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Subordinated debt prices and forward-looking estimates of bank asset volatility
~-HOILAND
Subordinated Debt Prices and ForwardLooking Estimates of Bank Asset Volatility Carolin D. Schellhorn and Lewis J. Spellman
We have estimated the forward-looking bank asset volatility using market prices of bank equity and subordinated debt. This is in contrast to estimation procedures which rely on historical stock price volatilities. Important for bank regulatory policy, we find that, during 1987-1988, a time of financial stress in the banking industry, most bank asset volatility estimates based on contemporaneous market information were on average 40% higher than historically-based readings. Our results suggest that elevated asset volatilities would require higher risk-based capital standards to protect the deposit guarantor.
Keywords: Bank asset volatility; Subordinated debt; Capital standards JEL classification: G21
I. Introduction The value of banks' assets and their volatilities have long been the interest of financial economists and others charged with safeguarding the soundness of the banking industry. But banks' assets are typically not publicly traded. Hence, the unobserved asset values and their volatilities must be estimated with a model which connects these variables to observed data. For this purpose, the option-based methodology developed by Ronn and Verma (1986) has been employed not only for banks [Kendall and Levonian (1991)], but also for savings and loan associations [Burnett et al. (1991)], insurance companies and investment banks [Santomero and Chung (1992)]. The standard procedure relies on the market value of bank equity, and on the historically observed equity price volatility as a proxy for the market's forward-look-
College of Business Administration, Northeastern University, Boston, MA (CDS); Department of Finance, The University of Texas at Austin, Austin, TX (LJS). Address correspondence to: Professor Lewis J. Spellman, Department of Finance, The University of Texas at Austin, Austin, TX 78712.
Journal of Economics and Business 1996; 48:337-347 © 1996 Temple University
0148-6195/96/$15.00 PII S0148-6195(96)00018-5
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C . D . Schellhorn and L. J. Spellman
ing estimate of bank equity volatility. But this constant-volatility assumption has been met with skepticism [Boyle and Ananthanarayanan (1977)]. Our results for the period 1987-1988 cast further doubt on that notion. We have modified the standard procedure for estimating a bank's asset volatility so that the market value of a bank's subordinated debt may be used as one of the observed variables instead of the historical equity price volatility. Both subordinated debt and equity prices impound investors' information regarding the future. Hence, substituting a bank's subordinated debt prices for its historical equity volatility is expected to yield a more accurate reflection of the market's assessment of forward-looking bank asset volatility. We chose 1987-1988 to compute a monthly time series of bank asset volatilities for a clinical study of four banks. During these years, volatility estimates based on forward-looking market information were most likely to deviate from estimates based on historical information because bank failures occurred in record numbers, ~ and investors were likely to sensitively update their pricing of bank assets and asset volatilities. Our clinical evidence for this time period suggests that most asset volatility estimates obtained from contemporaneous market prices were, on average, 40% higher than estimates derived from historical equity volatilities. It has frequently been suggested [White (1991)] that market information should not be ignored in regulating the risk-taking behavior of financial institutions. 2 In this spirit, we calculated, for the minimally capitalized bank, the capital adjustments required to protect the government guarantor from the bank's higher asset volatility levels, given the deposit insurance premium in effect during 1987-1988. Our asset volatility estimates indicate that substantially more bank capital would have been required. T o examine the market's forward-looking pricing of bank asset volatility we modify, in Section II, the basic option-based model by replacing the historical equity volatility with contemporaneous subordinated debt prices. Section III reviews the data and estimation procedures. Section IV compares our estimates of bank asset volatility based solely on contemporaneous price data with those based on some historical data. Section V provides an example of the capital adjustments required to make the higher asset volatilities consistent with the deposit insurance premium of 1987-1988. Section VI offers concluding remarks.
II. The Option-Pricing Model with Subordinated Debt Before presenting the option-based model with subordinated debt, we will summarize the relevant assumptions of the basic Ronn-Verma model (without subordinated debt). The bank's capital structure consists of equity and senior debt. Debt comprises insured deposits and uninsured senior debt. All debt issues are assumed iBy September 1987, the number of bank failures exceeded the 1986 record of 138 (FDIC Annual Report 1987, p. xv). 2Regulators may charge individual banks for the volatility of their asset values by adjusting deposit insurance premiums when capital requirements are uniform, or by setting risk-based capital standards in conjunction with a flat deposit insurance premium. Ronn and Verma (1989) show how their option-based methodology for the computation of risk-adjusted deposit insurance premiums [Ronn and Verma (1986)] may be inverted to obtain risk-based capital standards for a given uniform deposit insurance premium. Currently, both capital requirements and deposit insurance premiums are crudely adjusted for the asset volatility of individual banks.
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339
to have the same term to maturity, and the banks are audited at the end of one year at zero cost. The audit time coincides with the maturity of the bank's debt and with the expiration of the call option on the bank's assets. At the audit date, forbearance could be provided to the bank in that the insurer would tolerate a deterioration in the market value of the bank's assets, but only as long as the asset value did not fall below a fixed proportion p of the present value of its total debt. 3 Finally, there is no deposit-insurance uncertainty, and, hence, the interest rate on the bank's insured senior debt (deposits) equals the riskfree rate. In order to clarify the notation used in the following discussion, let V = the market value of the bank's assets including taxes or subsidies which result from deposit-insurance mispricing; E = the market value of the bank's equity; B = the maturity value of the bank's total zero-coupon debt; crv = the standard deviation of the rate of return on the value of the bank's assets per unit of time; ~rE = the standard deviation of the rate of return on the bank's equity per unit of time; r = the riskfree interest rate per unit of time; T = the time until the next regulatory bank audit; N(.) = the cumulative normal density function. In the basic model there is both insured and uninsured senior debt but no junior debt. An equity call formulation results in the following equations:
(ln(V/pB)+(r+~,2/2)T} E
=
_ e_rrpBN(In(V/pB) + (r- ~,2/2)T' ~,f~
(1)
E °'v = °rE
[ In
(V/pB) + (r +
~,2/2)T'
(2)
Be-rT,
p and T are assumed policy variables and the face value of total deposits, is observed on the bank's books. E and r are observed in the market, but the market value of the bank's assets and the market's estimates of the future volatilities of bank assets and equity are unobservable. This leaves three unknowns (~rE, o"v, and V) with but two equations. When the historical equity price volatility proxies for o-E, in order to allow solution for the forward-looking asset volatility, it is assumed that the historical price volatility will prevail in the future. The following sections will compare these asset volatility estimates with those derived from contemporaneous subordinated debt (and equity) prices. The use of subordinated debt prices requires the modification of some assumptions made in the basic model. In the augmented model, the bank's capital
]9 is a positive number that, when equal to 0.97, in Ronn and Verma (1986) yielded an aggregate deposit-insurance premium weighted average of approximately 1/12 of one percent.
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C.D. Schellhorn and L. J. Spellman structure comprises equity, senior and subordinated zero-coupon debt. Subordinated debt is substituted for the uninsured senior debt at maturity values, and all debt issues are assumed to have the same time to maturity. All senior debt is insured by a riskless guarantor. In the general case of no forbearance, a bank is declared insolvent when, at the end of the time interval T, the asset value is less than the value of total bank liabilities. In this case, senior debt holders are paid off by the deposit insurer who, in effect, has written a put option purchased by the bank's owners. Subordinated debt holders receive any residual which may remain. Alternatively, the deposit insurer may allow the bank to operate with a negative capital position, i.e., with an asset-to-debt ratio less than one. A p value less than one effectively lowers the closure threshold and represents a policy of forbearance. 4 When the uninsured portion of the senior debt in the basic model is replaced with subordinated debt subject to the constraint that total end-of-period leverage is constant, the following additional variables are defined: Dj = the market value of the bank's subordinated (junior) zero-coupon debt; Bs = the maturity value of the bank's senior zero-coupon debt (deposits). The valuation equation for subordinated debt equals the difference between two call options. 5 In order to adjust the model so that it allows for forbearance, subordinated debt holders are viewed as receiving a call option from the FDIC with exercise price equal to the minimum of pB and the maturity value of the senior debt, B s, while subordinated debt holders sell a call option to equity holders with exercise price equal to the maturity value of the bank's total debt, B. Hence, equation (3) is written to allow for a relaxation of the closure rule:
[ {ln(V/Min[pB, Bs])+(r+~,2/2)T) =V N ~,~/~ {ln(V/B)+(r+ -N
-
~,2/2)T ) ]
°'vV~
e -~T Min[ pB, B~]N[ ln(V/Min[ pB,
B~])
+ (r - %2/2)T
Vvf-T + e_~rBN [ In(V/B) + (r -
~,2/2)T
(3)
4Conversely,closure with p > 1 implies a regulatory policyof early intervention. 5The valuation equation for subordinated debt is derived in Black and Cox (1976) and Smith (1979). Cox and Rubinstein (1985) show that the subordinated debt value equals the difference between two call options:
D~= C(V; B~) - C(V; B). This representation illustrates particularlywell the junior position of subordinated debt holders relative to senior debt holders, and their simultaneous seniority relative to equity holders.
Estimates of Bank Asset Volatility
341
The use of equation (3) introduces a new variable, Dj, but eliminates the variable trE from the simultaneous estimation of V and o-v. Dj is observed in the market, but investors' forward-looking estimate of trE is not.
IlL
Data and Methodology
This section describes the data and procedures used for the estimation of asset volatilities under both the basic and the augmented models. Four firms from the group of the 100 largest bank holding companies met the following restrictive criteria: For each firm, all subordinated debt issues outstanding during 1987 and 1988 had to be publicly traded and priced in Standard and Poor's B o n d Guide. To obtain improved forward-looking asset volatility estimates with market prices of securities which approximated as closely as possible the theoretical assumptions of the options-pricing model, banks were excluded from our clinical study if any of their subordinated debt issues had conversion or sinking-fund features. Subordinated debt issues were required to be non-callable or, if they did have call features, to sell for no more than 100 basis points above par. For debt issues which were priced slightly above, at, or below par, the call feature was assumed to be of negligible value. 6 Using monthly data, we computed the market value of subordinated debt outstanding for each bank from March 1987 to December 1988. Bank equity prices and equity rates of return were obtained from the CRSP Daily Return tapes] M o o d y ' s B a n k and Finance M a n u a l provided face values for individual subordinated debt issues. The book value of total liabilities was taken from the Quarterly Industrial Compustat Tapes. We subtracted the total face value of a bank's subordinated debt from the book value of its total liabilities to obtain an estimate of the face value of its senior debt. Because, for banks, the senior debt consists primarily of deposits which are instantaneously puttable, the face value of the senior debt was assumed to equal its market value, Ds. 8 Finally, we assumed the time to maturity of the banks' debt, i.e., the length of the deposit insurance contract period, to equal one year. As outlined in Section II above, we computed solutions for asset value, 1/1, and asset risk, o-v, using two different methods. 9 The first method requires stock market prices and historical volatilities of equity returns to solve equations (1) and
6Only four of the top 100 bank holding companies satisfied all the above requirements for the period 1987-1988: AmSouth had one subordinated debt issue due in 1999 which was not listed on any exchange. Barnett Banks had two subordinated debt issues with maturity dates in 1996 and 1999, respectively, both listed on the New York Bond Exchange. Two unlisted subordinated debt issues, due in 1997 and 1999, respectively, were outstanding for First Interstate. KeyCorp. had one unlisted subordinated debt issue with a maturity date in 1999. 7In order to estimate the equity volatility for a particular end-of-monthdate, daily equity returns for three months (two months preceding the month in question) were collected. Using the SAS procedure MEANS, the variance of the distribution of daily equity returns was calculated based on this sample of historical data. The square root of this variance estimate was then multiplied by the square root of 250 to obtain the annualized standard deviation of the distribution of daily equity returns. 8For the value of the senior debt at maturity, Bs, this implies that B s = Dse rr. 9In order to solve the system of nonlinear equations, we used subroutines, NEQNF and ANORDF of the International Mathematical and Statistical Library (IMSL), Version 10.1.
342
C.D. Schellhorn and L. J. Spellman (2), a n d thus c o m p u t e s t h e e s t i m a t e s of V a n d trv which R o n n a n d V e r m a w o u l d have o b t a i n e d for e a c h m o n t h in 1987 a n d 1988. This m e t h o d will be r e f e r r e d to as " b a c k w a r d - l o o k i n g " , b e c a u s e historical equity volatilities a r e e m p l o y e d . 1° T h e s e c o n d m e t h o d is called " f o r w a r d - l o o k i n g , " b e c a u s e it solves e q u a t i o n s (1) a n d (3) for t h e s a m e two unknowns, using only c o n t e m p o r a n e o u s m a r k e t prices o f s u b o r d i n a t e d d e b t a n d equity. 11
IV. Clinical Evidence T o e s t i m a t e f o r w a r d - l o o k i n g b a n k a s s e t volatilities with the two p r o c e d u r e s described above, we chose t h e t i m e f r a m e 1987-1988 b e c a u s e the e x t r a o r d i n a r y n u m b e r o f b a n k failures in this p e r i o d m o s t likely t r i g g e r e d price r e a c t i o n s in the m a r k e t for b a n k assets. This t i m e p e r i o d also e n c o m p a s s e s the stock m a r k e t crash of O c t o b e r 1987, an e v e n t which has b e e n shown to e l e v a t e historical e s t i m a t e s o f equity volatilities for several consecutive m o n t h s . 12 F i g u r e 1 displays a n n u a l i z e d equity volatilities e s t i m a t e d over a 90-day lagged p e r i o d for the f o u r c o m m e r c i a l b a n k s d u r i n g 1987 a n d 1988.13 T h e t i m e series for each b a n k shows very similar o r d e r s o f m a g n i t u d e a n d p a t t e r n s o v e r time. Just p r i o r to t h e stock m a r k e t crash in O c t o b e r 1987, the b a n k s ' volatilities surged roughly b e t w e e n 60% a n d 200%, l i n g e r e d for a while, t h e n b e g a n to d e c l i n e a n d r e a c h e d p r e - c r a s h levels by t h e e n d o f M a r c h 1988. T o e x a m i n e how t h e use o f t h e s e historical equity volatilities affects e s t i m a t e s o f f o r w a r d - l o o k i n g asset volatility, we c o m p a r e d the e s t i m a t e s using b a c k w a r d - l o o k i n g data, ~r~, with t h o s e d e r i v e d f r o m f o r w a r d - l o o k i n g prices, ~rvf. R e c a l l t h a t the b a c k w a r d - l o o k i n g a p p r o a c h to t h e e s t i m a t i o n o f b a n k asset volatility uses b o t h the historical b a n k equity volatilities as well as the f o r w a r d - l o o k i n g b a n k equity prices. F i g u r e s 2 a - 2 d p l o t t h e O-vb a n d the crf e s t i m a t e s for each bank. T h e t i m e profiles o f the ~rvb e s t i m a t e s r e s e m b l e t h o s e of t h e historical b a n k equity volatilities d e p i c t e d in F i g u r e 1, p a r t i c u l a r l y for A m S o u t h in F i g u r e 2a a n d for First I n t e r s t a t e in F i g u r e 2c.
1°The sum of equity market value and total debt market value was used as the initial estimate for V. The historically-based ~E was scaled down by the leverage ratio to obtain the initial estimate for crV. 1Differences in the results computed from the two methods may arise not only from the difference between forward-looking and historical market information, but also from a difference in the way some of the underlying Black-Scholes assumptions (which do not always correspond to reality) influence either procedure's computational results. Some caveats regarding the application of the Black-Scholes option-pricing model to the valuation of contingent claims on a bank's assets include: i) While the bank's asset value is assumed to follow a random walk in continuous time, the stochastic process of the asset value may, in fact, be mean-reverting rather than random. (The authors thank Rex Thompson for pointing this out.) ii) The assumption that the variance of the instantaneous return on assets is constant at a point in time with the variance rate being proportional to the square of the asset value, constrains the bank's risk-taking behavior to remain unchanged during a given insurance period, iii) Information may be asymmetric. King and O'Brien (1991) identified typical assumptions which deviate from actual regulatory policy: iv) Regulators audit a bank at the end of one year, and v) the discovery of an insolvency is immediately followed by the decision to invoke receivership. These two assumptions are inconsistent with regulatory policies of forbearance and early intervention. 12For instance, Schwert (1990) reported that the 1987 stock market crash contained the largest one-day percent price change in a data set reaching back to 1885, and that the volatility of the S & P500 increased in late October 1987, and returned to normal levels by April 1988. 13In this section, the term "volatility" refers more specifically to the standard deviation of a given return distribution.
Estimates of Bank Asset Volatility
343
0.6 0.5 -
0.4
.....
Std. Dev. 0.3
Amsouth Barnett
. . . . . . . . . First Int.
0.2
....
0.1 0 ,
-
:
:
t
:
:
;
:
:
:
:;
:
; : :
;
;
:
:
:
:
:
Key Corp.
:
Figure 1. Annualized historical volatility of daily returns on equity for sample banks (January 1987 to December 1988).
In order to compare o-rf to o-b in the absence of the extreme price volatilities associated with the stock market crash, we created three sub-periods and isolated the period from October 1987 through March 1988. The period before the stock market crash, from March 1987 to September 1987, is identified as sub-period I. The time period during and shortly after the crash, extending from October 1987 to March 1988, is referred to as shock sub-period II. Subperiod III covers the time after the effect of the stock market crash had subsided, around April 1988 to December 1988. Comparisons of the ratio of estimated asset volatilities, O'v/trv, f b are summarized in Table 1. The mean volatility ratio for the four banks during the non-shock sub-periods (I and III) is 1.393, indicating that the estimates computed with the forward-looking method exceed those generated with the backward-looking method by almost 40%. During the shock sub-period, both methods produced the same higher asset volatility estimates. The virtual parity in the magnitude of the results is borne out by a mean asset volatility ratio of .986. Whereas the stock market crash impacted bank asset volatility estimates during the shock sub-period, during the non-shock sub-periods, investors' expectations regarding bank asset values and volatilities were likely shaped by the solvency crisis in the depository industry. The late 1980s saw a record number of bank and thrift failures and, in March 1987, the G A O declared the FSLIC insolvent. Banks at, or near, insolvency have a strong incentive to increase asset risk. Hence, a heightened anticipation of moral hazard might have raised the market's assessment of future bank asset volatilities. 14 To examine the influence of insolvency on forward-looking estimates of bank asset volatility, apart from the influence of the stock market crash, we compared average asset volatility ratios by the bank's solvency state during the non-shock sub-periods. The results reveal that trY dominates trb on
14Another reason security prices of insolvent banks are likely to reflect relatively high asset volatilities is a lack of credible information, which is typical for a bank threatened by a regulatory receivership decision. Firms in financial difficultyhave an incentive to delay the release of bad news which increases the uncertainty for investors in the market.
~-/
- \ / \ ,~
i
/
~
\!'
~/ \ \\
I
\I
(c)
~
.
-
~
/ /\
.....
_ _
trv.f
_ o,V f
0.01
Std. Dev. 0.02
0.03
0.04
0.01
Std. Dev. 0.02
0.03
0.04
\
i
q
)
t
(d)
i
; 2 , ,, J',
¢\ \
(b)
,,',,
Figure 2. Annualized asset volatilities for January 1987 to December 1988 for (a) Amsouth; (b) Barnett Banks; (c) First Interstate; and (d) Key Corp.
Std. Dev. 0.01
0.02
(a)
~
....
,,
°°;t ..... , .........
'~q~
-
I
s,~.o,,.o.o,i ,,/! \.. o.o,y-.qy,<--~.,%_
0.04
0.05
0.06
. . . . .
.....
~r V
avf
~J
l::r o
~r t~
©
345
Estimates of Bank Asset Volatility
Table 1: Mean Asset Volatility Ratios (~rfe/~r~.) for Sample Banks, March 1987-December 1988 Bank AmSouth Barnett First Int. Key Corp. All Banks
Shock Sub-Period
Non-Shock Sub-Periods
.802 .960 .937 1.243 .986
1.565 1.093 1.508 1.407 1.393
Note: Asset volatilities were estimated using the backward-lookingand forward-lookingmethods described in Section IlL
average by 60% w h e n e v e r a b a n k is perceived to be insolvent, as o p p o s e d to 16% when the b a n k is considered solvent. 15 T h e divergence o f the estimation results from the two methodologies during 1987-1988, particularly for the non-shock sub-periods, indicates that bank asset volatilities can be considerably higher than suggested by the backward-looking method. If, u n d e r conditions o f financial stress in the banking industry, asset volatilities are indeed higher than previously believed, then the higher asset volatility estimates would require c o m m e n s u r a t e adjustments in b a n k regulatory capital standards.
V. I m p l i c a t i o n s for R i s k - B a s e d Capital R e q u i r e m e n t s B a n k asset volatility impacts the exposure of the federal deposit g u a r a n t o r to an u n f u n d e d contingent liability. F o r a given deposit insurance premium, higher asset volatilities require additional b a n k capital to protect the guarantor. T h e actual deposit insurance p r e m i u m paid by banks varied between 1950 and 1990, depending on the size o f rebates r e m a n d e d as required by law. W i t h o u t rebates, the gross F D I C p r e m i u m equaled 8.33 basis points. However, with rebates, the net deposit insurance p r e m i u m has b e e n approximately four basis points over prior decades [Shaffer (1991a, b)]. ~6 O u r estimates of the capital infusions necessitated by higher b a n k asset volatility levels for the gross and net p r e m i u m s are shown in Table 2. W e examined the implications for risk-based capital standards which result f r o m higher asset volatilities by calculating the capital infusions which are required for a bank which initially complies with the m i n i m u m 4% capital-to-assets ratio. The
15In the interest of brevity, these results are reported in an appendix which is available from the authors upon request. 16While the gross premium remained flat at 8.333 basis points until 1988, the FDIC was required by law to provide a rebate from 1950 until the FDIC Assessment Rate Act of 1990 [Shaffer (1991a,b)]. As long as the FDIC reserve fund had not fallen below 1.1% of insured deposits, mandatory rebates equals 60% of net assessments (gross assessments net of operating expenses and insurance losses). This requirement led the agency to refund, on average, more than half its gross premium income during the years 1950-1980. In addition, until 1987, the gross assessment covered not only current losses but accumulated reserves for future losses so that the insured banks paid an effective rate of approximately four basis points. Net assessments were negative in 1987 and 1988, as insurance losses and expenses exceeded gross assessments so that no credits were remanded for these two years (GAO Report of April 1989). Nevertheless, based on past experience, the net deposit insurance premium is set to equal four basis points.
346
C. D. S c h e l l h o r n a n d L. J. S p e l l m a n
Table 2: Required Capital Adjustments as a Percent of Bank Equity for Varying Levels of Bank Asset Volatility (Capital-to-Assets Ratio = 4%) Bank Asset Volatility
O"V
.021 .023 .025 .027 .029 .032 .034
Increase Over Base
Gross F D IC Premium
Net F D I C Premium
0% 10 20 30 40 50 60
- 29.9% - 20.7 - 11.3 - 1.7 + 8.0 + 20.5 + 33.2
- 13.3% - 2.7 + 8.2 + 19.2 + 30.4 + 44.6 + 59.1
Notes: The assumed asset value for the representative bank is $25 billion, an approximate average asset value estimate for the four banks during 1987-1988. The base volatility level equals an average asset volatility estimate of .021. The riskfree rate is 7%, an approximate average Treasury bill rate for the same time frame. We assume a deposit insurance contract period of one year.
asset value of this representative bank equaled the average asset value estimate for our sample banks during 1987-1988. The average asset volatility estimate of .021 was used as the base volatility levelJ 7 We increased the asset volatility in increments of 10% to 60%. For the base asset volatility, the capital adjustment required to make the deposit insurance premium of 1987-1988 commensurate with the risk borne by the deposit guarantor was negative for both the gross premium and the net premium. Hence, when asset volatilities were relatively low, the actual deposit insurance premium may have allowed deposit insurance fund reserves to accumulate. When asset volatility is raised by 40%, for example, the required capital injections are 8%, if the gross premium is assumed to apply, and 30.4% assuming the net premium is applicable. This result suggests that, at relatively high asset volatility levels, fund reserves would have been insufficient to cover future losses. Thus, the asset volatility estimates computed with the forward-looking method would have required additional bank capital, provided the volatility persisted at these higher levels. 18
VI. S u m m a r y a n d C o n c l u s i o n We developed a procedure to estimate a bank's forward-looking asset volatility which relies on information in contemporaneous market prices of equity and subordinated debt instead of information in historical stock price volatilities. For 1987-1988, a time period of financial stress in both the equity market and the banking industry, we compared bank asset volatility estimates computed with two
17The average asset volatility estimate of .021 was computed using monthly asset volatility estimates obtained with the forward-looking method for the four banks in 1987-1988. is Wh en the representative bank was insolvent but continued to operate under a policy of forbearance, this qualitative result remains unchanged. Consistent with p = .97, we calculated the required capital infusions for a bank with an asset-to-debt ratio of .97. The amounts of the reqtiired infusions were all positive and substantially higher, even for the base asset volatility level of .021.
Estimates of Bank Asset Volatility
347
alternative methodologies. The clinical results suggest that volatility estimates obtained with the forward-looking method can vary substantially from historicallybased readings. In particular, we found that most asset volatility estimates computed with contemporaneous market prices were, on average, 40% higher than volatilities calculated with historical information. This difference in the estimation results increased to 60% when the banks were perceived to be insolvent. In conclusion, during periods of financial stress in the banking industry, asset volatilities may be higher than previously suggested by historical volatilities, thus necessitating higher risk-based capital in order to protect the deposit guarantor.
The authors wish to thank Ehud Ronn, Douglas Cook, Mark Kazarosian and an anonymous referee. This research was supported in part by the McAllister Centennial Chair for Savings Institutions.
References Black, F. and Cox, J. (May 1976). Valuing corporate securities: Some effects of bond indenture provision. Journal of Finance 31:351-367. Boyle, P. and Ananthanarayanan, A. L. (Dec. 1977.) The impact of variance estimation in option valuation models. Journal of Financial Economics 5:375-387. Burnett, A., Rao, K. S. and Tinic, S. (Oct. 1991.) Subsidization of S & Ls under the fiat-rate deposit insurance system: Some empirical estimates. Journal of Financial Services Research 5:143-164. Cox, J. and Rubinstein, M. (1985.) Options Markets. Englewood Cliffs, N J: Prentice-Hall. Kendall, S. and Levonian, M. (Sept. 1991.) A simple approach to better deposit insurance pricing. Journal of Banking and Finance 15:999-1018. King, K. K. and O'Brien, J. (April 1991.) Market-based deposit insurance premiums: An evaluation. Working Paper, Board of Governors of the Federal Reserve System. Ronn, E. and Verma, A. (Sept. 1986.) Pricing risk-adjusted deposit insurance: An optionbased model. Journal of Finance 41:871-895. Ronn, E. and Verma A. (March 1989.) Risk-based capital adequacy standards for a sample of 43 major banks. Journal of Banking and Finance 13:21-29. Santomero, A. and Chung, E. (Jan. 1992.) Evidence in support of broader bank powers. Financial Markets, Institutions and Instruments 1:1-68. Schwert, G. W. (1990.) Stock volatility and the crash of '87. The Review of Financial Studies 3:77-102. Shaffer, S. (May 1991a.) The impact of premium rates and rebates on the solvency of the FDIC reserve fund: An empirical approach. Proceedings of the 27th Annual Conference on Bank Structure and Competition. Federal Reserve Bank of Chicago, pp. 466-485. Shaffer, S. (Oct. 1991b.) Aggregate deposit insurance funding and taxpayer bailouts. Journal of Banking and Finance 15:1019-1037. Smith, C. (1979.) Applications of options pricing analysis. In Handbook of Financial Economics (J. L. Bicksler, ed.) 79-121. Amsterdam: North-Holland Publishing Company. White, L. J. (1991.) The S & L Debacle: Public Policy Lessons for Bank and Thrift Regulation. New York: Oxford University Press.
Subordinated Debt Prices and ForwardLooking Estimates of Bank Asset Volatility Carolin D. Schellhorn and Lewis J. Spellman
We have estimated the forward-looking bank asset volatility using market prices of bank equity and subordinated debt. This is in contrast to estimation procedures which rely on historical stock price volatilities. Important for bank regulatory policy, we find that, during 1987-1988, a time of financial stress in the banking industry, most bank asset volatility estimates based on contemporaneous market information were on average 40% higher than historically-based readings. Our results suggest that elevated asset volatilities would require higher risk-based capital standards to protect the deposit guarantor.
Keywords: Bank asset volatility; Subordinated debt; Capital standards JEL classification: G21
I. Introduction The value of banks' assets and their volatilities have long been the interest of financial economists and others charged with safeguarding the soundness of the banking industry. But banks' assets are typically not publicly traded. Hence, the unobserved asset values and their volatilities must be estimated with a model which connects these variables to observed data. For this purpose, the option-based methodology developed by Ronn and Verma (1986) has been employed not only for banks [Kendall and Levonian (1991)], but also for savings and loan associations [Burnett et al. (1991)], insurance companies and investment banks [Santomero and Chung (1992)]. The standard procedure relies on the market value of bank equity, and on the historically observed equity price volatility as a proxy for the market's forward-look-
College of Business Administration, Northeastern University, Boston, MA (CDS); Department of Finance, The University of Texas at Austin, Austin, TX (LJS). Address correspondence to: Professor Lewis J. Spellman, Department of Finance, The University of Texas at Austin, Austin, TX 78712.
Journal of Economics and Business 1996; 48:337-347 © 1996 Temple University
0148-6195/96/$15.00 PII S0148-6195(96)00018-5
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C . D . Schellhorn and L. J. Spellman
ing estimate of bank equity volatility. But this constant-volatility assumption has been met with skepticism [Boyle and Ananthanarayanan (1977)]. Our results for the period 1987-1988 cast further doubt on that notion. We have modified the standard procedure for estimating a bank's asset volatility so that the market value of a bank's subordinated debt may be used as one of the observed variables instead of the historical equity price volatility. Both subordinated debt and equity prices impound investors' information regarding the future. Hence, substituting a bank's subordinated debt prices for its historical equity volatility is expected to yield a more accurate reflection of the market's assessment of forward-looking bank asset volatility. We chose 1987-1988 to compute a monthly time series of bank asset volatilities for a clinical study of four banks. During these years, volatility estimates based on forward-looking market information were most likely to deviate from estimates based on historical information because bank failures occurred in record numbers, ~ and investors were likely to sensitively update their pricing of bank assets and asset volatilities. Our clinical evidence for this time period suggests that most asset volatility estimates obtained from contemporaneous market prices were, on average, 40% higher than estimates derived from historical equity volatilities. It has frequently been suggested [White (1991)] that market information should not be ignored in regulating the risk-taking behavior of financial institutions. 2 In this spirit, we calculated, for the minimally capitalized bank, the capital adjustments required to protect the government guarantor from the bank's higher asset volatility levels, given the deposit insurance premium in effect during 1987-1988. Our asset volatility estimates indicate that substantially more bank capital would have been required. T o examine the market's forward-looking pricing of bank asset volatility we modify, in Section II, the basic option-based model by replacing the historical equity volatility with contemporaneous subordinated debt prices. Section III reviews the data and estimation procedures. Section IV compares our estimates of bank asset volatility based solely on contemporaneous price data with those based on some historical data. Section V provides an example of the capital adjustments required to make the higher asset volatilities consistent with the deposit insurance premium of 1987-1988. Section VI offers concluding remarks.
II. The Option-Pricing Model with Subordinated Debt Before presenting the option-based model with subordinated debt, we will summarize the relevant assumptions of the basic Ronn-Verma model (without subordinated debt). The bank's capital structure consists of equity and senior debt. Debt comprises insured deposits and uninsured senior debt. All debt issues are assumed iBy September 1987, the number of bank failures exceeded the 1986 record of 138 (FDIC Annual Report 1987, p. xv). 2Regulators may charge individual banks for the volatility of their asset values by adjusting deposit insurance premiums when capital requirements are uniform, or by setting risk-based capital standards in conjunction with a flat deposit insurance premium. Ronn and Verma (1989) show how their option-based methodology for the computation of risk-adjusted deposit insurance premiums [Ronn and Verma (1986)] may be inverted to obtain risk-based capital standards for a given uniform deposit insurance premium. Currently, both capital requirements and deposit insurance premiums are crudely adjusted for the asset volatility of individual banks.
Estimates of Bank Asset Volatility
339
to have the same term to maturity, and the banks are audited at the end of one year at zero cost. The audit time coincides with the maturity of the bank's debt and with the expiration of the call option on the bank's assets. At the audit date, forbearance could be provided to the bank in that the insurer would tolerate a deterioration in the market value of the bank's assets, but only as long as the asset value did not fall below a fixed proportion p of the present value of its total debt. 3 Finally, there is no deposit-insurance uncertainty, and, hence, the interest rate on the bank's insured senior debt (deposits) equals the riskfree rate. In order to clarify the notation used in the following discussion, let V = the market value of the bank's assets including taxes or subsidies which result from deposit-insurance mispricing; E = the market value of the bank's equity; B = the maturity value of the bank's total zero-coupon debt; crv = the standard deviation of the rate of return on the value of the bank's assets per unit of time; ~rE = the standard deviation of the rate of return on the bank's equity per unit of time; r = the riskfree interest rate per unit of time; T = the time until the next regulatory bank audit; N(.) = the cumulative normal density function. In the basic model there is both insured and uninsured senior debt but no junior debt. An equity call formulation results in the following equations:
(ln(V/pB)+(r+~,2/2)T} E
=
_ e_rrpBN(In(V/pB) + (r- ~,2/2)T' ~,f~
(1)
E °'v = °rE
[ In
(V/pB) + (r +
~,2/2)T'
(2)
Be-rT,
p and T are assumed policy variables and the face value of total deposits, is observed on the bank's books. E and r are observed in the market, but the market value of the bank's assets and the market's estimates of the future volatilities of bank assets and equity are unobservable. This leaves three unknowns (~rE, o"v, and V) with but two equations. When the historical equity price volatility proxies for o-E, in order to allow solution for the forward-looking asset volatility, it is assumed that the historical price volatility will prevail in the future. The following sections will compare these asset volatility estimates with those derived from contemporaneous subordinated debt (and equity) prices. The use of subordinated debt prices requires the modification of some assumptions made in the basic model. In the augmented model, the bank's capital
]9 is a positive number that, when equal to 0.97, in Ronn and Verma (1986) yielded an aggregate deposit-insurance premium weighted average of approximately 1/12 of one percent.
340
C.D. Schellhorn and L. J. Spellman structure comprises equity, senior and subordinated zero-coupon debt. Subordinated debt is substituted for the uninsured senior debt at maturity values, and all debt issues are assumed to have the same time to maturity. All senior debt is insured by a riskless guarantor. In the general case of no forbearance, a bank is declared insolvent when, at the end of the time interval T, the asset value is less than the value of total bank liabilities. In this case, senior debt holders are paid off by the deposit insurer who, in effect, has written a put option purchased by the bank's owners. Subordinated debt holders receive any residual which may remain. Alternatively, the deposit insurer may allow the bank to operate with a negative capital position, i.e., with an asset-to-debt ratio less than one. A p value less than one effectively lowers the closure threshold and represents a policy of forbearance. 4 When the uninsured portion of the senior debt in the basic model is replaced with subordinated debt subject to the constraint that total end-of-period leverage is constant, the following additional variables are defined: Dj = the market value of the bank's subordinated (junior) zero-coupon debt; Bs = the maturity value of the bank's senior zero-coupon debt (deposits). The valuation equation for subordinated debt equals the difference between two call options. 5 In order to adjust the model so that it allows for forbearance, subordinated debt holders are viewed as receiving a call option from the FDIC with exercise price equal to the minimum of pB and the maturity value of the senior debt, B s, while subordinated debt holders sell a call option to equity holders with exercise price equal to the maturity value of the bank's total debt, B. Hence, equation (3) is written to allow for a relaxation of the closure rule:
[ {ln(V/Min[pB, Bs])+(r+~,2/2)T) =V N ~,~/~ {ln(V/B)+(r+ -N
-
~,2/2)T ) ]
°'vV~
e -~T Min[ pB, B~]N[ ln(V/Min[ pB,
B~])
+ (r - %2/2)T
Vvf-T + e_~rBN [ In(V/B) + (r -
~,2/2)T
(3)
4Conversely,closure with p > 1 implies a regulatory policyof early intervention. 5The valuation equation for subordinated debt is derived in Black and Cox (1976) and Smith (1979). Cox and Rubinstein (1985) show that the subordinated debt value equals the difference between two call options:
D~= C(V; B~) - C(V; B). This representation illustrates particularlywell the junior position of subordinated debt holders relative to senior debt holders, and their simultaneous seniority relative to equity holders.
Estimates of Bank Asset Volatility
341
The use of equation (3) introduces a new variable, Dj, but eliminates the variable trE from the simultaneous estimation of V and o-v. Dj is observed in the market, but investors' forward-looking estimate of trE is not.
IlL
Data and Methodology
This section describes the data and procedures used for the estimation of asset volatilities under both the basic and the augmented models. Four firms from the group of the 100 largest bank holding companies met the following restrictive criteria: For each firm, all subordinated debt issues outstanding during 1987 and 1988 had to be publicly traded and priced in Standard and Poor's B o n d Guide. To obtain improved forward-looking asset volatility estimates with market prices of securities which approximated as closely as possible the theoretical assumptions of the options-pricing model, banks were excluded from our clinical study if any of their subordinated debt issues had conversion or sinking-fund features. Subordinated debt issues were required to be non-callable or, if they did have call features, to sell for no more than 100 basis points above par. For debt issues which were priced slightly above, at, or below par, the call feature was assumed to be of negligible value. 6 Using monthly data, we computed the market value of subordinated debt outstanding for each bank from March 1987 to December 1988. Bank equity prices and equity rates of return were obtained from the CRSP Daily Return tapes] M o o d y ' s B a n k and Finance M a n u a l provided face values for individual subordinated debt issues. The book value of total liabilities was taken from the Quarterly Industrial Compustat Tapes. We subtracted the total face value of a bank's subordinated debt from the book value of its total liabilities to obtain an estimate of the face value of its senior debt. Because, for banks, the senior debt consists primarily of deposits which are instantaneously puttable, the face value of the senior debt was assumed to equal its market value, Ds. 8 Finally, we assumed the time to maturity of the banks' debt, i.e., the length of the deposit insurance contract period, to equal one year. As outlined in Section II above, we computed solutions for asset value, 1/1, and asset risk, o-v, using two different methods. 9 The first method requires stock market prices and historical volatilities of equity returns to solve equations (1) and
6Only four of the top 100 bank holding companies satisfied all the above requirements for the period 1987-1988: AmSouth had one subordinated debt issue due in 1999 which was not listed on any exchange. Barnett Banks had two subordinated debt issues with maturity dates in 1996 and 1999, respectively, both listed on the New York Bond Exchange. Two unlisted subordinated debt issues, due in 1997 and 1999, respectively, were outstanding for First Interstate. KeyCorp. had one unlisted subordinated debt issue with a maturity date in 1999. 7In order to estimate the equity volatility for a particular end-of-monthdate, daily equity returns for three months (two months preceding the month in question) were collected. Using the SAS procedure MEANS, the variance of the distribution of daily equity returns was calculated based on this sample of historical data. The square root of this variance estimate was then multiplied by the square root of 250 to obtain the annualized standard deviation of the distribution of daily equity returns. 8For the value of the senior debt at maturity, Bs, this implies that B s = Dse rr. 9In order to solve the system of nonlinear equations, we used subroutines, NEQNF and ANORDF of the International Mathematical and Statistical Library (IMSL), Version 10.1.
342
C.D. Schellhorn and L. J. Spellman (2), a n d thus c o m p u t e s t h e e s t i m a t e s of V a n d trv which R o n n a n d V e r m a w o u l d have o b t a i n e d for e a c h m o n t h in 1987 a n d 1988. This m e t h o d will be r e f e r r e d to as " b a c k w a r d - l o o k i n g " , b e c a u s e historical equity volatilities a r e e m p l o y e d . 1° T h e s e c o n d m e t h o d is called " f o r w a r d - l o o k i n g , " b e c a u s e it solves e q u a t i o n s (1) a n d (3) for t h e s a m e two unknowns, using only c o n t e m p o r a n e o u s m a r k e t prices o f s u b o r d i n a t e d d e b t a n d equity. 11
IV. Clinical Evidence T o e s t i m a t e f o r w a r d - l o o k i n g b a n k a s s e t volatilities with the two p r o c e d u r e s described above, we chose t h e t i m e f r a m e 1987-1988 b e c a u s e the e x t r a o r d i n a r y n u m b e r o f b a n k failures in this p e r i o d m o s t likely t r i g g e r e d price r e a c t i o n s in the m a r k e t for b a n k assets. This t i m e p e r i o d also e n c o m p a s s e s the stock m a r k e t crash of O c t o b e r 1987, an e v e n t which has b e e n shown to e l e v a t e historical e s t i m a t e s o f equity volatilities for several consecutive m o n t h s . 12 F i g u r e 1 displays a n n u a l i z e d equity volatilities e s t i m a t e d over a 90-day lagged p e r i o d for the f o u r c o m m e r c i a l b a n k s d u r i n g 1987 a n d 1988.13 T h e t i m e series for each b a n k shows very similar o r d e r s o f m a g n i t u d e a n d p a t t e r n s o v e r time. Just p r i o r to t h e stock m a r k e t crash in O c t o b e r 1987, the b a n k s ' volatilities surged roughly b e t w e e n 60% a n d 200%, l i n g e r e d for a while, t h e n b e g a n to d e c l i n e a n d r e a c h e d p r e - c r a s h levels by t h e e n d o f M a r c h 1988. T o e x a m i n e how t h e use o f t h e s e historical equity volatilities affects e s t i m a t e s o f f o r w a r d - l o o k i n g asset volatility, we c o m p a r e d the e s t i m a t e s using b a c k w a r d - l o o k i n g data, ~r~, with t h o s e d e r i v e d f r o m f o r w a r d - l o o k i n g prices, ~rvf. R e c a l l t h a t the b a c k w a r d - l o o k i n g a p p r o a c h to t h e e s t i m a t i o n o f b a n k asset volatility uses b o t h the historical b a n k equity volatilities as well as the f o r w a r d - l o o k i n g b a n k equity prices. F i g u r e s 2 a - 2 d p l o t t h e O-vb a n d the crf e s t i m a t e s for each bank. T h e t i m e profiles o f the ~rvb e s t i m a t e s r e s e m b l e t h o s e of t h e historical b a n k equity volatilities d e p i c t e d in F i g u r e 1, p a r t i c u l a r l y for A m S o u t h in F i g u r e 2a a n d for First I n t e r s t a t e in F i g u r e 2c.
1°The sum of equity market value and total debt market value was used as the initial estimate for V. The historically-based ~E was scaled down by the leverage ratio to obtain the initial estimate for crV. 1Differences in the results computed from the two methods may arise not only from the difference between forward-looking and historical market information, but also from a difference in the way some of the underlying Black-Scholes assumptions (which do not always correspond to reality) influence either procedure's computational results. Some caveats regarding the application of the Black-Scholes option-pricing model to the valuation of contingent claims on a bank's assets include: i) While the bank's asset value is assumed to follow a random walk in continuous time, the stochastic process of the asset value may, in fact, be mean-reverting rather than random. (The authors thank Rex Thompson for pointing this out.) ii) The assumption that the variance of the instantaneous return on assets is constant at a point in time with the variance rate being proportional to the square of the asset value, constrains the bank's risk-taking behavior to remain unchanged during a given insurance period, iii) Information may be asymmetric. King and O'Brien (1991) identified typical assumptions which deviate from actual regulatory policy: iv) Regulators audit a bank at the end of one year, and v) the discovery of an insolvency is immediately followed by the decision to invoke receivership. These two assumptions are inconsistent with regulatory policies of forbearance and early intervention. 12For instance, Schwert (1990) reported that the 1987 stock market crash contained the largest one-day percent price change in a data set reaching back to 1885, and that the volatility of the S & P500 increased in late October 1987, and returned to normal levels by April 1988. 13In this section, the term "volatility" refers more specifically to the standard deviation of a given return distribution.
Estimates of Bank Asset Volatility
343
0.6 0.5 -
0.4
.....
Std. Dev. 0.3
Amsouth Barnett
. . . . . . . . . First Int.
0.2
....
0.1 0 ,
-
:
:
t
:
:
;
:
:
:
:;
:
; : :
;
;
:
:
:
:
:
Key Corp.
:
Figure 1. Annualized historical volatility of daily returns on equity for sample banks (January 1987 to December 1988).
In order to compare o-rf to o-b in the absence of the extreme price volatilities associated with the stock market crash, we created three sub-periods and isolated the period from October 1987 through March 1988. The period before the stock market crash, from March 1987 to September 1987, is identified as sub-period I. The time period during and shortly after the crash, extending from October 1987 to March 1988, is referred to as shock sub-period II. Subperiod III covers the time after the effect of the stock market crash had subsided, around April 1988 to December 1988. Comparisons of the ratio of estimated asset volatilities, O'v/trv, f b are summarized in Table 1. The mean volatility ratio for the four banks during the non-shock sub-periods (I and III) is 1.393, indicating that the estimates computed with the forward-looking method exceed those generated with the backward-looking method by almost 40%. During the shock sub-period, both methods produced the same higher asset volatility estimates. The virtual parity in the magnitude of the results is borne out by a mean asset volatility ratio of .986. Whereas the stock market crash impacted bank asset volatility estimates during the shock sub-period, during the non-shock sub-periods, investors' expectations regarding bank asset values and volatilities were likely shaped by the solvency crisis in the depository industry. The late 1980s saw a record number of bank and thrift failures and, in March 1987, the G A O declared the FSLIC insolvent. Banks at, or near, insolvency have a strong incentive to increase asset risk. Hence, a heightened anticipation of moral hazard might have raised the market's assessment of future bank asset volatilities. 14 To examine the influence of insolvency on forward-looking estimates of bank asset volatility, apart from the influence of the stock market crash, we compared average asset volatility ratios by the bank's solvency state during the non-shock sub-periods. The results reveal that trY dominates trb on
14Another reason security prices of insolvent banks are likely to reflect relatively high asset volatilities is a lack of credible information, which is typical for a bank threatened by a regulatory receivership decision. Firms in financial difficultyhave an incentive to delay the release of bad news which increases the uncertainty for investors in the market.
~-/
- \ / \ ,~
i
/
~
\!'
~/ \ \\
I
\I
(c)
~
.
-
~
/ /\
.....
_ _
trv.f
_ o,V f
0.01
Std. Dev. 0.02
0.03
0.04
0.01
Std. Dev. 0.02
0.03
0.04
\
i
q
)
t
(d)
i
; 2 , ,, J',
¢\ \
(b)
,,',,
Figure 2. Annualized asset volatilities for January 1987 to December 1988 for (a) Amsouth; (b) Barnett Banks; (c) First Interstate; and (d) Key Corp.
Std. Dev. 0.01
0.02
(a)
~
....
,,
°°;t ..... , .........
'~q~
-
I
s,~.o,,.o.o,i ,,/! \.. o.o,y-.qy,<--~.,%_
0.04
0.05
0.06
. . . . .
.....
~r V
avf
~J
l::r o
~r t~
©
345
Estimates of Bank Asset Volatility
Table 1: Mean Asset Volatility Ratios (~rfe/~r~.) for Sample Banks, March 1987-December 1988 Bank AmSouth Barnett First Int. Key Corp. All Banks
Shock Sub-Period
Non-Shock Sub-Periods
.802 .960 .937 1.243 .986
1.565 1.093 1.508 1.407 1.393
Note: Asset volatilities were estimated using the backward-lookingand forward-lookingmethods described in Section IlL
average by 60% w h e n e v e r a b a n k is perceived to be insolvent, as o p p o s e d to 16% when the b a n k is considered solvent. 15 T h e divergence o f the estimation results from the two methodologies during 1987-1988, particularly for the non-shock sub-periods, indicates that bank asset volatilities can be considerably higher than suggested by the backward-looking method. If, u n d e r conditions o f financial stress in the banking industry, asset volatilities are indeed higher than previously believed, then the higher asset volatility estimates would require c o m m e n s u r a t e adjustments in b a n k regulatory capital standards.
V. I m p l i c a t i o n s for R i s k - B a s e d Capital R e q u i r e m e n t s B a n k asset volatility impacts the exposure of the federal deposit g u a r a n t o r to an u n f u n d e d contingent liability. F o r a given deposit insurance premium, higher asset volatilities require additional b a n k capital to protect the guarantor. T h e actual deposit insurance p r e m i u m paid by banks varied between 1950 and 1990, depending on the size o f rebates r e m a n d e d as required by law. W i t h o u t rebates, the gross F D I C p r e m i u m equaled 8.33 basis points. However, with rebates, the net deposit insurance p r e m i u m has b e e n approximately four basis points over prior decades [Shaffer (1991a, b)]. ~6 O u r estimates of the capital infusions necessitated by higher b a n k asset volatility levels for the gross and net p r e m i u m s are shown in Table 2. W e examined the implications for risk-based capital standards which result f r o m higher asset volatilities by calculating the capital infusions which are required for a bank which initially complies with the m i n i m u m 4% capital-to-assets ratio. The
15In the interest of brevity, these results are reported in an appendix which is available from the authors upon request. 16While the gross premium remained flat at 8.333 basis points until 1988, the FDIC was required by law to provide a rebate from 1950 until the FDIC Assessment Rate Act of 1990 [Shaffer (1991a,b)]. As long as the FDIC reserve fund had not fallen below 1.1% of insured deposits, mandatory rebates equals 60% of net assessments (gross assessments net of operating expenses and insurance losses). This requirement led the agency to refund, on average, more than half its gross premium income during the years 1950-1980. In addition, until 1987, the gross assessment covered not only current losses but accumulated reserves for future losses so that the insured banks paid an effective rate of approximately four basis points. Net assessments were negative in 1987 and 1988, as insurance losses and expenses exceeded gross assessments so that no credits were remanded for these two years (GAO Report of April 1989). Nevertheless, based on past experience, the net deposit insurance premium is set to equal four basis points.
346
C. D. S c h e l l h o r n a n d L. J. S p e l l m a n
Table 2: Required Capital Adjustments as a Percent of Bank Equity for Varying Levels of Bank Asset Volatility (Capital-to-Assets Ratio = 4%) Bank Asset Volatility
O"V
.021 .023 .025 .027 .029 .032 .034
Increase Over Base
Gross F D IC Premium
Net F D I C Premium
0% 10 20 30 40 50 60
- 29.9% - 20.7 - 11.3 - 1.7 + 8.0 + 20.5 + 33.2
- 13.3% - 2.7 + 8.2 + 19.2 + 30.4 + 44.6 + 59.1
Notes: The assumed asset value for the representative bank is $25 billion, an approximate average asset value estimate for the four banks during 1987-1988. The base volatility level equals an average asset volatility estimate of .021. The riskfree rate is 7%, an approximate average Treasury bill rate for the same time frame. We assume a deposit insurance contract period of one year.
asset value of this representative bank equaled the average asset value estimate for our sample banks during 1987-1988. The average asset volatility estimate of .021 was used as the base volatility levelJ 7 We increased the asset volatility in increments of 10% to 60%. For the base asset volatility, the capital adjustment required to make the deposit insurance premium of 1987-1988 commensurate with the risk borne by the deposit guarantor was negative for both the gross premium and the net premium. Hence, when asset volatilities were relatively low, the actual deposit insurance premium may have allowed deposit insurance fund reserves to accumulate. When asset volatility is raised by 40%, for example, the required capital injections are 8%, if the gross premium is assumed to apply, and 30.4% assuming the net premium is applicable. This result suggests that, at relatively high asset volatility levels, fund reserves would have been insufficient to cover future losses. Thus, the asset volatility estimates computed with the forward-looking method would have required additional bank capital, provided the volatility persisted at these higher levels. 18
VI. S u m m a r y a n d C o n c l u s i o n We developed a procedure to estimate a bank's forward-looking asset volatility which relies on information in contemporaneous market prices of equity and subordinated debt instead of information in historical stock price volatilities. For 1987-1988, a time period of financial stress in both the equity market and the banking industry, we compared bank asset volatility estimates computed with two
17The average asset volatility estimate of .021 was computed using monthly asset volatility estimates obtained with the forward-looking method for the four banks in 1987-1988. is Wh en the representative bank was insolvent but continued to operate under a policy of forbearance, this qualitative result remains unchanged. Consistent with p = .97, we calculated the required capital infusions for a bank with an asset-to-debt ratio of .97. The amounts of the reqtiired infusions were all positive and substantially higher, even for the base asset volatility level of .021.
Estimates of Bank Asset Volatility
347
alternative methodologies. The clinical results suggest that volatility estimates obtained with the forward-looking method can vary substantially from historicallybased readings. In particular, we found that most asset volatility estimates computed with contemporaneous market prices were, on average, 40% higher than volatilities calculated with historical information. This difference in the estimation results increased to 60% when the banks were perceived to be insolvent. In conclusion, during periods of financial stress in the banking industry, asset volatilities may be higher than previously suggested by historical volatilities, thus necessitating higher risk-based capital in order to protect the deposit guarantor.
The authors wish to thank Ehud Ronn, Douglas Cook, Mark Kazarosian and an anonymous referee. This research was supported in part by the McAllister Centennial Chair for Savings Institutions.
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