portfolio diversification at commercial banks

American Finance Association

Portfolio Diversification at Commercial BanksAuthor(s): Edward J. Kane and Stephen A. BuserSource: The Journal of Finance, Vol. 34, No. 1 (Mar., 1979), pp. 19-34Published by: Wiley for the American Finance AssociationStable URL: http://www.jstor.org/stable/2327141 .

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THE JOURNAL OF FINANCE * VOL. XXXIV, NO. 1 * MARCH 1979

Portfolio Diversification at Commercial Banks

EDWARD J. KANE and STEPHEN A. BUSER*

I. Introduction

IN PERFECT CAPITAL MARKETS, financial intermediaries lack a raison d"etre. Traditionally, intermediaries have been portrayed solely as issuers of indirect debt who develop and exploit a wedge between equilibrium borrowing and lending rates.'

But this explanation ignores the fact that nonmutual depository institutions intermediate for their shareholders, too. This paper seeks to explain how a firm can perform a useful function by holding a portfolio of efficiently priced securities that its stockholders could in principle have purchased directly.2 Clearly, the answer has to lie in models that allow a financial firm to build or maintain security portfolios for its shareholders more cheaply than its shareholders could on their own.

This insight leads us in Section II to a theory of financial intermediaries that features diversification costs and (via information risk) imperfect substitution between homemade diversification and diversification produced by firms. With differential diversification costs and benefits, it is rational for a firm to engage in a prior round of asset diversification on behalf of its shareholders even when all assets are priced efficiently and available for direct purchase by shareholders. Within this framework, the financial firm intermediates just as truly when it issues common stock as when it issues indirect debt. From the point of view of stockholders, financial institutions are specialized producers of diversification services.

Although comparative advantages in diversification might be used (along with limited liability) to explain the emergence of firms in general, firm-produced diversification services must be especially attractive to the subset of stockholders that invests in diversification specialists. The clientele theory of stock prices imparts new perspective on the operations of a value-maximizing financial institution.

* Everett Reese Professor of Banking and Monetary Economics, The Ohio State University and Assistant Professor of Finance, The Ohio State University, respectively.

The authors wish to express their gratitude for the invaluable research assistance provided by JoAnne Grolnic. Thanks are also due to Jerome Baesel, Andrew Chen, E. Han Kim, Burton Malkiel, Gordon Roberts, and Haim Levy for valuable comments on earlier drafts of this paper and to the Federal Reserve Bank of Boston and the National Science Foundation for financial support.

' The classic work of Gurley and Shaw [8] sets forth the traditional view of financial intermediaries. Pringle [19] reformulates the traditional view within the context of modern capital theory.

2 Mossin [18], Gort [7] and Hamada [9] are among the first to recognize that, in the absence of capital-market imperfections, the value of any firm is invariant to the composition, or even the existence, of its security holdings.

19



20 The Journal of Finance

As a way of testing this perspective empirically, in Section III we estimate a regression model designed to explain the number of distinct issues of U.S. Treasury and federal-agency debt held in a time series of cross sections of large U.S. commercial banks. Across the five reporting dates employed in our study, the estimated pattern of diversification proves remarkably consistent. This sta- bility in pattern is difficult to explain by theories that concentrate only on the variance-reducing benefits of diversification. Apparently, the values of banking firms of different sizes are not invariant to the composition of their security portfolios. Our empirical findings suggest that the simulation studies of Evans and Archer [4] and others, which indicate that "near maximal benefits" of diversification are achieved by holding a mere handful of securities, neglect an important half of the problem. As explained in Section II of this paper, diversification costs and benefits, acting in concert like the blades of Marshall's scissors, determine each investor's optimal diversification.

We interpret the systematic pattern of diversification observed for large U.S. commercial banks as evidence that bank stockholders form a relatively uniform diversification clientele. For a firm, marginal benefits from diversification take the form of reductions in the cost of equity funds offered by its specific clientele of stockholders. To maximize the value of the firm, these benefits must be weighed against the explicit and implicit marginal costs of diversification. The optimal degree of diversification exceeds the point of "near maximal benefits" if, at that point, the (small) marginal benefits exceed the (smaller yet) marginal costs of diversification. Apparently, marginal diversification costs decline as bank size increases, but level off when total deposits reach $500 million. We infer that beyond this point, marginal diversification costs are independent of institution size. Presumably, very large banks use similarly cost-efficient practices (including use of computer hardware and software) to manage diversification. We attribute the more diverse holdings of dealer banks to their dealer departments' interest in minimizing stockouts. However, volume-related trading economies available specifically to dealer banks may reduce their marginal diversification costs below those of ordinary banks. This would further explain dealer banks' relatively more diversified observed holdings.

H. Costly Diversification and the Diversification Clientele

Financial institutions do in fact diversify-albeit partly in response to regulatory constraints-and in so doing, they incur substantial diversification costs.3. This observation prompts two questions: (i) Why do shareholders (who must ultimately bear the costs of diversification) acquire and continue to hold these institutions' stock, and (ii) Why would they ever permit the managers of institutions to exceed the minimum diversification requirements imposed by the regulatory authorities?

Reasons for Being Skeptical of Simulation Studies

These questions are especially intriguing in light of simulation studies initiated by Evans and Archer [4] indicating that diversification benefits are nearly

3Studies by Treynor and Mazuy [22], Sharpe [21], Jensen [11] and Friend, Blume and Crockett [6] suggest that these costs prevent many financial institutions from earning rates of return implied by the capital asset pricing model pioneered by Sharpe [20], Lintner [14], and Mossin [18].



Portfolio Diversification 21

exhausted by portfolios containing relatively few securities.4 These studies suggest that, for investors with even modest financial resources, the stock of financial institutions should be relatively less attractive than the stock of firms that avoid extensive diversification costs by engaging in specialized activities.5 But this apparent implication is sensitive to a number of implicit assumptions.

For instance, by relaxing the assumption that security returns are normally distributed, Fama [5] develops cases in which the number of securities required to "nearly exhaust" diversification benefits exceeds one hundred. In addition, while the simulation studies presume that all relative investments are diluted in the diversification process, some investors may choose to maintain a high con- centration of their wealth in the stock of a single institution. In this case, merely increasing the number of securities in their portfolios will not diminish the unsystematic risk associated with the concentrated investment.6

Highly concentrated investments could be motivated by nonpecuniary rewards even more than pecuniary ones. Major stockholders in financial institutions have privileged access to insider information and can undertake some insider activities. Effectively, the parameters of the ex ante distribution of the rate of return from investing in the institution may differ between major and minor stockholders. Major stockholders may derive special satisfaction from being "big wheels" in some community or from wielding a powerful influence over the operations of the particular institution.

Technically, numerical techniques used to generate proxies for the unobserv- able true values of ex ante-systematic and unsystematic risks lead to nonuniform and imperfect estimates. Nonuniformity implies that, as more and more securities are added to a portfolio, the path tracing out reductions in portfolio variance is erratic and does not necessarily bottom out smoothly at the low numbers indicated in the simulation studies. Imperfect parameter estimation implies that even these erratic paths are only estimates of the true (but unknown) path. Even if the estimated paths are unbiased, they indicate levels of diversification to which one can attach only 50-percent confidence that portfolio risk is not above specified levels.

Noting the existence of information risk develops a richer view of what diversification accomplishes. One round of diversification is required to reduce the estimated variance of the portfolio return, and a second round of diversification is required to increase the confidence that the actual portfolio variance is at or below an acceptable level. It is inconsistent to assume that an investor is averse to estimated risk but indifferent to the risk associated with the estimation process.7 A consistent model would specify the interaction between the level of estimated risk and the required degree of confidence and trace out a risk-reduction path that accounts for the risk of having to estimate unknown risk-return parameters. Along the new curve, the number of securities producing "near

'Using Markowitz [16] -efficient weights, Johnson and Shannon [12] demonstrate that near- maximal diversification gains can be achieved with even fewer securities.

5 This point is supported by the empirical observation that mutual funds attract a disproportionate share of their funds from investors with limited resources.

6This observation generalizes Mayers' [17] work on nonmarketable assets. 7Klein and Bawa [13] summarize and extend the relatively limited literature on portfolio decisions

with imperfect parameter estimates.




maximal" diversification is strictly greater (perhaps substantially greater) than that indicated in traditional simulation studies.

Costs and Benefits of Diversification

Debating the number of securities required to achieve near-maximal benefits of diversification would be pointless if homemade diversification were costless and perfectly substitutable for the firm-produced variety. However, given differences between odd-lot and round-lot trading fees, marginal diversification costs appear substantial for investors with modest resources. Now that commission rates are "negotiable," an analogous differential exists even for traders of large blocks of stock. In addition, all investors should be sensitive to the explicit and implicit costs (safekeeping, data-processing, and analysis costs) of administering portfolios containing large numbers of distinct securities.

These observations lead us to the premise that in the U.S. today most, if not all, investors face positive (and possibly U-shaped) marginal costs of diversification. We take as our minor premise that rational shareholders diversify their own portfolio holdings up to, but never beyond, the point where the marginal benefits equal the marginal costs of diversification. Taken together, these two propositions imply that most, if not all, rational shareholders cannot hold perfectly diversified portfolios.

This conclusion holds a fortiori if, because of information risk, homemade diversification substitutes imperfectly for the firm-produced variety. We note that, while either homemade or firm-produced diversification reduces the variance of shareholders' portfolio returns, only the firm-produced variety stabilizes the firm's internal cash flow. By smoothing this cash flow, firm-produced diversification might improve the reliability of parameter estimates and thus may produce a diversification benefit beyond merely reducing the estimated risk in the portfolios of shareholders. Moreover, shareholders may worry specifically about the extent to which an institution's level of unsystematic risk conditions the institution's regulated operations and/or its risk of ruin (as distinct from its impact on the variance of the return).8 Unsystematic risk in the return on an institution's asset portfolio makes its overall cash flow more uncertain, thereby increasing the threat of insolvency. A ceteris-paribus increase in unsystematic risk may require managers to shift funds from high-yield assets into low-yield ones (even into idle reserves), something that would reduce the institution's overall return. Such links between unsystematic risk and shareholder concern are reinforced by actions (or threat of actions) by regulatory authorities ranging from scolding, fines and penalties to direct interference with the operations of the institution. Under our broad interpretation, rational shareholders should favor ceteris-paribus reductions in a financial institution's unsystematic risk achieved by diversifying the institution's own portfolio.

Summary and Transition

To summarize the preceding arguments, we hypothesize that impediments exist that prevent some or all individual investors from economically achieving

8 Kim [14] examines the interaction of costly bankruptcy and mean-variance portfolio selection.




maximal benefits from diversification directly within their own portfolios. On the cost side, investors with limited financial resources are affected both by differences between odd-lot and round-lot trading fees9 and by asset indivisibilities. Moreover, even wealthy investors should be sensitive to administrative costs associated with selecting, evaluating, managing, and continually keeping track of a large number of securities. Finally, if homemade diversification bears inordi- nately high levels of information risk, some benefits of firm-produced diversification might not be reproducible by individual investors acting on their own.

Assuming that institutions can diversify more efficiently than most individuals (if only for reasons of scale), the stock of financial institutions is potentially of considerable value to investors whose own marginal diversification costs are high. On the other hand, no matter how effectively financial institutions manage their diversification costs, stock in these institutions should be relatively unattractive to investors who are able on their own to construct portfolios free of unsystematic risk. Such shareholders are asked to accept a smaller return in exchange for services of no direct benefit to them. In accordance with the "clientele" theory of stockholding (which associates particular types of investors with particular types of institutions), we argue that shareholders in financial institutions must feel that they derive appropriate benefits from these firms' otherwise "excessive" diversification. Only in this case, could the price of, and the return on, these institutions' stock depart from the values that would obtain if the stock were valued as in the capital asset pricing model solely on the basis of expected return and systematic risk.'0

III. Security Portfolio Diversification at Large U.S. Commercial Banks

Our theory suggests that focusing on the marginal costs and marginal benefits of institutional opportunities for diversification should help us to interpret differences in the number of securities held in real-world portfolios. Our empirical work focuses on diversification data for one class of financial institutions (large commercial banks) and for one class of securities (debt issues of the U.S. Treasury and Federal Agencies). The study uses semiannual call-report data for more than 800 of the nation's largest banks covering the two-year period from December of 1965 to December of 1967.

A Preliminary Look at the Data

Table 1 presents data on the mean and standard deviation of n, the number of issues of U.S. Government securities (distinct in some feature: coupon, maturity, call provision, etc.) held by banks in four size classes at each of five call dates:

9 The recent abolishment of the fixed-commission schedule for securities trading does not eliminate the likelihood of a competitively-determined odd-lot trading differential.

10 The notion of a more general asset pricing model in which the prices of at least some stocks depend on unsystematic as well as systematic risks is a logical extension of the work of Jacob [10], Brennan [2], and Elton, Gruber and Padberg [3] on imperfect diversification by individuals. The generalized model thus offers a direct explanation for empirical observations summarized by Jensen [11], which indicate that unsystematic risks influence security prices.




Table 1

Mean and Standard Deviation of the Number of Securities Held by Banks in Different Size Groups on Five Different Dates

December June December June December Deposit Class 1965 1966 1966 1967 1967

A-All Banks Over $1 billion

mean 51.89 50.69 49.14 51.17 53.06 standard deviation 38.41 39.81 39.63 37.57 37.26

$500 mil.-$1 bil. mean 31.10 30.81 31.57 31.69 33.95 standard deviation 23.73 26.14 26.40 25.45 26.73

Under $500 million mean 19.71 18.68 18.47 18.44 20.63 standard deviation 9.04 9.17 9.52 8.89 9.86


B-Non-Dealer Banks Only Over $1 billion

mean 21.47 18.71 21.06 22.12 23.94 standard deviation 14.48 12.07 12.14 12.95 11.19

$500 mil.-$1 bil. mean 18.82 17.15 16,91 17.76 19.61 standard deviation 8.72 9.54 8.29 7.19 8.51



December of 1965, and June and December of 1966 and 1967.1" Panel A of the Table reports figures for all banks, irrespective of dealer status. Since the mean value of n increases with deposit size, these figures provide no evidence that portfolio-scale economies are bounded.

However, once we remove dealer banks from the sample, a strikingly different picture emerges.12 Panel B of Table 1 shows that, although the mean value of n is slightly higher for banks with more than $1 billion in deposits, this mean value is more or less the same for non-dealer banks of quite-different sizes. Moreover, standard deviations become more homogeneous as well.

" Specifically, the. sample consists at each date of the 1,010 FDIC-insured commercial banks holding at least $5 million dollars in Treasury and Agency securities at each date, minus all members of this group whose Schedule B reports proved incomplete or failed validity checks. Because banks had not previously had to catalogue their holdings of individual securities, incomplete forms and invalid records became less common through time as respondents became familiar with the form.

Data for n represent a count of individual security issues with one notable exception: regular issues of Treasury Bills maturing in any given month were reported as a single issue.

12 Designation as a government-securities dealer was determined on the basis of listings in Standard & Poor's Securities Dealers of North America (New York: 1969 Edition).




A Cross-Section Regression Analysis

Recognizing potential distinctions between various classes of dealers, we define a national dealer as one that was trading regularly with the Federal Reserve Open Market Desk in New York"3 and we define a regional dealer as any other bank that designated itself as a dealer in government securities in Standard & Poor's Securities Dealers of North America (New York: 1969 edition). If we had sufficient a priori knowledge of these banks' specific operations, we would distin- guish further between broad and narrow regional dealerships. Presumably, public- relations benefits to claiming dealer status make our definition too inclusive. Our criterion includes a number of banks that make markets in only a narrow range of security issues.

Our regression experiments are variations on the following strategic equation:

n = [bo + bldN+ b2dR]- b3NW+ b4(D-L) - b5L + u. (1)

The last term in this equation, u, is an error term recording the effects of any and all omitted variables that influence a bank's choice of n. The b's are regression coefficients, and dN and dR are dummy variables that take on the value of unity for banks that are national and/or regional dealers respectively but are zero otherwise. Two measures of bank size are investigated: NW is net worth, and D - L is the amount of deposits not allocated to customer loans. We also include total loans, L, separately in (some versions of) the equations tested to investigate the viability of constraining its coefficient to equal the negative for D. The constraint would hold if loan demand constituted a prior claim on bank funds. But two further considerations suggest that the magnitude of the loan coefficient should exceed that of the deposit coefficient when portfolio size is an important factor: (a) presuming that the loan portfolio is less perfectly marketable, the impact on the allocation to the security portfolio would be harsher for an increase in L than for an equal decrease in D; and (b) unloaned funds might be more accurately described by (1 - r)D - L where r represents the bank's desired reserve ratio.

Our statement of equation (1) combines the first three terms within brackets to indicate that together they determine the effective intercept of an equation that is linear in our three proxies for opportunity costs: net worth, loans, and the amount of deposit funds not loaned back to customers.

For each date and size class, the equation is interpreted as follows: bo represents the minimal number of government and agency issues in the optimally diversified portfolio of commercial banks in our sample; bi + b2 represents the number of additional issues a national dealer needs to inventory; bo + b2 indicates the number of issues a regional dealer holds; b3, b4, and b5 state the number of additional issues held for each increase of $10 million in net worth, (D - L), and loans respectively. Finally, the error term u captures management or locational effects specific to a particular bank.

For the four deposit-size classes distinguished in Table 1, regression estimates are given in Table 2 for a model from which L is excluded and represented only

13 Bankers Trust, Chemical, First National City, First National of Chicago, Continental Illinois, Morgan, Harris Trust and Savings, and United California.




Table 2

Standard Error of

Date

and

Deposit-Size

Group

Intercept

dN

dR

NW

(D - L)

L

Estimate

R2

N

December,

1965

Deposits

under

$100

milion

17.83

-

1.79

-12.43

2.66

exc.

7.96

.053

456

(16.0)

(0.7)

(4.2)

(4.8)

(-2.3)

Deposits

under

$500

million

17.51

-

2.20

-4.36

1.30

exc.

8.85

.060

729

(34.5)

(1.6)

(4.4)

(5.8)

(-1.9)

Deposits

between

$500

mil-

25.47

-

21.65

0.10

-0.24

exc.

19.05

.257

48

lion

and $1

biHion

(2.1)

(3.8)

(0.0)

(0.6)

(0.3)

Deposits

over $1

billion

24.52

59.51

29.18

0.28

-0.13

exc.

21.97

.709

40

(3.6)

(5.3)

(3.7)

(0.5)

(0.8)

(0.7)

June,

1966 Deposits

under

$100

fiiiHion

17.00

-

.74

-15.81

3.12

exc.

7.81

.078

456

(15.6)

(0.3)

(5.4)

(5.7)

(-2.0)

Deposits

under

$500

milion

16.52

-

2.63

-3.28

1.06

exc.

8.93

.049

729

(32.2)

(1.9)

(3.3)

(4.7)

(-1.8)

Deposits

between

$500

mil-

27.78

-

26.02

-0.23

-0.34

exc.

21.96

.273

48

lion

and $1

biHion

(2.0)

(4.0)

(0.1)

(0.7)

(1.2)

Deposits

over $1

biHion

21.22

66.28

27.99

0.31

-0.13

exc.

19.72

.778

40

(3.5)

(6.6)

(4.0)

(0.7)

(0.8)

(0.4)

December,

1966

Deposits

under

$100

million

17.12

-

1.24

-15.87

3.15

exc.

8.08

.089

496

(16.0)

(0.5)

(6.0)

(6.3)

(-2.4)

Deposits

under

$500

milion

16.35

-

2.88

-3.99

1.19

exc.

9.18

.052

795

(32.3)

(2.1)

(4.2)

(5.4)

(-1.6)

Deposits

between

$500

mil-

22.45

-

28.85

-0.43

-0.11

exc.

21.46

.317

52

lion

and $1

biHion

(1.6)

(4.7)

(0.2)

(0.2)

(0.8)

Deposits

over $1

biHion

20.83

65.53

21.00

0.17

-0.04

exc.

20.49

.743

41

(3.3)

(6.5)

(2.9)

(0.5)

(0.3)

(-0.3)

June,

1967 Deposits

under

$100

milion

17.86

-

-0.12

-15.96

2.82

exc.

7.80

.086

496

(17.3)

(0.0)

(6.2)

(5.8)

(-2.5)

Deposits

under

$500

milion

16.48

-

2.19

-3.44

1.05

exc.

8.67

.045

795

(34.4)

(1.7)

(3.9)

(5.0)

(-1.5)




Deposits

between

$500

mil-

22.77

-

26.05

-0.70

-0.03

exc.

20.77

.286

52

lion

and $1

biHion

(1.7)

(4.4)

(0.3)

(0.1)

(0.7)

Deposits

over $1

billion

21.94

61.30

23.47

0.07

-0.02

exc.

19.72

.742

41

(3.6)

(6.3)

(3.4)

(0.2)

(0.1)

(-0.3)

December,

1967

Deposits

under

$100

million

19.54

-

-0.7

-16.54

2.93

exc.

8.35

.087

521

(18.7)

(0.3)

(6.4)

(6.2)

(-1.6)

Deposits

under

$500

milion

18.32

-

2.40

-5.37

1.38

exc.

9.45

.064

820

(36.4)

(1.7)

(5.4)

(6.5)

(-1.3)

Deposits

between

$500

mil-

22.32

-

27.67

0.38

-0.15

exc.

22.68

.281

52

lion

and $

biHion

(1.5)

(4.3)

(0.1)

(0.3)

(0.8)

Deposits

over $1

bilion

23.84

50.93

24.88

0.44

-0.10

exc.

20.76

.707

41

(3.8)

(4.8)

(3.4)

(1.1)

(0.9)

(0.0)

Note:

Figures in

parentheses

represent

values of

the t

statistic

for

the

coefficients

immediately

above

them;

exc.

means

that

the

variable

was

excluded

from

the

regression

being

reported;

NW, D,

and L

are all

measured in

ten

millions of

dollars.




by a column of t-statistics. In general, coefficient estimates accord with the costs- and-benefits interpretation underlying the model:

1. The coefficients of NW and (D - L) decline in magnitude as bank size increases, with the magnitude of the NW coefficient nearly always in excess of that for (D - L). For banks with $500 million or more in deposits, the coefficients often reverse signs and are never significantly different from zero.

2. The intercepts for all equations are consistent with our hypothesis that a high degree of diversification is not necessarily excessive for banks.

3. The dealer-status variables behave as expected, except that only in Decem- ber, 1966 do dealer banks with less than $500 million in deposits hold a significantly greater variety of securities than nondealer banks of similar size. We attribute this finding to difficulties in identifying just which of the smaller banks claiming dealer status accept any real commitment to make markets."4

The coefficient estimates in Table 2 suggest that iational dealers inventory between 100 and 115 (bo + bi + b2) different issues, while large regional dealer banks generally inventory between 40 and 48 (bo + b2) different issues.

4. For the smallest-size class at four of tho five sample dates, the magnitude of the L coefficient significantly exceeds that of the D coefficient. But the constrained model proves superior for the other three groupings. Table 3 estimates the alternative model for the smaller banks. Including L reduces the NW coefficient substantially, but other coefficients are hardly disturbed at all.

5. While estimated intercepts are larger for larger banks, the large-bank coefficients also show much higher standard errors. Test statistics to be reported in Table 4 establish that these coefficients are not significantly different from the values shown by banks in the smaller deposit-size groups.

Supplementary Estimates and Tests

Table 4 presents weighted least-squares estimates of Table 2 equations fitted at each date to the sample constructed by pooling the banks from every deposit- size class. The Table also gives t-statistics summarizing the outcomes of tests of ancillary hypotheses concerning differences in the slope and intercept values that apply to "smaller" and larger banks."5

Weighted-least-squares (WLS) estimates are employed because the standard errors of estimate reported in Tables 2 and 3 prove significantly larger for larger banks. In these circumstances, standard errors of the ordinary-least-squares (OLS) coefficient estimates derived from the pooled sample would be biased

14 Separate regressions of the number of Treasury-bill issues, the number of Agency issues (so- called "FANGS": Federal Agencies, Not Guaranteed), and the number of non-bill Treasury issues on these same variables suggest that small dealer banks do make markets in Treasury bills and often also make markets in some agency securities.

15 We use quotation marks to remind the reader that even the smallest bank in our sample is large relative to the universe of U.S. banks.




Table 3 Estimates of Alternative Model for Banks with 1967 Deposits under $100 Million

Standard Error of

Date Intercept dR NW (D - L) L Estimate R2 N

December, 1965 18.59 2.41 -6.93 2.69 -1.18 7.92 .065 456 (16.1) (0.9) (1.8) (4.8) (2.3)

June, 1966 17.65 1.27 -11.16 3.14 -1.00 7.78 .086 456 (15.5) (0.5) (3.0) (5.7) (2.0)

December, 1966 17.78 1.51 -10.37 3.21 -1.14 8.05 .099 496 (16.2) (0.6) (2.9) (6.4) (2.4)

June, 1967 18.53 0.15 -10.45 2.88 -1.14 7.76 .097 496 (17.4) (0.1) (3.1) (5.9) (2.51)

December, 1967 19.94 -.68 -12.81 2.97 -0.73 8.34 .091 521 (18.6) (0.3) (3.7) (6.3) (1.6)

Note: Figures in parentheses represent values of the t statistic for the coefficients immediately above them.

downward. However, the OLS coefficient estimates themselves would be unbiased. Although the OLS estimates are not reported here, in this instance they prove almost identical to the corresponding WLS estimates.

The correction employed here to generate "weighted" regression estimates was to deflate, for each of the last three deposit-size groups distinguished in Tables 2 and 3, all variables (including the intercepts and intercept dummy variables) by the ratio of the standard error of estimate for the group to the standard error of estimate recorded for the less-than-$500 million group."6

The dummy variables used in these tests are defined as follows:

dloo- : equals unity for banks with deposits less than $100 million and is zero otherwise;

d5oo- : equals unity for banks with deposits less than $500 million and is zero otherwise;

d5w0+ : equals unity for banks whose deposits lie between $500 million and $1 billion and is zero otherwise;

dlooo+ : equals unity for banks with deposits in excess of $1 billion and is zero otherwise.

dR+ = [ 1- d5oo_ I* [ dR- dN] dR = (d5oo_) [dR- dN].

Table 4 reaffirms the findings of Table 2 with respect to the relative magnitudes of dealer inventories for banks serving different markets and with respect to the signs and magnitudes of b3 and b4. The coefficient of net worth proves negative and that of unloaned deposit funds (D - L) proves positive for banks with less than $500 million in deposits, but these coefficients are not significantly different from zero for larger banks. Most importantly, the t-values for d500+ and d1000+ establish that the larger estimates of bo recorded in Table 2 for the two categories of largest banks are not significantly different from the value of bo at smaller banks.

16 See Belsley [1].




Table 4

Weighted-Least-Squares

Estimates of

(and

Supplementary

Tests

Related to)

n = bo +

bldN +

6fd- +

b2dk +

b3(dsoo_)NW+

b4(d5oo-)(D -

L) +

b5d5oo+ +

b6do000+ + u

at

Five

Successive

Call-Report

Dates,

1965-1967

Call-Report

Date

bo

b1

b2

b2

b3

b4

bs

b6

NW

(D - L)

S.e.e.

N

December,

1965

17.60

88.86

29.66

1.40

-4.36

1.29

-.36

1.54

exc.

exc.

8.70

817

(35.4)

(9.4)

(7.2)

(1.1)

(4.5)

(5.8)

(0.1)

(0.3)

(0.3)

(-0.4)

June,

1966

16.62

96.66

30.97

1.90

-3.28

1.04

.24

-1.16

exc.

exc.

8.02

817

(32.9)

(10.1)

(7.4)

(1.4)

(3.3)

(4.6)

(0.1)

(0.2)

(0.6)

(-0.7)

December,

1966

16.41

93.97

29.61

2.28

-4.12

1.20

1.04

-.38

exc.

exc.

9.08

888

(32.8)

(9.56)

(7.0)

(1.6)

(4.4)

(5.5)

(0.3)

(0.1)

(0.6)

(-0.4)

June,

1967

16.53

89.20

28.94

1.51

-3.57

1.07

.98

2.26

exc.

exc.

8.57

888

(35.0)

(9.6)

(7.3)

(1.2)

(4.1)

(5.1)

(0.3)

(0.5)

(0.2)

(0.0)

December,

1967

18.42

83.75

27.92

2.03

-5.27

1.34

1.97

3.95

exc.

exc.

9.40

913

(36.9)

(8.2)

(6.4)

(1.4)

(5.3)

(6.4)

(0.6)

(0.8)

(0.9)

(-0.6)

Note:

Same as

Table 3,

with

the

additional

point

that

the

t-values of

the

excluded

variables

refer to a

regression in

which

d5so+

and

d1ooo+

are

deleted

and

NW

and (D -

L)

are

added

simultaneously.




Measuring the Rate of Decline of Diversification Pressures

Table 5 utilizes slope dummies to let b3 and b4 vary with size over the range of banks whose deposits do not exceed $500 million. These estimates employ two dummy variables not defined previously:

1. do00/200, which equals unity for any bank whose deposits lie between $100 and $200 million, and is zero otherwise;

2. d200/500, which equals unity for banks with deposits in the range between $200 and $500 million, and is zero otherwise.

We also include a column in the variable (d0oo0 . L). This column reports the results of a test of the auxiliary hypothesis that loan and securities portfolio- allocation decisions are not completely separable at banks whose deposits are less than $100 million. Since the coefficient of this variable is consistently negative and its t-value flirts with significance, incomplete separability may exist at banks in this size class. However, introducing this term into the equations has virtually no effect on the regression coefficients of any variable except that of (d0ooX NW), whose magnitude and significance are reduced.

All equations continue to affirm the hypothesized tendency for marginal diversification benefits to decline with size. Moreover, differences between three b3 coefficients and between the three b4 estimates always lie in the hypothesized direction, but with the exception of the difference between b4' and b4", they show insignificant t-statistics.

III. Summary and Implications

Although there is no recognized and widely promulgated rule of thumb governing these decisions, our estimates indicate that for bank security subportfolios, diversification increases modestly with bank size up to approximately the $500- million deposit level. Beyond that point, we observe that: 1) banks (other than dealer banks) hold approximately 20 distinct government issues; 2) banks that advertise themselves as regional dealers in government securities inventory about 50 different issues, and 3) recognized national dealer banks typically hold between 100 and 110 issues (a number that is about 80 percent of the issues outstanding during the sample periods).17

Although our empirical estimates validate our view that marginal diversification costs and benefits act in concert, our regression equation is tailored to U.S. commercial-banking operations. Moreover, our results focus on opportunity costs specific to a particular subportofolio of banks' marketable assets. To assess diversification costs and benefits at other financial institutions or in other countries, it will be necessary to devise proxy variables to represent the marginal

17 These findings have implications for federal debt management. They suggest that the Treasury and Federal agencies would be wise to reduce the number of distinct securities existing in the market at any one time. The Treasury ought to expand the domain of the Federal Financing Bank designated in 1975 as a central financing agent for the smaller federal credit agencies and it ought more frequently to reopen outstanding issues and packages of issues instead of "tailoring" the terms of new issues to supposed gaps in the current market. Both policies would make life easier for dealers and should, through competition, reduce investors' transactions costs and the Treasury's own costs of administering the national debt.




Table 5

Weighted-Least-Squares

Estimates of

Two

Alternative

Models at

Successive

Call-Report

Dates,

1965-1967

n = bo +

bldN +

b2dR +

b2ddR +

(b3d+100-b3,d1O/200 +

b'd2oo/5oo)NW+

(b4dioo- +

bMdioo2o +

b4'd2oo/w1o)(D -

L) + u

Call-Report

Date

bo

bi

b2

b2

b3

b 3

b 3

b4

b4

b4"

(d1oo-L)

S.e.e.

N

December,

1965

17.14

90.86

30.22

1.39

-8.04

-5.46

-2.43

2.24

1.43

0.94

exc.

8.67

817

(18.2)

(11.1)

(94)

(1.0)

(2.9)

(3.0)

(1.9)

(4.0)

(3.7)

(3.3)

(-1.9)

June,

1966

16.13

95.99

31.18

1.95

-10.16

-4.80

-0.46

2.56

1.28

0.49

exc.

8.75

817

(17.0)

(11.6)

(9.6)

(1.5)

(3.6)

(2.6)

(0.4)

(4.5)

(3.3)

(1.7)

(-1.7)

December,

1966

15.63

94.37

30.64

2.30

-10.93

-4.69

-1.31

2.94

1.26

0.67

exc.

8.99

888

(16.8)

(11.1)

(9.2)

(1.7)

(4.4)

(2.6)

(1.1)

(5.7)

(3.2)

(2.4)

(-1.8)

June,

1967

16.06

91.94

30.41

1.55

-10.14

-4.35

-1.08

2.62

1.11

0.58

exc.

8.50

888

(18.3)

(11.5)

(9.7)

(1.2)

(4.3)

(2.5)

(0.9)

(5.3)

(3.0)

(2.2)

(-1.8)

December,

1967

18.10

88.03

30.53

2.02

-11.69

-5.53

-2.66

2.71

1.24

0.87

exc.

9.34

913

(19.9)

(10.0)

(8.8)

(1.4)

(4.6)

(2.9)

(2.0)

(5.6)

(3.3)

(3.2)

(-1.4)

Note:

Same as

Table 2.




costs and benefits appropriate to the particular markets and contracts in which these other institutions deal.

On the theoretical side, our work underscores the need for researching tradeoffs between information risk and conventionally estimated elements of portfolio risk and return. Recognizing that firms' ex ante risks and returns are not truly knowable provides a solid motivation for firms to endeavor to diversify their internal operations. In standard models of asset pricing, firm-produced diversification has no real justification.

REFERENCES

1. Belsley, David A. "Specification With Deflated Variables and Specious Spurious Correlation," Econometrica, 40 (September 1972), pp. 923-28.

2. Brennan, M. J. "The Optimal Number of Securities in a Risky Asset Portfolio When There Are Fixed Costs of Transacting: Theory and Some Empirical Results," Journal of Financial and Quantitative Analysis (September 1975), pp. 483-96.

3. Elton, Edwin J., Martin J. Gruber, and Manfred W. Padberg. "Simple Cirteria for Optimal Portfolio Selection," Journal of Finance, 31 (December 1976), pp. 1341-1357.

4. Evans, John L., and Stephen H. Archer. "Diversification and the Reduction of Dispersion: An Empirical Analysis," Journal of Finance, 23 (December 1968), pp. 761-767.

5. Fama, Eugene F. "Portfolio Analysis in a Stable Paretian Market," Management Science, (January 1965), pp. 404-419.

6. Friend, I.,.M. Blume, and J. Crockett. Mutual Funds and Other Institutional Investors: A New Perspective, New York: McGraw-Hill, 1970.

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11. Jensen, Michael C. "The Foundations and Current State of Capital Market Theory," in Studies in the Theory of Capital Markets, ed. Michael C. Jensen, New York: Praeger, 1972.

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13. Johnson, K. H., and D. S. Shannon. "A Note on Diversification and the Reduction of Dispersion," Journal of Financial Economics (1974), pp. 365-372.

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15. Klein, Roger W., and Vijay S. Bawa, "The Effect of Limited Information and Estimation Risk on Optimal Portfolio Diversification," Journal of Financial Economics, 5 (1977), pp. 89-111.

16. Lintner, John. "The Valuation of Risk Assets and the Selection of Risky Investment in Stock Portfolios and Capital Budgets," Review of Economics and Statistics, XLVII (February 1965), pp. 13-37.

17. __. "Security Prices, Risk, and Maximal Gains From Diversification," Journal of Finance, 20 (December 1965), pp. 587-615.

18. Markowitz, Harry M. "Portfolio Selection," Journal of Finance, 7 (March 1952), pp. 77-91. 19. Mayers, David. "Nonmarketable Assets and Capital Market Equilibrium Under Uncertainty," in

Studies in the Theory of Capital Markets, Michael C. Jensen (ed.), New York: Praeger Publishers, 1972.

20. Mossin, Jan. "Equilibrium in a Capital Asset Market," Econometrica, 34 (October 1966), pp. 768-783.




21. Myers, Stewart C., "Procedures for Capital Budgeting under Uncertainty," Industrial Manage- ment Review, 9 (Spring 1968) pp. 1-15.

22. Pringle, John J. "The Capital Decision in Commercial Banks," Journal of Finance, 29 (June 1974), pp. 779-795.

23. Sharpe, William F. "Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk," Journal of Finance, 19 (September 1964), pp. 425-442.

24. . "Mutual Fund Performance," Journal of Business, Supplement on Security Prices, (January 1966), pp. 119-138.

25. Treynor, J. L., and K. K. Mazuy. "Can Mutual Funds Outguess the Market?" Harvard Business Review, 44 (July-August 1966), pp. 131-136.



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