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FRBSF

WEEKLY LETTER

May 22,1987

Regulating Bank Capital
Over the past several years, greater emphasis
has been placed on increasing bank capital
through regulation. For example, the three
federal bank regulatory agencies have raised
capital requirements for banks and bank holding
companies and established more uniform standards. Most recently, the federal bank regulatory
agencies have put forth proposals for risk-based
capital requirements to be coordinated with the
Bank of England.

capital standards alone would not give a bank
more of an incentive to increase the riskiness of
its assets. Instead, the incentive to increase asset
risk falls as a bank's capital increases. This finding implies that, as long as regulatory and supervisory efforts to limit asset risk (such as bank
examinations) are not relaxed, increasing a
bank's capital will lower the bank's chance of
failure and reduce the expected liability of the
deposit insurance system.

These regulatory measures, in part, reflect concern over the rising risk exposure of the deposit
insurance system. With the sharp rise in bank
failures in recent years, the Federal Deposit
Insurance Corporation's (FDIC's) expenses,
which ranged from about $50 million to $200
million per year in the 1970s, rose to about $2
billion per year in 1985 and 1986. More stringent capital regulation in response to these
developments is based on the presumption that
higher bank capital (equity) relative to assets can
insulate the deposit insurance fund from fluctuations in bank earnings. With more capital relative to assets (lower leverage) and a given
riskiness of assets, a bank would be less likely to
fail; even if it were to fail, the failure would
impose smaller losses on the deposit insurance
fund.

Heads I win ...
Bank risk depends on the bank's capital position
(leverage) and the riskiness of its assets. Under
the deposit insurance system in the U.s., a
bank's insurance premium rate is fixed and
therefore unrelated to risk. Moreover, as long as
insured depositors are confident about the
viability of the deposit insurance system, they
will be willing to lend to a bank at an interest
rate that does not vary with the bank's risk since
their funds are insured. As a result, a bank can
benefit at the expense of the deposit insurance
system by increasing its leverage and/or asset
risk.

The move to more stringent capital standards in
banking, however, has met with considerable
controversy as well as some skepticism. The
popular view seems to be that higher capital
requirements will cause banks to invest in riskier
assets in an attempt to maintain a given rate of
return on equity. Such a response by banks
could subvert the goals of capital regulation
since riskier assets would be associated with a
greater likelihood of bank failure and a larger
liability for the deposit insurance fund, all other
things equal.
The central issue in bank capital regulation,
then, is whether banks would respond to higher
regulatory capital requirements by choosing
riskier assets to offset or even more than offset
the desired effects of higher capital.
In this Letter, we address this issue and find that,
in contrast to the popular view, more stringent

The situation is essentially one of "Heads I win;
tails you lose." When a bank is lucky and its
assets have high realized returns, the bank can
increase its earnings by leveraging risky assets.
However, when the same bank is unlucky and
fails because the realized asset returns are insufficient to meet obligations to depositors and
debtholders, the bank can shift losses that
exceed its capital to the deposit insurance
system.
Under these circumstances, the bank owners'
losses would be limited to their investment in
the bank when the bank fails regardless of the
extent of their promised liabilities to depositors
and other debtholders, whereas all the gains
from risk-taking would go to the owners when
the bank does not fail. Thus, a bank acting in the
best interest of its stockholders to maximize the
value of their stock has an incentive to risk
failure.
Deposit insurance as an option
The connection between the value of the deposit
guarantee and risk was developed formally by

FRBSF
economist Robert Merton. Merton has shown
how the value of the deposit insurance guarantee can be related to leverage and asset risk
using an options-pricing formula developed by
economists Fisher Black and Myron Scholes for
the valuation of stock options.
A put option for a particular stock, for example,
is a contract that gives the purchaser the right,
but not the obligation, to sell a certain number
of shares of the stock to the seller of the option
at a predetermined exercise price. The purchaser
of the option would exercise the option only if
the market price of the stock were lower than
the option's exercise price. The options-pricing
formula developed by Black and Scholes is a
mathematical way of calculating how much a
particular stock option is worth (that is, the
option's price). The value of a put option is
negatively related to the current price of the
stock, and positively related to the variation in
the stock's rate of return (that is, its risk), the
exercise price, and the time to maturity of the
agreement.
In Merton's adaptation of the stock option formula to deposit insurance, the bank is viewed as
"purchasing" an option from the deposit insurance system to sell ("put") its assets to the system at a price equal to the value of the bank's
insured deposits, which, for simplicity, we
assume represent all bank liabilities. The bank
would exercise this option only when its assets
are worth less than its liabilities - that is, when
it is insolvent. The value of the deposit guarantee to the bank is negatively related to the value
of the bank's assets, and positively related to the
variation in the rate of return on the bank's
assets (asset risk), the. level of insured deposits,
and the time interval between bank examinations. (In applying the formula to deposit insurance, the value of the bank's assets replaces the
stock price, the variation in the value of the
assets substitutes for the variation in the stock
price, the value of the insured deposits corresponds to the exercise price, and the examination interval is used in place of the time to
maturity of the option contract.)
This options pricing formula indicates that the
value of the deposit insurance guarantee

increases as the bank's leverage (the ratio of its
assets to invested capital) declines, or as the
variability of the bank's return on assets (asset
risk) increases. The reason is that an increase in
either leverage or the riskiness of assets makes it
more likely that the option will be exercised.
Thus, a bank not required to pay the full value of
the option could increase the value of its own
stock by increasing leverage and/or asset risk if
allowed to do so by regulators.

Asset risk and the deposit guarantee
The effects of varying leverage and asset risk on
the value of the deposit guarantee and hence the
value of the bank are illustrated graphically in
the figure using the options pricing formula. For
purposes of the figure, the initial assets of the
bank (excluding the value of the deposit insurance guarantee) are arbitrarily set at $1 million.
We also assume that the bank pays a deposit
insurance premium of 1!T2th of a percent of
deposits (the statutory rate).
In the figure, for a given level of leverage (staying on any given line), it is evident that the value
of the deposit insurance guarantee to the bank
rises as asset risk increases. Similarly, for any
given level of asset risk, increasing leverage by
increasing deposits relative to initial assets (moving vertically from one line up to the next) also
increases the value of the deposit insurance
guarantee. Thus, a bank can increase its stockholder's wealth by increasing either asset risk or
leverage, if permitted to do so.

The incentive to increase risk
Of key importance to the issue of capital regulation, however, is the observation that the incentive (the increase in value for a given change in
risk) to increase asset risk declines as leverage
declines. In graphical terms, for a given asset
risk (standard deviation), the slopes of the lines
become less steep as leverage declines.
Put another way, as the capital of an insured
bank increases, the bank's incentive to increase
asset risk falls. Thus, banks with the lowest capital ratios are those that have the greatest incentives to take on risky asset portfolios. Such
banks, therefore, pose the gravest threat to the
deposit insurance fund.

Net Value of the Deposit Insurance Guarantee
for a Bank with $1, 000, 000 in Assets

Dollars

140,000

Deposits:
$950,000__________

••••.•
•.••.•••
$900,000~~..••.•••.•.••••.

120,000
100,000

:~gg.ggg~/:::/

80,000

::.::~<:::~:;~:;;~:;~;;:;::.:::::>/
0.06

0.12

0.18

0.24

0.30

0.36

0.42

asset risk before capital requirements were
increased, they certainly would be sufficient to
do so afterward.
With more capital, banks would have less of an
incentive to evade regulatory restrictions on
asset risk. Consequently, as long as regulators do
not react to lower leverage (higher capital)
requirements by relaxing regulatory and supervisory efforts (through reduced bank examinations, for example) to limit asset risk, banks will
not increase the riskiness of their assets. As a
result, the risk exposure of the deposit insurance
fund consequently will decline.

Standard Deviation of Rate-of-Return on Assets

Conclusions
These results, based on the options-pricing formula, also may be derived from another framework known as the state-preference model. A
number of economists have used the state-preference model to show that with underpriced
deposit insurance, banks will try to maximize
leverage and/or asset risk. In an article in this
Bank's Spring 1987 Economic Review, we
extend the state-preference framework to show
that it also implies that the incentive to increase
asset risk declines as leverage declines.

Currently, deposit insurance premiums are unrelated to bank risk, which depends on both leverage and asset risk. Moreover, insured depositors
are not concerned with bank risk-taking and are
willing to lend to banks at a risk-free rate since
their deposits are insured. Under such a system,
banks can benefit by increasing asset risk and/or
by increasing leverage. As a result, some degree
of capital regulation is needed to limit the liability of the deposit insurance fund. Similarly, for
any given degree of leverage, the expected liability of the deposit insurance system can be
lowered by reducing asset risk.

Capital regulation
The fact that the incentive to increase asset risk
falls as capital increases (leverage declines)
means that more stringent capital requirements
would not give banks more of a reason to invest
in riskier assets. On the contrary, it would give
them less of an incentive to do so. Therefore, if
regulatory efforts were sufficient to constrain

The analysis in this Letter indicates that regulatory increases in capital standards will not
require greater efforts to restrain asset risk. On
the contrary, the incentive to increase asset risk
declines as capital increases. Thus, regulatory
efforts to raise capital in banking would not by
themselves lead to more risky asset portfolios.

Michael C. Keeley and Frederick T. Furlong

Opinions expressed in this newsletter do not necessarily reflect the views of the management of the Federal Reserve Bank of San
Francisco, or of the Board of Governors of the Federal Reserve System.
Editorial comments may be addressed to the editor (Gregory Tong) or to the author •... Free copies of Federal Reserve publications
can be obtained from the Public Information Department, Federal Reserve Bank of San Francisco, P.O. Box 7702, San Francisco
94120. Phone (415) 974-2246..

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BANKING DATA-TWELFTH FEDERAL RESERVE DISTRICT
(Dollar amounts in millions)

Selected Assets and Liabilities
Large Commercial Banks
Loans, Leases and Investments 1 2
Loans and Leases 1 6
Commercial and Industrial
Real estate
Loans to Individuals
Leases
U.S. Treasury and Agency Securities 2
Other Secu rities 2
Total Deposits
Demand Deposits
Demand Deposits Adjusted 3
Other Transaction Balances4
Total Non-Transaction Balances 6
Money Market Deposit
Accounts-Total
Time Deposits in Amounts of
$100,000 or more
Other Liabilities for Borrowed MoneyS
Two Week Averages
of Daily Figures

Amount
Outstanding

Change from 4/30/86
Dollar
Percent?

Change
from

4/29/87

4/22/87

204,711
182,739
53,818
67,722
37,182
5,413
14,717
7,255
207,317
53,815
49,664
19,578
133,924

-

-

-

0.1
1.8
0.0
1.9
- 8.9
4.2
35.0
- 8.1
0.6
2.3
2.8
24.0
2.6

-

1,293

-

2.7

5,204
6,764

-

14.0

- 23.4

-

44,915

-

533

31,967
22,029

26

-

- 2,992

-

Period ended

4/20/87

-

-

-

-

-

-

-

Penod ended

4/6/87

Reserve Position, All Reporting Banks
Excess Reserves (+ }/Deficiency (-)
Borrowings
Net free reserves (+ }/Net borrowed( -)

89
72
17

9
9
1

Includes loss reserves, unearned income, excludes interbank loans
Excludes trading account securities
Excludes U.s. government and depository institution deposits and cash items
ATS, NOW, Super NOW and savings accounts with telephone transfers
S Includes borrowing via FRB, TT&L notes, Fed Funds, RPs and other sources
6 Includes items not shown separately
7 Annual ized percent change
1
2
3
4

-

301
3,485
40
1,306
3,676
240
3,823
641
1,359
1,218
1,398
3,802
3,661

505
747
434
359
34
14
206
36
2,549
968
932
1,250
331

-