 0.0022 4.02** 122 n/a n/a n/a

- 0.0082 5 40** 132 - 0.0075 5 21** 2029

Return on assets. R - 0.0011 - 0.0007

3.63** 1.39

Return on equity, R, - 0.0111 - 0.0073

2.47* 1.06

122 1907

122 1907

Cross-section Panel

Cross-section Panel

Cross-section Panel

Cross-section Panel

Cross-section Panel

Cross-section Panel

t-statistics are against the null hypothesis that the slope coefficient is zero. **(*) indicates significantly different than zero at 99% (95%) confidence.

bin panel data tests, sample size is smaller with R or R, the dependent variable than it is with Tobms 4 dependent. Computation of returns requires differencing, and that results in the loss of the first sample date.

Panel data regressions include dummy variables for the time period. For brevity, these coeffi- cients and t-statistics are not reported. In these regressions, r-statistics are also adjusted to account for random firm-specific effects. Cross-section tests employ a correction for conditional hetero- skedasticity using Whites (1980) method.

The size group statistics are intended primarily as a check for the existence of a specific cutoff size for the too big . . . policy, which might be obscured in the regressions. Generally speaking, however, the analysis of size groups in table 1 is quite consistent with the regression results in table 2. In what follows, therefore, we do not discuss the size group comparisons.12

There is also considerable uncertainty as to when this policy, mformal as it is. was first put into effect. OHara and Shaw (1990) date the formal statement of the policy at the Comptrollers 1984 testimony. Yet that testimony itself dealt with the bailout of a large banking firm, Continental Ilhnois, that had occurred earher the same year It is clear. therefore, that the pohcy was operative prior to the Comptrollers statement. Ten years earlier in 1974, the Franklin National Bank, then 20th largest, was bailed out of financial difficulty by the government. Subsequent testimony and analyses clearly suggest that the pohcy existed even then. [For example, see Federal Reserve Bank of New York (1974) Annual Report.] Arguments for such a pohcy can be found earlier still, most notably m Friedman and Schwartz (1963. pp 309-311).

*One significant exception IS the results with Tobins r~ dependent Row 1 m table 2 suggests that there is no meaningful relationship between size and Tobins 4. The grouped data in table 1 do display a difference in group means that is statistically significant at about the 1% level.

60 J. H. Boyd and D. E. Runkle. Sm and performance of bankmg firms

Row 1 in table 2 shows a negative relationship between size and Tobins q. not significantly different than zero at even 90% confidence.13 Row 2 suggests that there is no meaningful relationship between size and Z-score. However, row 3 displays an inverse relationship between size and S, the standard deviation of the rate of return on assets, which is significantly different than zero at a high confidence level. The ratio of equity to assets, -K, is negatively related to size at a high significance level, and that result is obtained in both cross-section and panel data tests (row 4). The rate of return on assets, R, is also negatively related to size, and significance levels are high in the cross-section regression, but not in the panel regression (row 5). However, the cross-section results may be spurious because, on average, the smaller banks have fewer observations from the first half of the sample, during which R was lower, on average, for all banks. Finally, the rate of return on equity, R,, appears to be weakly negatively related to size (row 6).

Table 3 shows the results of the same regressions as in table 2, but estimated with data from the last half of the sample period, 198 l-90. There are two reasons to look at the subperiod. First, a considerable number of firms entered the sample well after 1971. Thus, the second subperiod has many more firms (20 more) and less missing data than the first. Therefore, inference with this sample is more robust. In addition, it is worth investigating whether the regression results are sensitive to choice of time period. In general, comparison of the regressions in table 2 and table 3 suggests thats not so. Results in both tables are very similar when the dependent variable is the Z-score (row 2), equity/assets ( - K) (row 4), and rate of return on assets (R) (row 5). As previously mentioned, the probable cause for these differences is that small banks have many missing observations in the first half of the sample, when the average value of several of the dependent variables was substantially different from the average value in the second half of the sample.

Both tests also suggest a negative relationship between size and S, the standard deviation of R (row 3). However, it appears that this relationship got stronger over time, in terms of both the regression coefficient and the r-statistic. The same is true of the negative relationship between size and Tobins q. In the case of Tobins q, the change is quite marked. The fact that the results generally differ little between the two time periods shows that the results are robust with respect to sampling difference. These sampling differences also explain why size does not explain return on equity in the cross-section during the second half of the sample.

However. this IS entirely due to the difference between intertor size group III and the other groups, and can be dtsmtssed as economtcally unimportant. (The other stze groups dtsplay mean and medtan values of Tobins y whtch are almost tdenttcal in table 1.)

r3Keeley (1990) also reports findmg no stgmficant relattonship between size and Tobins q in tests conducted with a stmrlar sample of large BHCs. However, his regresstons include several addttional explanatory vartables bestdes ttme pertod and firm stze.

J.H. Boyd and D.E. Runkle, Si:e and performance of bankmgjrms 61

Table 3

Performance and risk measures regressed on BHC size, annual data, 1981-90, 121 firms.

Dependent variable

1.

2.

3.

4.

5.

6.

Tobins 4 - 0.0038 3.39** 122 Cross-section - 0.0028 2.13* 1160 Panel

Z-score. (R + K)/S 0.03 16 0.17 122 Cross-section nla n/a n/a Panel

Standard deviation of R, S - 0.0032 6.45** 122 Cross-section n/a n/a n/a Panel

Equity/assets. -K - 0.0101 6.36** 122 Cross-section - 0.0088 5.25** 1160 Panel

Return on assets, R - 0.0010 2.3-P 122 Cross-section - 0.0013 2.14* 1142 Panel

Return on equity, R, - 0.0056 0 71 122 Cross-section - 0.0130 1.38 1142 Panel

Slope coefficient of size, In(A) t-statisti?

Sample size

Type of regressionb

at-statistics are against the null hypothesis that the slope coefficient is zero. **(*) Indicates sigmficantly different than zero at 99% (95%) confidence.

Panel data regressions mclude dummy variables for the time period. For brevity, these coeffi- cients and t-statistics are not reported. In these regressions, f-statistics are also adlusted to account for random firm-specific effects. Cross-section tests employ a correction for conditional hetero- skedasticity usmg Whites (1980) method.

We shall discuss these findings in a moment. First, we examine some data on actual failure rates.

5.1. Actual rates of bank failure

Table 4 shows actual rates of failure of commercial banks for two size classes: total assets of less than $1 billion (small) and total assets of $1 billion or more (large). These data are for all (FDIC-insured) banks and are quite different than our sample of large BHCs. It would be nice to have more than two classes in the size range examined in our other tests. However, the number of banks with total average assets of $1 billion or more is small (about 200), and the failure rates are relatively low. As a result, there are not enough data points to partition more finely. As it is, we refrain from presenting significance tests.i4

lA failed bank is defined as an FDIC-insured bank, includmg an FDIC-insured savings bank, that was closed because of financial difficulties or that required financial assistance from the FDIC. Failure data apply to banks, not BHCs. Thus, to determine BHC failures would require counting multiple bank-affiliate failures within one BHC as a single failure. The available data do not permit

JMon- C

62

Table 4

Bank failure rates by size class. 1971-91.

Asset size of banksh 1971-80 1981-91 1971-91

Small (assets less than $1 bilhon) Large (assets of $1 btllton or more)

0.56 9.9 I 1026 2 74 IO.45 16.15

Source: Federal Deposit Insurance Corporation. This table is an updated version of one appearmg m Boyd and Graham (1991)

For each size class. percentages are based on the cumulative number of failures and the average annual number of banks of that size over the time period specified. Over this 21-year period. the average number ofsmall banhs was 14.031 and the average number of large banks was 260. Failures ofsmall banks averaged 52 per year and large banks averaged 2. Data reported by the FDIC Include federally Insured savmgs banks.

hThe 41 commercial and aavmgs banks with assets of $1 billton or more that failed or required FDIC assistance are hsted here grouped by the year of failure (assistance) 1972. Bank of Common- wealth: 1973. Umted States NB: 1974, Frankhn NB: 1980, First Pennsylvama NB; 1981. Greenwich SB. Umon Dime SB. 1981. Western NY SB. NY Bank for Savmgs, Western Savmgs Fund Society of Philadelphia. 1983. Dry Dock SB. First NB Midland, Texas: 1984, Contmental Illinois: 1985. Bowery SB: 1986, First NB&T, Oklahoma City, BankOklahoma: 1987, Syracuse SB: 1988, First City Bancorp.. Texas (one bank). Ftrst Repubhc Texas (four banks), Umted Bank Alaska: 1989, M Corp., Texas (four banks). Texas-American Bankshares (one bank), NBC, Texas (one bank), First American B&T. Palm Beach, Florida 1990, Seamens Bank for Savmgs. NB of Washington. DC. 1991. Bank of New England (three banks). Mame SB. First NB ofToms River, New Jersey, Goldome SB. First Mutual Bank for Savmgs, Boston. Citytrust. Bridgeport. Corm., Mechamcs & Farmers SB. Bridgeport. Corm., New Hampshire SB, Connecticut SB

Table 4 shows that the large-bank failure rate was consistently higher than the small-bank failure rate. That is true over the full period 1971-91 and over both subintervals. For both size classes, failure rates were much higher in the 1980s than in the 1970s; this is not surprising since the banking industrys problems in the 1980s have been widely documented. ls

identification of BHC afhhation of failed banks Where atlihation is obvious. we treat multiple bank failures as a smgle fatlure This 15 done m Just two cases, both m Texas. This adJuatment (mvolv- mg large banks) tends to understate the large-bank failure rate relative to the small-bank fatlure rate

Work by Kuester and OBrien (1990) supports some of the results reported here Uamg data for 225 BHCa, they find that the standard deviation ofasset returns is negatively related to size. at a high significance level They also directly estimate the value of government msurance. usmg the BlackScholes put-pricmg equation, In their tests, the option value of government msurance is not related to size at any reasonable sigmficance level. A study by OHara and Shaw (1990). however, suggests that equitv mvestors may value too big to fail status. They examme the announcement of the too big to fali pohcy by the Comptroller of the Currency m 1984 Usmg an event testmg approach, they find that the announcement resulted m positive short-run wealth effects for share- holders of some large BHCs

J.H. Boyd and D.E. Runkle, See and performance of bankrngjirms 63

5.2. Discussion qf results

The data provide no support for ~~ed~crio~ 1 from the deposit insurance theory: that large banking firms will either be less likely to fail than small ones, or be more heavily subsidized, or both. In all our tests, the Z-score risk measure is unrelated to size. And data on actual failure rates suggest that over the last 20 years large banking firms have failed more frequently than small ones. As argued earlier, the predicted size-linked subsidies ought to be reflected in Tobins q. In our tests with data for the full 20year period, the relationship between size and q is of the wrong sign (negative), but confidence levels are low. In tests using 198 l-90 data, that relationship is also negative, but with reasonable confidence that the true coefficient of the size term is negative (the opposite of what is predicted). Again, in sum, there is no support for Prediction I from deposit insurance theory.

Obviously, our C~~~~cr~~e, that large banking firms are more tightly risk- regulated than small ones, is not supported either. Arguably the simplest risk measure for regulators to monitor and control is financial leverage. Yet, the data suggest an inverse relationship between size and -K, the ratio of equity to assets - the opposite of that conjectured. Guessing that bank supervisors pay more attention to accounting than to market data, we repeated these tests employing an accounting measure of -K. Again, an inverse and highly signifi- cant relationship with size was revealed. (For brevity, these results are not reproduced.) To summarize, the authorities may .SUJ theyre especially con- cerned about the risk of large BHCs, but if theyve been doing anything about it, these efforts do not show up in the data.

Modern intermediation theory is supported by our results in one important respect. That theory assumes that scale confers a diversification advantage via contracting with more agents. Our finding of a consistent and significant negative relationship between size and S. the standard deviation of rates of return, is consistent with the theory. However, it appears that better diversifica- tion, as reflected in S, does not result in lower risk of failure (reflected in Z-scores or actual failure rates.) The data strongly suggest that. whereas the larger BHCs may be better diversified, they employ more financial leverage and earn lower rates of return on assets. These factors (at least) offset the diversification advantage. Finally, if there are contracting cost efficiencies of scale as suggested by the theory, these do not show up in the Tobins q performance measure. In sum, the data provide only limited support for Prediction 2 from modern intermediation theory.

6. Are these results affected by differences in market power?

As indicated in eq. (4), an additional factor which could result in performance differences across BHCs is variations in market structure, 8, or the ability to

64 J.H Boyd und D. E. Runkie. See und prrfornmce qf barking firm

earn rents. Some believe it is possible to statistically separate performance differences due to technology from those due to market power using variables which represent the size distribution of firms in an industry [Smirlock, Gilligan, and Marshall (1984)]. Others argue this is not possible, or at least very difficult [Stevens (1990)]. Here no attempt has been made to directly control for differences in market power across firms. Therefore, it is possible that actual scale efficiencies (or size-linked subsidies) are obscured in our tests ~ offset by systematic differences in market power according to banking firm size. This would necessitate an inverse relation between size and market power, which may seem intuitively unlikely to some.

Additional evidence can be brought to bear on this issue. The sample period 1971-90 was a time of very significant deregulation in banking, including the Banking Acts of 1980 and 1982. A priori. one would expect deregulation to reduce rents. If the smaller sample BHCs were the ones systematically advan- taged in terms of market power, one would expect to see that advantage diminishing over time with deregulation. But, as shown in table 5, that is not what happened.

Table 5 shows the mean (median) value of Tobins q for four different size classes of BHC, for the first half of the sample period (1971-80) and for the second (1981-90). To obtain roughly equal cell sizes, different asset-size groupings must be employed in the two subperiods. However, the results are clear. In the first subperiod, Tobins ~1 is, if anything, positively related to size. In the second subperiod. the relationship is negative. Table 5 also displays the rate of return on assets (R) by size class. Although the cell-by-cell comparisons look somewhat different, it is clear that R is negatively related to size in both subperiods. In sum, there is no evidence that smaller BHCs did relatrt!e/y better than large ones in the 1970s compared to the 1980s. Indeed, Tobins q comparisons suggest the exact opposite. Thus, it seems most unlikely that economies of scale or size-related subsidies are being obscured in our tests by an inverse association between BHC size and market power. b

lhBy no means are we argumg that deregulation has had no effect on banking firms abtlity to earn rents. However, one would expect such effects to be greatest for the thousands of commumty and agrrcultural bankmg firms whtch operate m very restrtcted geographtc markets These are not pubhcly traded and are not m our sample of BHCs Table 4 provides some evidence on thts tssue whtch IS at least suggesttve. All the sample BHCs have average assets of $1 bullion or more, and their affihated banks are generally Included m the large-size category m table 4. For banks m thts stze category, the cumulattve fatlure rate over 1971-80 was about 1.74. whtle over the 1981-91 pertod tt was about 10.45. roughly a 30090 Increase. Commumty and agrtcultural banks are all Included m the small-stze category Durmg the same submtervals. their cumulattve fatlure rate mcreased from about 0.6 to about 9.9 an mcrease of more than 1.600~ Of course. these fatlure stattsttcs have been mfluenced by many factors bestdes deregulatton.

J.H. Boyd and D.E Runkle. Sre and performance of bankingjirms 65

Table 5

Size class comparisons. first and second half, group means (medians m parentheses)

Variable --~ _ ~- Number of firms

Total assets. A

Tobins q

Return on assets. R

Variable ____ ~-~

1. Number of firms

2. Total assets. A

3. Tobms q

4 Return on assets. R

(I) Under $1.5 bd.

27

1.12 (1.13)

0.99 1 (0.987)

0 0050 (0.0041)

First half (1971MO) ___~

Size class (average total assets) ~__

(II) $1.5 bill (III) $2 bil.- $3 bd. $3.5 bd.

~___.

35 21

I .80 2.56 (1.76) (3.34)

0.990 0.997 (0.986) (0.996)

0.0020 0.0022 (0.0022) (0.0020)

(IV) Over $3 5 bll

-

28

17.40 (8.85)

1000 (0 996)

0.0025 (0.0030)

Second half (1981-90)

Size class (average total assets) ~~~__ ~_~

(I) $1 b1l.m (II) $3 bll- (III) $5 b& (IV) Over $3 bll $5. bd $15 bll $15 bll.

~__~__

27 29 35 30

2 39 3.84 8.24 40.6 (2.47) (3 6.5) (7.57) (25.5)

1.010 1007 1001 1002 (1.008) ( 1.007) (0.999) (0 998)

0.0070 0.0070 0.0066 0.0049 (00061) (0.0072) (0.0066) (0.0038)

__ __ ~___~~~~_

7. Conclusion

Our main conclusion, unfortunately. is that the two banking firm theories are not yet sufficiently advanced to take to the data. Significant predictions of these theories are not supported, and interesting regularities in the data are not predicted. Anecdotal explanations abound, but we know of no theoretical model of the banking firm with equilibria in which financial leverage is positively related to size. Nor are we aware of theory which predicts an inverse relationship between size and rates of return on assets in equilibrium. Unfortunately, it is not difficult to find policy studies which treat one prediction of theory as a stylized fact - the prediction that large banking firms will be less likely to fail than small ones. Obviously, our findings suggest that this is counterfactual, and we refrain from citing specific references.

66 J H. Boyd und D.E Rut~kie. SIX and performance ofharking.firms

In our view, there are two directions in which theory could be profitably extended, and some work is already being done in each. First, policy interven- tions such as deposit insurance need to be introduced and studied in equilib- rium models in which banking firms exhibit meaningful technologies and thus have a raison dbtre. An example of recent work along these lines is Chart, Greenbaum, and Thakor (1992). In addition, more detailed study of the optimal mix of claims against banking firms is warranted. Bernanke and Gertler (1989) have done very interesting work in this area, but further extensions would be useful, perhaps allowing for the existence of outside as well as inside equity.

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