# A methodological investigation of risk exposure of bank off-balance sheet loan commitment activities.

Bank off-balance sheet activities in general, and loan commitments in particular, have grown rapidly in recent years (Hirtle 1987). The growth in off-balance sheet banking can be explained by increases in direct finance, minimization of regulatory taxes, and the development of secondary markets for loans. Kareken (1987) attributes this growth in off-balance sheet banking to technological advances that decrease the cost of acquiring and processing information which open the direct credit market to a large number of issuers. The costs of federal deposit insurance premiums, the constraints upon increased financial intermediation owing to regulators' capital requirements, and the opportunity cost of legal reserves are referred to as regulatory taxes. Off-balance sheet activities allow banks to generate fee income, and bypass the costs imposed on them by regulatory taxes.The most prominent bank off-balance sheet activity is loan commitments which grew from $520 billion in 1984 to $783 billion in 1988, a 50 percent increase over this five year period (see Table 1 for growth statistics). The extant literature on loan commitments has examined theoretically the pricing of loan commitments as contingent claims, and loan commitment as completing financial markets (Campbell 1978; Thakor 1982; James 1982; Melnik and Plaut 1986; Boot, Thakor, and Udell 1987; Berkovitch and Greenbaum 1991; Thakor and Udell 1987; Boot and Thakor 1991).

[TABULAR DATA 1 OMITTED]

The issue of the risk of bank loan commitment is worthy of study because there is a perception among regulators that loan commitments increase the risk exposure of banks and, ultimately, the deposit insurer. Regulators fear that a loan commitment imposes a contingent liability on a bank because the exercise of a loan commitment option imposes a loss on the bank. Although the commitment fee is expected to compensate the bank for its risk exposure, the regulators argue that the potential liability of a loan commitment is not quantified and reflected in the deposit insurance premium. This may encourage a bank to take on excessive risk by expanding its loan commitments which may result in an underestimation of the risk exposure of the deposit insurer. Therefore, regulators have imposed capital requirements against bank loan commitments to control their growth. Risk-based capital requirements for loan commitments mandate that unused commitments with an original maturity greater than one year receive a 50 percent weighting for capitalization. Commitments with less than a one year maturity require no capital. This study examines empirically if bank regulators' risk perceptions of loan commitments are warranted. This research finds that loan commitments reduce bank risk.

The extant empirical literature examines the risk exposure section of the shop. The groups were randomly allocated to an autonomous or a non-autonomous (control) category when representatives publicly drew cards from a bin. Subsequently, one-half of the autonomous and non-autonomous groups were randomly assigned to a pre-test category. The remaining groups were a posttest condition.

The work groups contributed to determining the content of a questionnaire. At the meetings arranged by the author the groups were asked to list the problems

they experienced. They also were required to state what they believed were the causes of these problems, e.g., communication, as well as the likely consequences, i.e., job dissatisfaction, if the problems were not resolved. These presumed determinants and consequences were the variables that were examined to assess the effects of the introduced self-managed work practices. Standard instruments were employed, and an extensive questionnaire was administered at two monthly intervals.

A new form of work organization was installed at the beginning of the work year (February). The author adopted a role of facilitator. The autonomous groups arranged and held weekly meetings (which included the supervisor) at a time suitable to the group. These meetings, which endeavored to address work-related problems, were about one-half an hour in duration. They were held in one of the many amenities rooms (same place) which were dispersed, about the site, on the same day of the week at the same time (regularity) (Witte, 1980). Each group had an elected chairperson and secretary, brief notes were kept on prepared forms, and there was a meeting agenda. The main guidelines given to a group were that they should address specific work issues, and that safety and award matters should be directed to the safety representatives or shop steward, respectively (this did not prevent groups from discussing safety and award issues, and later evaluating solutions). The non-autonomous groups continued to employ the traditional work practices, which normally lacked an opportunity for group meetings.

The weekly group meeting was a strategy for restructuring the work arrangements. Prior to the intervention work groups employed more traditional work practices which were adopted when the Workshops was established in 1904. In this traditional arrangement there was an absence of participative goal setting and positive performance feedback. Moreover, the role of the Supervisor was to implement the plans of management by controlling the conduct of the group followers. The new arrangements were instituted to attain a more consultative pattern of supervision.

The autonomous work groups were encouraged to address work-relevant issues. Each one of these groups acquired a white board and marker pens, and on this board was written the goals the group wished to achieve. New goals were added.

All the goals were given a priority rating as well as an achievement date. In addition, the self-regulating groups developed strategies for attaining their short- and long-term goals. An important feature of the strategy was to identify the resources that were vital for goal achievement. In some instances, this was information, and the knowledge holders were invited to meetings so that appropriate action could be undertacommitment.

The downside risk of a bank-issued loan commitment depends in part on "material adverse change clauses" written into the commitment that permit a bank to cancel its obligation when a borrower's financial condition deteriorates over the commitment's life. Otherwise, the bank is obligated to extend credit in the future at terms that it would prefer to refuse because of a decline in the borrower's creditworthiness. An additional risk aspect is the potential cyclicality of the loan commitment obligation. Banks may find an excessive number of commitments being drawn down in periods when funds are tight.

The theoretical literature has focused on the existence of commitments in a number of articles. Campbell (1978), Thakor (1982),James (1982), and Melnik and Plaut (1986) explained loan commitments as completing financial markets. Commitments have also been explained as solutions to moral hazard and adverse selection problems which arise in spot loan markets. Boot et al. (1987) and Berkovitch and Greenbaum (1991) show that a two-part pricing structure of commitments (an up-front fee plus a loan interest rate) allows a bank to charge a lower loan interest rate without violating the zero-profit competitive constraint. This lower rate reduces moral hazard and improves efficiency. Thakor and Udell (1987) show that multiple fee structures on commitments (up-front fee, usage fee, and interest rate) can solve some adverse selection problems on spot loan contracts by inducing self-selection, provided that take-down probabilities are related to risk. Avery and Berger (1991) focus on moral hazard and adverse selection problems created by commitments, rather than viewing commitment contracts as methods of alleviating these problems on spot contracts. They show that while commitments increase a bank's risk exposure (credit risk), the rationing or sorting of commitments among borrowers according to their association with moral hazard and adverse selection problems could offset this risk. Loans issued under commitments, therefore, could be safer on average than other loans. Empirically, they find that commitments tend to lower bank portfolio risk.

Recently, Boot and Thakor (1991) theoretically showed that loan commitments may reduce a bank's portfolio risk and lower the exposure of the federal deposit insurer. They showed that the loan commitment contract can be designed to resolve the asset substitution problem between the bank and the bank borrower. Loan commitments may reduce the borrower moral hazard problem through upfront commitment fees because such fees reduce the promised interest rate on the loan, which gives the borrower more of a stake in the project and less incentive to increase project risk. They also argue that safer banks will issue more loan commitments, and banks with more loan commitments will become safer. The intuition behind these arguments is that loan commitments are uninsured contingent future claims on the bank which are subordinated to other claims on the bank. The value of a loan commitment to a customer increases with the safety of the bank, providing incentives for banks that issue commitments to increase their safety and encouraging exogenously safer banks to issue more commitments. These arguments suggest that loan commitments are negatively related to bank risk.

Boot and Thakor (1991) also argue that loan commitment customers are not only safer than spot borrowers, but also the spot borrowers chosen by the bank are themselves safer than those the bank would choose in the absence of a loan commitment. Their research generates two policy implications. First, the deposit insurer should insist on all of the bank's outstanding commitments being voided if the bank is liable to pay off its depositors and is bailed out by the insurer. Second, the imposition of an explicit capital requirement against unexercised loan commitments is counterproductive if the purpose is to reduce risk taking by banks.

Berger and Udell (1993) present a monitoring technology hypothesis to explain securitization in banking. The principal implication of this hypothesis is that securitization by itself is not likely to have a significant impact on bank risk or liquidity. Securitization, they point out, takes two forms. The first, termed as "disintermediation type securitization" (a loan sale without recourse is an example), implies a movement away from intermediated bank loans towards direct financing of debt by capital markets. Disintermediation-type securitization is predicted to be independent of bank risk and liquidity. In the second form, called "off-balance sheet securitization" (a loan commitment is an example), the bank retains the default risk of the loan and continues its role of monitoring the borrower, but the funding is provided by a third party. The monitoring technology hypothesis predicts that off-balance sheet securitization has no effect on bank risk or bank monitoring, and will simply rearrange the claims to bank returns. However, the association between off-balance sheet securitization and bank risk will be determined by whatever the casual factor motivating this securitization.

Berger and Udell (1993) argue that borrowers lie on an information continuum. Borrowers with "high", "medium" and "low" levels of information problems borrow from insiders, intermediaries, and direct lenders, respectively. They argue that banks have always lent to "information-problematic" borrowers. As information technology improves, some borrowers become informationally unproblematic and gain access to capital markets for borrowing, but other borrowers that previously could not borrow at all become suitable for bank lending.

In summary, LNCOMMs may be theoretically related to bank risk in four ways. First, LNCOMMs may entail credit risk of the bank customer because the bank has to extend a loan in adverse circumstances. Second, overextension on LNCOMMs increases bank leverage thus creating liquidity risk for the bank. Third, LNCOMMs may signal higher credit quality of the bank borrower and the bank itself. Banks with loan commitments will reduce their asset risk in order to attract more commitment customers. Fourth, banks may use LNCOMMs to diversify their asset portfolio and reduce risk.

Empirical research concerning the risk exposure caused by loan Commitments is inconclusive. Lynge and Lee (1987) found that loan commitments are insignificant in models explaining both systematic risk and equity risk. Brewer, Koppenhaver, and Wilson (1986) found similar results using a two-factor CAPM model. Berger and Udell (1990) found a negative relationship between used commitments and risk, where risk is measured by premium of the loan rate over the Treasury rate of comparable duration. Avery and Berger (1991) regressed three bank performance measures, namely, non-performing loans, loan charge-offs and income against on-balance sheet control variables and loan commitments. The results indicate that commitment loans tend to have slightly better than average performance, suggesting that either commitments generate little risk or that this risk is offset by the selection of safer borrowers to receive commitments. Hassan (1993) used a variety of bank risk measures including implied asset risk to examine the risk-behavior of several off-balance sheet activities including loan commitments. He found that loan commitments reduce bank equity risk, but do not affect systematic risk or implied asset risk.

Berger and Udell (1993) regressed four risk measures, namely, failure dummy, return on assets, standard deviation of the return on assets, and a standardized z-score, against loan commitments, and found an ambiguous relationship between loan commitments and bank risk. They did not, however, use any implied asset risk measure in their study. Hassan, Karels, and Peterson (1993) examined the "market discipline" of off-balance sheet banking activities by employing contingent valuation techniques to derive implied asset risk from bank equity, and from risk-premia for bank subordinated debt. They found that market discipline exists for loan commitments because both bank subordinated debtholders and equityholders price commitments as reducing bank asset risk.

None of the empirical studies have attempted to include the effect of regulatory behavior, nor allow for nonlinear risk measurement. This study reexamines the impact of LNCOMMs on bank risk reporting three additional risk measures, which include the contingent claims nature of bank liabilities, deposit insurance, and regulatory closure rules.

DATA AND METHODOLOGY

Data Analysis

This research focuses on the 100 largest U.S. banks and BHCs, as these approximately represent those having publicly traded stock, subordinated debt, and debentures. The sample is restricted to lead BHC banks which account for the majority of bank holding company assets. Market values of equity for each bank or bank holding company are collected from COMPUSTAT annual tapes. Daily bank stock returns and market returns are collected from the CRSP daily tapes (NYSE/AMEX and NASDAQ tapes). Data on yield measures were gathered on all BHCs for bank subordinated debt, debentures and capital notes which were publicly traded on the NYSE, AMEX, or NASDAQ with quoted bid and sale prices from Moody's and Standard and Poor's bond manuals for years ending 1984 through 1988. To make each BHC debt issue as homogeneous as possible, all zero coupon issues and floating rate issues were dropped from the sample. This produced 171 issues for 50 BHCs in 1984,137 issues for 49 BHCs in 1985, 160 issues for 48 BHCs in 1986, 174 issues for 43 BHCs in 1987, and 223 issues for 49 BHCs in 1988. Virtually all of these bonds were issued against the BHCs rather than the bank. There was a fair amount of heterogeneity in terms of maturity, coupons, issue size and callability. One-fourth of these debt issues were not callable. Because the callability feature introduces bias in the risk premium of a subordinated debt, this study used only noncallable debt risk premium. Omitting callable issues provides a clean sample of risk premiums, which are devoid of any call risk premium and any timing issue that is more related to the business cycle than to the inherent riskiness of BHC or bank. Acquisitions or name changes of banks have been confirmed from Moody's Bank and Finance Manual in order to maintain continuity in data collection.

The risk-free rates of Treasury securities identical in maturity to each BHC noncallable debt were collected from Moody's Bond Records. The risk premium of each issue of BHC noncallable debt is simply the difference between the yields of debt and Treasury securities of identical maturity. The risk-premium (SUBPRM) used in this study is the average premium of all outstanding issues for each BHC for each year. The on-balance accounting risk-variables and off-balance sheet LNCOMMs are constructed from variables available in the FDIC Call and Income Reports for the years 1984 through 1988. The risk-premia and market values of equity, of each BHC are matched against on-balance measures of risk and LNCOMMs from the FDIC Call and Income Reports, and this results in a final sample of 30 banks and BHCs for each year.

Betas ([Beta]) are calculated from daily equity returns for each bank for which 200 or more trading days are available each year from the CRSP tapes. The standard market model is used in this study to estimate betas and the CRSP equally-weighted return with dividends is used to represent the market index. SIGMAE is the annualized standard deviation of daily equity returns. SIGMAEs are calculated for those banks for which 200 or more trading days annually are available on the CRSP tapes.

SIGMA1 is defined as the standard deviation of asset returns and is calculated for each bank for each year 1984 through 1988 by using Ronn-Verma option pricing methodology. A system of two non-linear simultaneous equations, Equations 4 and 6 are solved for two unknowns, asset value (V) and the standard deviation of asset returns SIGMA1), for each observed annual market value of equity and annualized standard deviation of equity returns (SIGMAE). The initial estimates used for V were the sum of the market value of equity and face value of debt and that for SIGMA1s were SIGMAE scaled down by leverage ratios. The cumulative normal distribution function is calculated by using a polynomial approximation developed by Cox and Rubinstein (1985).

SIGMA2 is the implied asset risk calculated from the Gorton-Santomero model. The pricing formula, Equation 7, is inverted, with all necessary inputs given, to calculate asset risk. After deriving the unknown standard deviations of asset returns (SIGMA1 and SIGMA2) implied by the Gorton-Santomero nonlinear subordinated debt option pricing model, these variables were then used as the dependent variables in the regression analysis. The descriptive statistics of the five market measures of risk, the on-balance accounting measures of bank risk and also the LNCOMM are given in Table 2.

[TABULAR DATA 2 OMITTED]

Specification of Empirical Model

This research is an empirical test of the relationship between five control variables and loan commitment activity, repeated over five risk measures. The following linear model is estimated over cross-section and time-series data using Generalized Least Squares (GLS) to test bank risk exposure as affected by LNCOMM activities:

Market Risk Measure

(1) = f(LNCOMM, LEV, INDEX, CREDIT, INTEREST, LNSIZE)

where the five alternative market risk measures are:

1. beta (systematic risk)

2. standard deviation of bank equity returns

3. default-risk premium of subordinated debt

4. bank implied asset risk (Ronn-Verma option pricing methodology) 5. bank implied asset risk (Gorton-Santomero subordinated debt pricing methodology)

and where:

LNCOMM = dollar volume of loan commitments deflated by total assets,

LEV = ratio of total liabilities to total assets,

INDEX = an index of diversification of the bank's loan portfolio,

CREDIT = ratio of loan-loss reserves to total assets, INTEREST = absolute dollar differences between rate-sensitive assets (RSA) and rate sensitive liabilities (RSL), divided by total assets, where the RSA and RSL are those scheduled to be repriced or mature within one year,

LNSIZE = logarithm of total bank assets.

LEV, INDEX, CREDIT, INTEREST and LNSIZE are proxies for the leverage ratio, diversification index, credit risk, interest rate risk and bank size, and are used as control variables in the model. Like Avery and Berger (1991) and Berger and Udell (1990), we used a variety of different measures of bank risk based on call and income report data, but these control risk variables were found to be insignificant, and these results are not reported. We reestimated the models with the five control variables found to be significant and reported the results. It should be noted that Avery and Berger used three performance measures (nonperforming loans, loan charge-offs and net income) as dependent variables, while Berger and Udell (1990) used risk premium as the lone dependent variable. This research used five market measures of risk calculated from market prices of debt and equity as dependent variables. These balance-sheet and income statement variables were calculated for the lead bank holding company bank which accounts for the majority of holding company assets. The expected relationships between dependent and independent variables are rationalized as follows:

1. Commercial banks use a high degree of financial leverage, which is directly related to financial risk. LEV is expected, therefore, to be positively related to market measures of risk.

2. The Diversification index (INDEX) is a Herfindahl index calculated as:

[Mathematical Expression Omitted]

where [L.sub.i] is the loan to asset ratio for loan type i at the end of each year from 1984 through 1988. Like Pavel (1988), ten loan categories from Schedule C of the Report of Condition were used. The construction of a diversification index implies that the greater the diversification index, the greater the level of diversification in the loan portfolio. Therefore, INDEX is expected to be inversely related to market measures of risk.

3. The credit risk variable (CREDIT) represents the probability of future defaults that may be expected to reduce earnings and dividends. Other things being equal, a higher CREDIT reflects a higher degree of expected loss in the loan portfolio. Therefore, CREDIT is expected to be positively related to market measures of risk.

4. The interest rate risk (INTEREST) variable is the difference between market rate assets and liabilities with maturities less than or equal to one year. A positive INTEREST value indicates a bank is asset sensitive and negative value indicates a bank is liability sensitive. Positive INTEREST values indicate the bank is exposed to the risk that interest rates will fall and negative values indicate that the bank is exposed to the risk that interest rates will rise. The greater the absolute value of INTEREST, the more the bank is exposed to unexpected changes in interest rates. Therefore, INTEREST is expected to be positively related to market-related risk measures.

5. The larger the size of a bank, the greater its potential to diversify its asset portfolio and lower its earning variability. The larger the size of a bank, the more information security analysts are likely to collect about the bank's stock and debt instruments and the lower the information risk from holding its liabilities. Moreover, investors may believe that large banks are protected from failure by greater degree of regulatory support. These implicit failure guarantees by regulators rise with bank size. Each of these reasons suggests that risk and size should be negatively related.

These on-balance accounting measures of bank risk have been found in previous studies. For example, Lee and Brewer (1985) found leverage, loan-loss and gap variables to be significantly related to market measures of bank risk. Jahankhani and Lynge (1980) found similar variables were significantly related to systematic risk and equity risk. Pettway (1976) found that dividend and earnings were significant in explaining total and systematic risk. Avery, Belton, and Goldberg (1988) conducted a cross-section study of subordinated debt pricing for both 1983 and 1984. Examining the spread over the comparable Treasury yields, these authors were unable to demonstrate the effect of any balance sheet or income statement data on bank costs. Recently, Gorton and Santomero (1990) used a contingent pricing model and regulatory closure rule to examine the relationship between bank risk and accounting risk factors. They found that credit and interest risk variables were insignificant in models in which bank debt is assumed homogeneous with one year maturity.

Although these balance sheet and income statement variables have been used mostly in explaining bank systematic risk, equity risk and liability costs, the same variables can be used in explaining subordinated debt risk premiums and implied asset risk. This research employs similar bank accounting risk variables in addition to dollar volume of loan commitments to examine the riskiness of LNCOMMs and the existence of market discipline.

Discussion of Bank Market Measures of Risk

Five market measures of bank risk will be used in this research, as follows:

Beta or Systematic Risk: The following market model is estimated for each bank over the study period to calculate beta:

(2) [Mathematical Expression Omitted]

where: [Mathematical Expression Omitted] = [R.sub.it] - [R.sub.ft] is the ex post return for the [i.sup.th] bank over period t in excess of the risk-free rate of interest, [Mathematical Expression Omitted] = [R.sub.Mt] - [R.sub.ft] is the ex-post return on the market portfolio over period t in excess of the risk-free rate of interest, [[alpha].sub.i] = the intercept, [e.sub.it] = the [i.sup.th] bank-specific factor which is independent of [Mathematical Expression Omitted] [[beta].sub.i] = is the slope of the linear relationship between bank i's return and the market return.

The beta estimates reflect differing investor expectations about the relationship between each bank's return and the market return. Each beta estimate is a market measure which incorporates all information about the bank as digested by market participants.

Standard Deviation of Bank Equity Return: Equity returns data for the sample of banks are available over the study period, and the standard deviation of equity returns for each year from 1984-88 will be estimated for each bank using this formula:

(3) [Mathematical Expression Omitted]

where:

[bar]K = Ex-post daily equity return during given year, [bar][K.sub.Avg] = Average of daily returns during given year.

Default-risk Premium of Subordinated Debt: Subordinated debtholders are subject to a larger risk of loss than uninsured depositors. Market discipline by uninsured depositors appears limited by: (1) these depositors' ability to withdraw funds quickly once a problem situation becomes apparent; and (2) by the fact that they typically receive de facto insurance coverage when the FDIC uses the method of purchase and assumption to resolve a problem situation. In contrast, subordinated debt can be a source of funding that cannot be withdrawn during adversity and is generally not assumed by the purchasing bank in a purchase and assumption technique. Thus, subordinated debtholders are generally subject to greater risk than uninsured depositors. The potential of subordinated debt to enhance market discipline is examined empirically by calculating yield spreads between subordinated debt and Treasury securities of identical maturities and regressing on LNCOMMs.

The risk premiums for noncallable BHC securities were computed directly as the difference between their yields to maturity and those of Treasury securities with the same maturity. The risk-premium (SUBPRM) used in this research is the average risk premium outstanding for each BHC for each year-end 1984 through 1988. Therefore, these risk-premiums do not suffer from confounding effects arising from callability of bonds.

Bank Implied Asset Risk under the Ronn-Verma Option Pricing Methodology: The first measure of asset risk in this study is the risk-based deposit insurance premium estimated by Ronn and Verma (1986). Ronn-Verma demonstrate that empirical estimation of risk and deposit insurance premiums is tractable when time-series data on the market value of the bank's equity and the book value of its debt are available. They modeled market perceptions of the FDIC's bailout policy in their construction to eliminate the bias in implied asset values and their variances.

The equity of a bank can be written as:

(4) E = VA(x) - [rho]BN([chi] - [[sigma].sub.[upsilon]][squareroot of] T)

where:

(5) [Mathematical Expression Omitted]

(6) [[sigma].sub.[upsilon]] = [[sigma].sub.E] E/VN(x)

E = market value of equity,

[[sigma].sub.E] = instantaneous standard deviation of equity return,

V = the unobserved post-insurance value of bank assets,

B = book value of debt liabilities,

[[sigma].sub.[upsilon]] = instantaneous standard deviation of asset return,

T = time until next audit of bank assets.

Equations 4 and 6 can be solved simultaneously for two unknowns, V and [[sigma].sub.[upsilon]], for each observed E and [[sigma].sub.E]. An exogenously determined closure rule is required to solve these simultaneous equations. Banks are audited each year and at audit time a bank is closed if [V.sub.T] < [[rho].sub.B] where [V.sub.T] is the terminal value of assets at time T and [rho] [less than or equal to] 1 is a policy parameter. Therefore, the maturity of debt is assumed to be 1 (i.e., one year). Ronn-Verma show that a [rho] of .97 yields an aggregate deposit premium weighted average of about 1/12 of one percent, the flat rate premium historically charged by the FDIC. Once implied asset variances ([[sigma].sub.[upsilon]]) are calculated, they will be regressed on LNCOMMs to test for their effect on risk.

Bank Implied Asset Risk Under the Gorton-Santomero Subordinated Debt, Pricing Methodology: The second measure of bank risk is the implied asset volatility calculated from subordinated debt risk-premia option pricing methodology (Gorton-Santomero 1990). They have demonstrated that these implied asset volatilities are better than risk-premia in proxying total risk because they consider both the nonlinear nature of a contingent claims model and the impact of closure rules.

The risk-premium has been modeled as an option in the following way:

(7) R - [R.sub.f] = -ln [V/B exp ([R.sub.f]T) N(-[d.sub.1]) + N([d.sub.2]) / T

where:

[d.sub.i] = [ln (V/B) + ([R.sub.f] + [[sigma].sup.2] / 2) T] / [sigma][squareroot of] T,

[d.sub.2] = [d.sub.1] - [sigma][squareroot of] T,

[[sigma].sup.2] = instantaneous asset variance,

R = yield on subordinated debt and debentures,

[R.sub.f] = yield on Treasury securities of the same maturity,

V = value of bank assets,

T = maturity of subordinated debt (assumed to be 1),

B = face value of debt,

N([multiplied by]) = univariate cumulative normal distribution function.

It can be seen that the greater the volatility of a bank's assets, the higher the default risk-premium.

Given the default-risk premia (SUBPRM) and other necessary information, the above pricing formula is inverted to find the volatility of assets, [[sigma].sup.2], implied by that default-risk premia. Like Gorton-Santomero (1990), the maturity of debt is assumed to be one year under the assumption of annual bank audits. At examination time, the stockholders have the choice of satisfying the regulatory criteria or forfeiting the bank to the regulators. Once implied asset risks are calculated, they will be regressed on LNCOMMs to examine their effect on risk.

Calculations of both implied asset variances (Ronn-Verma and Gorton-Santomero) require the usual assumptions made by Black-Scholes (1973). A maintained assumption of the Black-Scholes option pricing model is that [[sigma].sup.2] is constant and normally distributed. The applicability of contingent claims models in discrete time has been demonstrated by Gorton-Santomero (1990) and Ronn-Verma (1986) in their market studies of bank risk. Moreover, the interest rate is assumed to be nonstochastic. Ronn-Verma (1986) show that the relative contribution of interest rate variance to overall variance appears small.

EMPIRICAL RESULTS

Analysis of Results

Table 3 presents the coefficient estimates of the regression model (Equation 1) using five different market measures of risk as dependent variables. The coefficients of loan commitments (LNCOMM) are significantly negative at the 5 percent level in equity risk (SIGMAE) and Ronn-Verma implied asset risk models, and significantly negative at the 10 percent level in risk-premium and Gorton-Santomero asset risk models. These results contrast with those of Lynge and Lee (1987) who found loan commitments to be insignificant in explaining equity risk. These findings, however, support the theoretical assertion of Boot and Thakor (1991) that loan commitments reduce bank portfolio risk. The coefficient of loan commitments is insignificant in the beta risk model. This result indicates that well-diversified stockholders are not concerned about banks' issuing loan commitments. None of the results indicate that loan commitments are risk-increasing. The fact that LNCOMMs reduce equity risk and implied asset risk implies that LNCOMMs may contribute to the overall diversification of a bank's asset portfolio.

[TABULAR DATA 3 OMITTED]

The accounting measures of risk variables, generally, retain their expected signs. The diversification index (INDEX) variable is significantly negative in explaining all five market measures of risk. The leverage variable (LEV) has the expected positive signs and is statistically significant in all five risk-measure models. The LNSIZE variable has the expected significant negative coefficients for all but the beta risk model.

The coefficients of credit risk (CREDIT) are positive and significant for models explaining beta ([beta]), equity risk (SIGMAE) and implied asset risk (SIGMA1) calculated from Ronn-Verma methodology. However, this variable is insignificant in models explaining the risk premium (SUBPRM) and Gorton-Santomero (SIGMA2) implied asset risk models. The coefficients of the interest rate risk variable (INTEREST) are positive and significant in the risk premium (SUBPRM), Ronn-Verma implied asset risk (SIGMA1) and Gorton-Santomero implied asset risk models. However, this variable is insignificant in equity risk (SIGMAE) and beta risk ([beta]) models. The coefficients of on-balance measures of accounting risk variables, generally, are in agreement with earlier studies of Pettway (1976), Lee and Brewer (1985), and Jahankhani and Lynge (1980).

Both measures of asset risk (SIGMA1 and SIGMA2) yield superior results compared to equity risk (SIGMAE). When equity risk (SIGMAE) is used as a market measure of risk, the on- and off-balance sheet financial ratios explain about 37 percent of risk among the sample banks. When both asset risk measures are used as market risk proxies, on- and off-balance sheet financial ratios explain about 64 percent and 86 percent of variability in asset risk (SIGMA1 and SIGMA2) respectively. These results suggest that implied asset risk measures are superior to equity risk in proxying total risk. Moreover, the pooled cross-section and time-series analysis on LNCOMM banking risk provides better coefficient estimates (increased t-statistics) and increases the statistical significance of models (increased F-statistics).

CONCLUSIONS AND IMPLICATIONS

This study has investigated the market's perception of the riskiness of banks that provide loan commitments to their customers. The market reaction to off-balance sheet loan commitments has been examined by using implied asset risk calculated from option-pricing models, in addition to systematic risk, equity risk and default risk-premia of subordinated debt. Drawing on test results of five capital market risk measures concerning LNCOMM activities, it is found that LNCOMMs reduce equity risk, risk premium (SUBPRM) and implied asset risk calculated from Ronn-Verma and Gorton-Santomero option pricing models. However, LNCOMMs are insignificantly related to beta risk.

Given the growing role of LNCOMMs and the attendant problem for bank regulators, this research finds no evidence that LNCOMMs are risk-increasing. The material adverse change clauses in loan commitments limits the issuing bank's risk-exposure. This may be the reason why systematic bank risks are unaltered by loan commitment guarantees. The reduction in bank equity risk and implied asset risk by LNCOMMs implies that LNCOMMs may contribute to the overall diversification of bank portfolio risk.

The risk-based capital requirements of LNCOMMs can be partially analyzed in light of the empirical findings of this research. Bank equity and subordinated debt-holders view loan commitments as reducing bank risk. The pricing signal that the banking industry receives from the equity and subordinated debt market appears to be at odds with regulatory prescription, which requires that these loan commitment activities be included in the calculation of a risk-based capital requirement. These results here indicate that such activities are, in general, risk-reducing.

NOTES

(*) Direct all correspondence to M. Kabir Hassan, University of New Orleans, Department of Economics and Finance, New Orleans, LA 70148. (**) The authors gratefully acknowledge the helpful suggestions and comments of Tom Lindley, Mike Madaris, Ernie King, Eric Hirschhorn, Robert Eisenbeis, Pochara Theerathorn, and an anonymous referee. The usual disclaimer applies. Partial support for this project was provided by a University of Southern Mississippi summer research grant.

REFERENCES

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Author: | Hassan, M. Kabir; Sackley, William H. |
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Publication: | Quarterly Review of Economics and Finance |

Date: | Sep 22, 1994 |

Words: | 6498 |

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