This paper shows that large bank holding companies (BHCs) are better diversified than small BHCs based on market measures of diversification. We find, however, that better diversification does not translate into reductions in risk. The risk-reducing potential of diversification at large BHCs is offset by their lower capital ratios and larger C&I loan portfolios. Our results suggest that diversification may provide an important motive for consolidation by allowing BHCs to pursue riskier lending while operating with greater leverage.
A fundamental implication of modern portfolio theory is that diversification reduces the return variance of a portfolio of financial assets. Applied to banking, portfolio theory suggests that diversification can potentially reduce the probability of failure. Diversification across borrower projects may also reduce the costs of providing a bank with the appropriate incentives to monitor borrowers and make payments to depositors (Diamond 1984).
The banking literature tends to presume that diversification and size go hand in hand. This paper demonstrates empirically that this presumption is valid. We measure the diversification of a sample of bank holding companies (BHCs) using stock market data and quantify a strong, positive effect of size on BHC diversification. We also show how large bank holding companies use their diversification advantage. Large BHCs, while better diversified than small BHCs, have historically been no less risky. Large BHCs have used their diversification advantage to operate with lower capital ratios and pursue riskier activities.
Our findings with respect to capital are consistent with Liang and Rhoades (1991), who find that capital ratios decline with balance sheet measures of asset diversification, and with McAllister and McManus (1993), who show that large banks realize a cost advantage over small banks because of their ability to operate with less capital. Our results regarding the pursuit of riskier activities are consistent with Akhavein, Berger, and Humphrey (1997), who show that the profit efficiency associated with large-bank mergers is at least in part attributable to a shift in outputs from low-risk securities to higher-risk loans.
Our results have policy implications particularly relevant today, as banking consolidation accelerates following the passage of the 1994 Reigle-Neal Interstate Banking and Branching Efficiency Act. Consolidation can enhance diversification, but the resulting change in risk will depend on the extent to which consolidation is accompanied by changes in banks' activities. In the past, large BHCs used their diversification advantage to increase risky lending and to operate with lower capital ratios but not to operate at lower levels of overall risk. If this pattern is indicative of the behavior of banks involved in today's merger wave, then we should not expect consolidation to reduce bank risk.
If the riskier activities pursued by large banks are profit enhancing on average, however, then growth via mergers should increase profits. This is consistent with Akhavein, Berger, and Humphrey, discussed above, and with Benston, Hunter, and Wall (1995), who model the price bid by acquiring banks in takeover deals and conclude that acquiring banks "seek earnings diversification in an effort to generate higher levels of cash flow for the same levels of total risk." Nevertheless, Boyd and Runkle (1993) find that size is not positively correlated with profits at BHCs.
We use a measure of BHC diversification derived from a decomposition of stock return variance into explained and unexplained variance, labeled "systematic risk" and "firm-specific risk." Portfolio theory tells us that a BHC's diversification will decrease its firm-specific risk but leave its systematic risk unaffected; hence, we are primarily interested in the relationship between BHC size and firm-specific risk. The problem is that diversification is not the only factor affecting a BHC's firm-specific risk. The riskiness of the individual components of a BHC's asset, liability, and off-balance sheet positions affects its stock return variance, as does the BHC's leverage. Moreover, both leverage and the riskiness of individual portfolio components are likely to be related to BHC size.
We address this problem in two ways. First, we create a diversification index by scaling systematic risk by stock return variance. At BHCs with a high diversification index (a high return-generating model [R.sup.2]), the fraction of risk stemming from idiosyncratic factors is small. This approach allows us to demonstrate a positive relationship between BHC size and diversification without explicitly controlling for differences in the portfolio components of large and small BHCs.
Our second approach is to estimate the conditional relationship between firm-specific risk and BHC size by regressing firm-specific risk on size and a vector of portfolio components related to both size and risk. The [R.sup.2] approach has the advantage of simplicity, but the regression approach allows us to quantify the elasticity of firm-specific risk with respect to BHC size and thus gauge the economic importance of size-related diversification. Both approaches indicate a strong positive relationship between diversification and BHC size.
To our knowledge, we are the first to use a return-generating model [R.sup.2] to measure the relationship between BHC size and diversification; however, we are not the first to use the [R.sup.2] as a diversification measure applied more generally. Barnea and Logue (1973) use the [R.sup.2] from a simple market model to measure the industrial diversification of the conglomerate corporation. Roll (1988) explores [R.sup.2] as a measure of diversification for publicly traded firms in general.
While the banking literature has overlooked [R.sup.2] as a measure of diversification, both risk and diversification have been explored previously, and some papers apply a risk decomposition similar to ours. For instance, Templeton and Severiens (1992) show that diversification into nonbank activities has no effect on systematic risk but has a negative effect on stock return variance. Rosenberg and Perry (1981) build a large empirical model for the purpose of forecasting both systematic and firm-specific risk at BHCs. Because their model incorporates dozens of independent variables (including lagged values of the dependent variables), it is difficult to draw a comparison between their results and ours. Size is not a focus of their analysis, nor is BHC diversification, but they report a negative coefficient on size in their firm-specific risk regression and an insignificant coefficient on size in their systematic risk regression, consistent with our results.
In the next section, we use the [R.sup.2] approach to demonstrate a strong positive relationship between BHC size and diversification. In section 2, we use the regression approach to confirm our findings and quantify the importance of size-related diversification in reducing firm-specific risk. We also describe how large BHCs use their diversification advantage. Section 3 concludes.
1. [R.sup.2] AS A DIVERSIFICATION INDEX
The simplest kind of return-generating model is a regression relating a company's stock return to the return on a stock market index:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
In equation (1), the market index serves as a proxy for systematic factors common to the returns on most stocks. Since the residual vector is uncorrelated with the vector of market returns, the following variance decomposition holds:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] represents the estimated return variability stemming from systematic factors; [Sigma].sup.2]([Epsilon]) represents the estimated return variability specific to the given BHC. Following conventional terminology, we refer to the two risk components as systematic risk and firm-specific risk, respectively.
For the purposes of this analysis, we estimate a richer market model, including additional factors that commonly affect BHC stock returns but are not adequately captured by the stock market index. Our market model is defined as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Yield is the change in the yield on a three-month Treasury Bill. Term is the change in the spread between thirty-year and three-month Treasury rates. Credit quality spread is the change in the spread between rates on Moody's Baa-rated corporate bonds and thirty-year Treasury Bonds.(1)
Because equation (3) may still exclude some relevant systematic factors, we also estimate a second return-generating model. This model differs in concept from the market model. Rather than estimating a regression based on a set of economically interpretable independent variables, we apply factor analysis to our sample of BHC stock returns and endogenously derive a set of five vectors whose linear combination best explains the returns on our sample of stocks. Though these five vectors are not interpretable economically, they can be considered systematic factors common to the returns on the BHCs in our sample. The factor analysis approach has the advantage that systematic risk is not constrained to be a function of observable economic variables. Consequently, this alternative approach provides a check on the robustness of results derived from our market model.(2)
One advantage of the factor analysis approach is that risks systematic to banks, including regulatory risks such as changes in capital requirements or deposit insurance premia, contribute to the systematic component of risk, whereas in the market model such risks would likely be absorbed by the firm-specific component. On the other hand, if most BHCs in our sample have a common risk, such as large exposure to problems in the commercial real estate sector, a BHC with that exposure may appear better diversified than others when using the factor analysis approach.
We estimate both return-generating models using data from the Center for Research in Securities Prices (CRSP). We identified over 150 publicly traded BHCs by referring to the 1985 Bank Compustat database. Our analysis is based on those BHCs that traded for at least thirty weeks in a given calendar year between 1980 and 1993 and for which we could retrieve both CRSP return data and data from BHC consolidated financial statements (the Y-9C Reports) describing BHC characteristics.(3) Our sample size ranges from 81 in 1993 to 134 in 1986 (see Table 1). This variability arises because several of the BHCs in our sample did not have traded equity in every year between 1980 and 1993. In the case of mergers, we dropped acquired companies from the sample after the date of acquisition. Acquirers remain in the sample.
TABLE 1 Summary Statistics for BHC Returns and Return-Generating Model [R.sup.2]s Weekly Returns Median Adjusted [R.sup.2] Standard Multifactor Factor Analysis N Mean(a) Deviation(b) Market Model Model (1) (2) (3) (4) (5) 1980 118 0.35% 3.49% 42.8% 1981 118 0.41% 3.14% 29.1% 1982 119 0.29% 3.75% 34.7% 1983 129 0.62% 3.31% 6.6% 26.0% 1984 131 0.25% 2.96% 10.9% 30.1% 1985 132 0.69% 3.28% 8.8% 28.2% 1986 134 0.11% 4.10% 20.0% 38.6% 1987 130 -0.36% 4.90% 39.9% 50.8% 1988 120 0.17% 3.90% 10.9% 29.0% 1989 112 0.28% 3.70% 9.5% 26.5% 1990 105 -0.85% 5.54% 18.5% 42.5% 1991 98 0.88% 5.52% 21.8% 38.1% 1992 89 0.74% 4.12% 5.4% 34.8% 1993 81 0.06% 3.62% 3.2% 40.7%
(a) Annual means, averaged over the BHCs in our sample.
(b) Annual standard deviations, averaged over the BHCs in our sample.
We constructed weekly (Friday-to-Friday) BHC stock returns using daily CRSP return data.(4) In the market model, [R.sub.mt] is measured using the weekly return on an equally weighted portfolio of stocks trading on the NYSE or AMEX.(5) Yield, term, and credit quality spread are each measured on a Friday-to-Friday basis as well. We estimate both return-generating models by year because the estimated parameters may change over time.(6)
Columns 2 and 3 of Table 1 report return summary statistics by year. The lowest mean weekly return of -0.85 percent occurred in 1990, amidst growing concern regarding bank asset quality. The mean weekly return for 1987, the year of the stock market "crash," is also low, at -0.36 percent. The highest mean weekly return of 0.88 percent occurred in 1991, as the economy pulled out of its recent recession. Return standard deviations tend to rise over most of the sample period, illustrating an increasing trend in overall bank risk.(7) Table 1 also presents the median [R.sup.2] for each yearly sample (columns 4 and 5).(8) Median market model [R.sup.2]s range from 3.2 percent in 1993 to 39.9 percent in 1987. A relatively high median [R.sup.2] is observed in 1987 because the "crash" of October 1987 resulted in a large degree of explained variance (systematic risk) for most stocks. Median [R.sup.2]s from the factor analysis model range from 26.0 percent in 1983 to 50.8 percent in 1987.
We attribute the low [R.sup.2]s from the market model in 1992 and 1993 (5.4 percent and 3.2 percent, respectively) to changes in the regulatory environment, including full implementation of risk-based capital standards and increases in deposit insurance premia. These events represent risks particular to banks; that is, risks that will not be captured by the systematic factors underlying the market model. Note that the [R.sup.2] derived using factor analysis remains high in 1992 and 1993, since it reflects systematic factors common to the BHCs in our sample. In general, the factor analysis approach results in higher [R.sup.2]s and greater stability of [R.sup.2]s over time.
Table 2 reports the correlation between the log of asset size and the [R.sup.2] from each of the two return-generating models outlined above.(9) Since we look only at publicly traded BHCs, our sample asset size distribution is not fully representative of all BHCs. It does provide ample size variation, however. In 1993, the asset sizes of the BHCs in our sample ranged from $340 million to $214 billion, with a median of $10 billion. Taken as a group, these BHCs held close to half of all banking assets in the United States. The correlation coefficients in columns 1 and 2 of Table 2 are positive and statistically significant for almost every year in our sample period, suggesting that the relationship between BHC size and diversification is both strong and robust.(10)
TABLE 2 Correlation of BHC Size with Adjusted [R.sup.2] and with Stock Return Variance(a) Multifactor Market Factor Analysis Model [R.sup.2] Model [R.sup.2] Stock Return Variance (1) (2) (3) 1980 0.44(**) 0.20(*) 1981 0.61(**) 0.18 1982 0.42(**) 0.45(**) 1983 0.60(**) 0.55(**) 0.24(**) 1984 0.57(**) 0.59(**) 0.45(**) 1985 0.57(**) 0.46(**) -0.01 1986 0.62(**) 0.62(**) 0.03 1987 0.30(**) 0.44(**) 0.04 1988 0.17 0.42(**) -0.07 1989 0.63(**) 0.54(**) -0.13 1990 0.33(**) 0.50(**) -0.03 1991 0.45(**) 0.51(**) -0.03 1992 0.29(**) 0.65(**) -0.30(**) 1993 0.01 0.68(**) -0.35(**)
(a) The Person correlation is computed using the log of total assets as of the end of the prior year and [R.sup.2] or total stock return variance over the current year. Values marked (**) are statistically significant at the 1 percent level; those market (*) are significant at the 5 percent level.
Some interesting differences emerge when comparing the correlation coefficients based op the market model [R.sup.2] with those based on the factor analysis [R.sup.2]. When we use the market model to calculate [R.sup.2], correlation coefficients for 1988 and 1993 are not significantly different from zero. When we use factor analysis to calculate [R.sup.2], however, 19&8 and 1993 correlation coefficients rise to magnitudes comparable to those of the other years in the sample period and are significant at the 1 percent level. Again, we attribute differences in results derived from the alternative return-generating models to events that had systematic effects on BHC stock returns but are not reflected in our multifactor model.(11) Despite the robust relationship between size and diversification, column 3 of Table 2 shows little evidence of a negative relationship between size and stock return variance. Correlation coefficients are generally insignificant, with the exception of the early 1980s and 1992-93. The positive coefficients in the early 1980s likely reflect problems related to LDC lending on the part of the largest BHCs. The negative coefficients in 1992 and 1993 are discussed in the next section. Overall, the correlation coefficients in column 3 suggest that large BHCs have not used their superior diversification to reduce risk.
2. A CLOSER LOOK AT SIZE-RELATED DIVERSIFICATION
This section quantifies the relationship between size and firm-specific risk, conditional on portfolio components related to both size and risk, and explores how BHCs use their diversification advantage. We also discuss the change in the size/risk relationship in recent years.
We estimate the following regression of firm-specific risk on BHC assets and a set of portfolio characteristics:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where E/A equals the BHC's equity capital-asset ratio; [Gamma] is a kx1 vector of parameters; and [Zeta].sub.t-1,i] is a vector of portfolio characteristics, dated as of the beginning of the period over which the pooled time series/cross-section data from 1987 to 1993 and include a set of time fixed-effects to control for changes in risk common to all BHC stocks in our sample.(13)
We are particularly interested in [Beta.sub.1], which measures the elasticity of firm-specific risk with respect to size. To the extent that [Zeta] controls fully for differences in the risks of individual portfolio components, [Beta.sub.1] quantifies the effect of size-related diversification. Our [Zeta] vector includes variables (described below) measuring each BHC's asset composition, liability composition, geographic dispersion, and off-balance sheet positions. Since some of these variables proxy for certain aspects of BHC diversification, [Beta.sub.1] may actually understate the economic importance of size-related diversification.
Variables in [Zeta]
Asset Composition. We measure asset composition using the ratio of commercial and industrial (C&I) loans to assets, real estate loans to assets, consumer loans to assets, agricultural loans to assets and trading-account-assets, to assets. We also include an index of loan concentration to control for the dispersion in lending across real estate loans, C&I loans, consumer loans, agricultural loans and other loans. Our index is modeled after the Herfindahl-Hirschman index (HHI), commonly used in analyses of market concentration for antitrust purposes. As applied to the case at hand, the HHI equals the sum of the squared share of each loan category relative to total loans. Increases in this index represent increases in specialization in a given loan category.
Liability Composition. We include three measures of liability composition: the ratio of total deposits to total assets (measuring the contribution of the banking subsidiaries to the total business of the BHC), the ratio of non-interest bearing deposits to total deposits (providing a crude description of the funding of the bank portion of the holding company), and the ratio of foreign deposits to total deposits (measuring reliance on funding sources outside the United States).(14)
Geographic Dispersion. We also differentiate BHCs operating broadly throughout the nation from those operating only within one region by including an indicator variable equal to one for BHCs with commercial bank subsidiaries located in more than one census region. While the secondary loan market permits BHCs to hold loans originated in many regions, BHCs operating more widely throughout the country may have increased protection against regional downturns.(15)
Off-Balance Sheet Activities. Two variables are included to measure each BHC's use of derivative instruments: (1) the ratio of the notional principal on interest rate swaps to total assets; and (2) the ratio of the notional principal on foreign exchange futures to total assets. We use the notional principal amounts of these derivatives to reflect the scale of derivatives activities, while acknowledging that they do not represent either the marked-to-market value or the risks associated with the contracts. No better measures of derivatives activities were available throughout the sample period.(16)
We include the ratio of noninterest income to net interest income as a measure of each BHC's reliance on off-balance sheet activities more generally. Boyd and Gertler (1994) show that the ratio of noninterest income to net interest income may be interpreted as the ratio of the present value of the BHC's off-balance sheet contracts to the present value of its on-balance sheet assets. This interpretation holds under two assumptions: (1) the average returns to off- and on-balance sheet assets are equal; and (2) noninterest expenses are allocated to off- and on-balance sheet assets in proportion to their value.
Capital. Since a given fluctuation in asset value translates into larger variation in the value of equity at more highly leveraged firms, we also control for each BHC's equity capital-asset ratio.(17)
Trading Frequency. We recognize that the variables in [Zeta] may not fully control for portfolio components correlated with both BHC size and stock return variance. After estimating equation (4) as described above, we try adding a "catch-all" variable presumably correlated with the underlying variances of BHC assets, liabilities, and off-balance sheet positions. This variable, turnover, measures the frequency with which each BHC's stock is traded. It is defined as total trading volume divided by the average shares outstanding over the year in which stock return variability is measured and is meant to capture the rate of arrival of new information about the economic value of the stock.(18)
Table 3 contains simple summary statistics for all of the independent variables included in equation (4), along with the correlation between each variable and the log of total assets. As shown, large BHCs engage more heavily in C&I lending, hold more assets in the trading account, hold more foreign deposits, and hold more derivative instruments than small BHCs. More large BHCs operate across multiple census regions than small BHCs. Small BHCs are more likely to be dominated by their banking subsidiaries than large BHCs, as measured by the ratio of deposits to total liabilities. Small BHCs tend to have higher capital ratios than large BHCs.(19)
TABLE3 Summary Statistics for BHC Portfolio Characteristics
Mean Correlation (Standard Deviation) with Log Size(a) (1) (2) Log Size 16.000 1 (1.248) C&I Loans/Assets 0.178 0.30(**) (0.065) Real Estate Loans/Assets 0.236 -0.27(**) (0.098) Agricultural Loans/Assets 0.005 -0.04 (0.007) Consumer Loans/Assets 0.128 -0.01 (0.062) Loan Concentration 0.326 -0.30(**) (0.058) Trading Account Assets/Assets 0.010 0.32(**) (0.031) Total Deposits/Assets 0.777 -0.57(**) (0.092) Noninterest Deposits/Deposits 0.214 -0.09(*) (0.070) Foreign Deposits/Deposits 0.067 0.56(**) (0.142) Multi-Census Indicator 0.432 0.50(**) (0.496) Notional Principal on Interest Rate Swaps/Assets 0.150 0.48(**) (0.442) Notional Principal on FX Futures/Assets 0.239 0.52(**) (0.725) Noninterest Income/Net Interest Income 0.626 0.01 (3.251) Log [(Book Value of Capital/Assets)2] -5.552 -0.28(**) (0.442) Turnover(b) 0.647 0.39(**) (0.477)
(a) correlations are based on pooled data over the 1987-1993 period. These correlations are adjusted for time fixed effects. That is, the table present correlation coefficient, based on the difference between the variable and the annual means of that variable using the pooled data. Values marked(**) are statistically significant at the 1 percent level; those marked (*) are significant at the 5 percent level. (b) Turnover equal annual trading volume divided by the rage shares outstanding during the year.
Table 4 reports the results from estimating equation (4).(20) Column 1 includes the regression results with only the size variable (along with time fixed effects), while column 2 contains the results including size and the control variables described above. In column 3, we add the variable turnover. Table 4A reports results when the market model is used to derive firm-specific risk; Table 4B reports results when factor analysis is used to derive firm-specific risk.
TABLE 4A Regressions of Multifactor Market Model Firm-Specific Risk on BHC Size and Portfolio Components. Pooled Data from 1987 to 1993, with time fixed effects
Without With With Controls Controls Controls and Turnover (1) (2) (3) Log of Assets -0.077 -0.134 -0.205 (3.06)(**) (-4.07)(**) (-6.26)(**) C&I Loans/Assets 2.951 2.642 (6.70)** (6.24)(**) Real Estate Loans/Assets 0.733 0.630 (1.89) (1.70) Agricultural Loans/Assets 16.056 10.569 (4.21)(**) (2.84)(**) Consumer Loans/Assets 0.351 0.281 (0.70) (0.58) Loan Concentration 2.243 1.710 (3.74)(**) (2.96)(**) Trading Assets/Assets -1.923 -0.838 (-1.38) (-0.62) Total Deposits/Assets -0.127 -0.361 (-0.29) -0.85) Noninterest Deposits/ Total Deposits 0.160 -0.425 (0.38) -1.03) Foreign Deposits/Total Deposits -0.212 -0.360 (-0.57) (-1.00) Multi-census Indicator -0.318 -0.276 (-5.38)(**) (-4.86)** Interest Rate Swaps/Assets 0.107 0.022 (0.74) (0.16) FX Futures/Assets 0.121 0.123 (1.42) (1.51) Noninterest Income/Net Interest Income 0.007 0.014 (0.87) (1.88) Log [(Book Value of Capital/Assets)(2)] -0.988 -0.868 (-15.53)(**) (-13.85)(**) Turnover 0.479 (8.04)(**) N 720 720 720 Adjusted [R.sup.2] 11.12% 45.46% 50.01%
T-statistics in parentheses.(**) indicates statistical significance at the 1 percent level. (*) indicates statistical significant at the 5 percent level.
TABLE 4B Regressions of Factor Analysis Model Firm-Specific Risk on BHC Size and Portfolio Components. Pooled Data from 1987 to 1993, with time fixed effects
Without With With Controls Controls Controls and Turnover (1) (2) (3) Log of Assets -0.155 -0.199 -0.264 (5.97)(**) (-5.73)(**) (-7.58)(**) C&I Loans/Assets 2.584 2.299 (5.57)** (5.10)(**) Real Estate Loans/Assets 0.447 0.351 (1.10) (0.89) Agricultural Loans/Assets 16.889 11.812 (4.20)(**) (2.99)(**) Consumer Loans/Assets 0.056 -0.008 (0.11) (-0.02) Loan Concentration 2.422 1.929 (3.84)(**) (3.14)(**) Trading Assets/Assets -2.049 -1.046 (-1.39) (-0.73) Total Deposits/Assets -0.155 -0.372 (-0.33) (-0.83) Noninterest Deposits/ Total Deposits 0.131 -0.672 (0.30) (-1.54) Foreign Deposits/Total Deposits -0.293 -0.429 (-0.74) (-1.12) Multi-census Indicator -0.309 -0.270 (-4.97)(**) (-4.47)(**) Interest Rate Swaps/Assets 0.083 0.005 (0.55) (0.04) FX Futures/Assets 0.082 0.084 (0.91) (0.96) Noninterest Income/Net Interest Income 0.011 0.018 (1.42) (2.30)(*) Log [(Book Value of Capital/Assets)(2)] -1.047 -0.936 (-15.62)(**) (-14.03)(**) Turnover 0.443 (6.99)(**) N 720 720 720 Adjusted [R.sup.2] 13.47% 45.51% 49.01%
T-statistics in parentheses. (**) indicates significance at the 1 percent level. (*) indicates significance at the 5 percent level.
Overall, the results in Table 4 show that size-related diversification leads to important reductions in firm-specific risk. As we add the controls discussed above, the magnitude of the (negative) size coefficient increases markedly, from -0.08 to -0.20 in Table 4A and from -0.16 to -0.26 in Table 4B. The coefficient on size is biased upward when the control variables are omitted because, on average, the port folio components of large BHCs enhance risk and therefore offset the risk-reducing benefits of diversification.
These results indicate the BHCs can achieve economically important reductions in risk through size-related diversification. Holding the control variables fixed, a 10 percent increase in asset size leads to a reduction in firm-specific risk of 2.0 to 2.6 percent. If we use systematic risk in place of firm-specific risk as the dependent variable, [Beta.sub.1] is not significantly different from zero. This result helps substantiate our interpretation of [Beta.sub.1] as a measure of size-related diversification, since portfolio theory tells us that diversification should leave systematic risk unaffected.(21)
Tables 3 and 4 also help explain the lack of a negative correlation between size and stock return variance documented in Table 2. From Table 3, we see that large BHCs engage in more C&I lending and hold less capital than small BHCS. Table 4 shows that C&I lending and low capital ratios are positively associated with firm-specific risk. In fact, other than size, these two variables are the most important predictors of firm-specific risk.(22) The riskier portfolio components of the typical large BHC tend to offset the risk-reducing potential of diversification.
Of course, not all portfolio components typical of large BHCS are positively related to risk. For example, large BHCs are more likely to operate in more than one census region, which reduces firm-specific risk. Large BHCs also have better diversification across the loan portfolio, as measured by our loan concentration index. Since these two variables measure part of the diversification benefits of BHC size, our estimates actually understate the effects of size-related diversification. If we drop these two variables from the regressions, the Table 4A coefficients on size increase in magnitude from a range of -0.13 to -0.20 (excluding and including turnover) to a range of -0.22 to -0.28. Table 4B coefficients on size increase in magnitude from a range of -0.20 to -0.26 to range of -0.29 to -0.34.
Looked at another way, our results suggest that large BHCs are able to operate with higher leverage and engage more in risky (potentially profitable) lending without increasing risk because of their diversification advantage. Diversification may thus be an important motivation for bank consolidation. This interpretation is consistent with Akhavein, Berger, and Humphrey (1997), who find that bank profits increase following mergers as outputs shift from securities to loans. They suggest that better diversification allows the merged banks to hold riskier, more profitable portfolios.
While the positive relationship between size and diversification is robust throughout the 1980-1993 period, large BHCs do show significantly lower stock return variance in 1992 and 1993. In another paper (Demsetz and Strahan 1995), we show that the portfolio components of large and small BHCs in the bottom size-quartile of our sample. By 1993, small BHCs had only 3.5 percent more capital than large BHCs. We suggest that regulatory changes (in particular, implementation of risk-based capital adequacy standards and passage of the FDIC Improvement Act) affected the risk-taking propensity of large BHCs more than that of small BHCs. As a result, the diversification advantage of size has recently become evident in lower stock return variance at large BHCs.
This paper provides strong evidence of a link between size and diversification at publicly traded bank holding companies. The correlation between the log of assets and the [R.sup.2] from each of two return-generating models is consistently positive and significant from 1980 to 1993. Controlling for risky portfolio components, we find that a 10 percent increase in BHC assets leads to a reduction in firm-specific risk of 2.0 to 2.6 percent. This results is important but not surprising, since it is generally accepted that large banks have better opportunities to deversify.
We also show that the positive relationship between BCH size and diversification does not result in a negative relationship between BHC size and stock return variance during most of the sample period. This second results has important implications for the policymaker, who must fully understand the risks that particular institutions introduce into the banking system. Large BHCs have used their diversification advantage to operate with greater leverage and to pursue riskier, potentially more profitable lending. This suggests that diversification may provide an important motive for bank consolidation.
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(1.) Positive values of yield represent increases in short-term rates. Specifically, [yield.sub.t] = (three-month [rate.sub.t]) - (three-month [rate.sub.t-1]). Positive values of term represent a steepening of the yield curve. Specifically, term, = [(thirty-year rate - three-month rate).sub.t] - [(thirty-year rate - three-month rate).sub.t-1]. Positive values of credit quality spread represent an increase in the premium charged for credit risk. Specifically, credit quality [spread.sub.t] = [(Baa rate - thirty-year rate).sub.t] - [(Baa rate - thirty-year rate).sub.t-1].
(2.) We have also estimated a six-factor decomposition of BHC stock returns and found nearly identical results to those generated using the five-factor model.
(3.) Compustat and CRSP both use "cusip" numbers as company identifiers. However, the only identifier common to Compustat and the Y-9C is the company's name. Our sample includes only those BHCs for which the match between the name provided by Compustat and that appearing on the Y-9C was unambiguous.
(4.) Daily returns are adjusted by CRSP to account for dividend payouts and stock splits. In cases where Friday was a holiday and no stocks were traded, we used the Thursday-to-Friday or Friday-to-Thursday returns instead. In cases where the return was not available for a given stock on a given Friday, that stock's weekly return was coded as missing.
(5.) Since we are particularly interested in the relationship between the market model [R.sup.2] and asset size we use an equally weighted index rather than a value-weighted index. A market model estimated using a value-weighted index will induce some degree of correlation between [R.sup.2] and asset size.
(6.) Using a switching regression model, Kane and Unal (1988) find that the parameters of return-generating models for depository institutions changed significantly in 1979 and 1982.
(7.) Neuberger (1991) reports a similar pattern for his sample of eighty-four large BHCs.
(8.) All reported [R.sup.2]s are adjusted [R.sup.2]s. We do not report estimates for the market model in 1980-1982 because the data used to construct the credit quality spread variable were unavailable for those years.
(9.) Asset size is measured as of the beginning of each year in order to avoid a potential simultaneity problem. Abnormally strong performance by a set of BHC stocks may lead to a spurious negative correlation between asset size and the market model [R.sup.2] if that strong performance promotes asset growth.
(10.) Roll (1988) compares firm size to the [R.sup.2]s from a market model and a five-factor analysis model, using the stocks of all companies traded an the New York and American Stock Exchanges from September 1982 through August 1987. He also funds a positive relationship between firm size and the market model [R.sup.2] but finds "a much less perceptible positive relation" when comparing firm size with the [R.sup.2] from the five-factor analysis.
(11.) Possibilities for 1988 include the S&L crisis, the full impact of which may not have been felt until that year; BHC-specific events from 1993 include changes in the regulatory environment for banks and rising deposit insurance premia.
(12.) A theoretical derivation of this particular specification is available
(13.) We begin this analysis in 1987 because the data reported to regulators, particularly for off-balance sheet activities, increased significantly after 1986. We have also estimated these regressions over the 1982-1993 period using all variables that were collected over the full sample period. These results are qualitatively similar and are available on request from the authors.
(14.) The non-interest bearing deposits variable includes demand deposits, non-interest bearing passbook savings accounts, and non-interest bearing time deposit accounts.
(15.) Levonian (1994) shows that bank accounting profits across states exhibit low correlations, suggesting that banks operating in many states may be able to reduce risk through diversification.
(16.) Since collection of data on foreign exchange swaps began only in the third quarter of 1990, we do not include a measure of foreign exchange swap activity in the regression analysis.
(17.) The particular functional form of this variable in equation (4) is motivated in a model available from the authors.
(18.) The causal interpretation of the regressions with turnover may be somewhat problematic because large movements in the price of a stock (and thus high measured risk) may be related to high volume (and thus high turnover).
(19.) Boyd and Runkle (1993) also find that large banks have smaller capital ratios than small banks.
(20.) The number of observations equals 720 because data required for estimation of Table 4 were unavailable for 15 of the 735 original 1987-1993 observations.
(21.) The systematic risk regressions are not reported but are available from the authors.
(22.) Samolyk (1994) finds that banks with a higher proportion of C&I loans to assets have higher levels of nonperforming assets and net charge-offs, providing further evidence that C&I lending is high risk relative to other…