1.1.1.1 Equity Value Change
E = – [3 – (0.901)] $500 million (0.0050 / 1.12) = –$4,687,500.
To find the percentage change in equity, divide both sides of the equation by E:
E = $500 million (1-0.90) or E = $50 million so that:
E/E = – [3 – (0.901)] ($500 million/$50 million) (0.0050 / 1.12) = – 9.375% or E/E may
be more simply found as -$4,687,500 / $50,000,000 = -9.375%.
Changes in the value of equity for different duration gaps
Recall that duration measures the value change of the assets or liabilities for a given interest rate
change. If we assume similar rate changes for assets and liabilities then the following
generalizations can be made:
Duration Gap
Interest Rate
Change
Biggest Value
Change
1.2 Equity
Value
Positiv
e
2 Increas
e
Assets Decreases
Decrease Assets Increases
Negative Increase Liabilities Increases
Decrease Liabilities Decreases
Both asset and liability values for fixed income contracts increase when rates fall and decrease
when rates rise. However, for a positive duration gap the absolute value of the change in value
of the assets is greater than the change in value of the liabilities when interest rates change. With
a negative duration gap the change in value of the liabilities will be larger in absolute terms than
the change in value of the assets.
Teaching Tip: The duration of a variable rate contract may be thought of as the time until the rate
reset. This will typically be much shorter than the maturity. Thus, a 30 year mortgage with a
rate adjustment due in 6 months has a 6 month duration. Contracts with a maturity of 3 months
or less may be thought of as having a duration equal to their maturity without substantively
affecting the analysis. This simplifies the duration calculations for many accounts.
If the bank has a positive duration gap and is forecasting rising rates, they may wish to switch to
shorter term assets and/or variable rate assets and try to lengthen the duration of the liability
portfolio. Alternatively, the off balance sheet tools discussed in Chapter 23 could be used. If the
leverage adjusted duration gap is zero, the equity value will be approximately unchanged for
small changes in interest rates.
Problems with the duration model include:
Duration matching can be time consuming and costly. Although this is still true, with
today’s computing power this criticism is less valid than in the past.
Immunization (setting and keeping the duration gap at zero) is a dynamic process. The
durations of the assets and liabilities will change every time interest rates change and will
change at uneven rates over time (the duration formula is not linear with respect to time).
This implies that maintaining a given duration gap requires frequent on or off balance
sheet adjustments, and implies that trading costs have to be weighed against the benefits
of duration management.
Immunization does not provide protection for large interest rate changes due to convexity
because duration predicts a linear price change with respect to interest rates. In actuality
the capital loss associated with a given percentage interest rate increase is less than the
capital gain associated with a given interest rate decrease. Duration thus overpredicts
capital losses and underpredicts capital gains because of convexity.
Teaching Tip: The duration model can cause bankers to become complacent about the interest
rate risk they face. Aside from convexity, which can be a significant problem in an abnormal
market, the duration model suffers from many of the same problems as the RPM. For instance,
the effects of defaults, prepayments, and call features of securities are difficult to include in the
duration calculations. This can lead to the belief that the bank precisely knows its risk level
when in fact a large interest rate move that changes investor behavior is not incorporated into the
model.1
1. Insolvency Risk Management
a. Capital and Insolvency Risk
Equity is the FI’s main cushion against insolvency. It also serves as a source of funds and as a
requirement for growth given the minimum capital to asset requirements in force for DIs. Equity
can be thought of as either the book value of assets minus the book value of liabilities, with
some adjustments allowed by regulators, or as the market value of assets minus the market
value of liabilities. Book values are only rarely accurate representations of market values.
Teaching Tip: Book values are not necessarily good representations of liquidation values either.
It is not clear to this author exactly what book value of equity actually measures. It is roughly
the sum of past decisions on asset acquisitions less the face amount borrowed. As such it appears
to be roughly a measure of net sunk costs by managers. It has the advantage of being calculated
according to a set of rules that limit management’s ability to manipulate equity value, and it
provides a fairly predicable number on a day to day basis. For those who remember their
economics training, this very stability implies that the book value of equity cannot be a fair
representation of the ongoing day to day value of the firm in a dynamic marketplace.
The Capital Purchase Program (CPP) was part of the TARP funding in 2008-2009. The
Treasury purchased over $200 billion of senior preferred equity under the program. These
purchases qualified as Tier 1 capital for FIs. Citigroup and Bank of America received additional
special funding under this program totaling $25 billion and $20 billion respectively. The CPP
was designed to help FIs increase their capital with the aim of increasing lending to the general
public. Lending fell in 2008, 2009 and 2010, so in this sense the program was a failure, although
presumably lending would have fallen even farther without it and more failures may have
occurred. The program came with stipulations on maximum executive pay, golden parachutes
and clawback provisions on executive pay based on earnings and limits on tax deductions
1This is a false precision problem. VAR suffers from similar criticisms, as the failure of Long
Term Capital Management showed.
associated with executive compensation.
Capital and credit risk:
Loan losses are written off against capital. As loans are marked to market, capital is reduced.
When enough loan losses eliminate all the existing equity, the institution is insolvent.
Capital and interest rate risk:
Realized losses in value of securities and loans are also written off against capital. If losses due
to rising interest rates (net of the reduced value of liabilities) are large enough to wipe out the
FI’s capital, the institution becomes insolvent.
Market value accounting and insolvency
If regulators closed an institution as soon as its market value of capital became zero, theoretically
no liability holders or taxpayers would suffer any losses and the FDIC’s DIF would never be
required. This is not the case if regulators wait until the book value of equity is zero to close the
institution. Book value of equity is composed of par value + surplus + retained earnings + loan
and lease loss reserves. It is not automatically adjusted downward as credit or interest rate losses
occur. For instance, under GAAP, FI managers do not have to recognize loans as ‘bad’ and write
them off in the year in which payment problems develop. Managers may also sell other assets
that have gains in value (these are marked to market when sold) and inflate the book value of
capital even though losses on other loans and securities have not been recognized. This practice
is called ‘gains trading’ and can be used to postpone insolvency (while generating larger losses).2
The use of book value does not recognize losses due to interest rate risk either. As interest rates
rise, an institution with a positive duration gap suffers losses to the market value of equity. The
book value of equity is unchanged until the assets and liabilities are marked to market. This
explains why over half of all S&Ls were insolvent in the early 1980s under market value
accounting but were allowed to continue to operate. The insolvent S&Ls went on to generate
even larger losses that eventually bankrupted the industry’s insurer, the FSLIC. Examinations
help limit the difference between book value and market value of capital by forcing FIs to
recognize its true losses. Loan and security sales also reduce the difference. However, in times
of high credit losses and high interest rate volatility, the difference between the book and market
value of equity can become quite large. One can attempt to measure this difference by
examining an institution’s market to book ratio. The market to book ratio is the market value
of equity divided by the book value of equity. In a small sample of large banks, the market to
book ratios ranged from a low of 0.849 for Deutsche Bank to as high as 3.312 for Bank of New
York Mellon.3
In summary, using book value accounting increases the government’s potential liability to
depositors and other claimants.
Predictably, the industry is against implementing market value accounting. The reasons usually
cited are:
1. Banks and thrifts maintain that implementing market value accounting is difficult and
burdensome, particularly for smaller institutions that have many nontraded assets for which it
2 New market value accounting rules should help minimize gains trading.
3 The text data includes thrifts.
would be difficult to obtain a market value. However, it seems fairly easy to impute a market
value for financial assets and liabilities, so this argument does not seem particularly relevant
except perhaps for very small institutions.
2. Managers do not want unrealized (paper) gains and losses to be reflected in income, claiming
this would excessively destabilize earnings and equity. Accounting theory tells us that the
purpose of income as it is measured is to smooth out fluctuations in cash flows through time
to provide a better picture of value than short term, highly variable cash flows. Accruals
adjustments supposedly give a truer picture of the cash flow potential of the firm over the
long term. Stock prices appear to more closely follow income than short term cash flows or
EVA adjusted cash flow measures. Managers claim they hold many of their assets and
liabilities to maturity and marking them to market would simply distort the value of the bank
to shareholders. Moreover, the FDIC claims that marking to market could cause them to
have to close an institution that might otherwise survive simply because of a short term
interest rate movement. Both arguments have some validity but are incorrect theoretically.
The managers’ claim that we should not update values as market conditions change implies
that equity should measure something other than present value of expected future cash
flows.4 An economic variable that measures future prospects must be unstable if those
prospects are changing. Bankers and accountants don’t think this way though. They want a
measure of value that is stable and encourages accountability. The FDIC’s argument forgets
that during the 1980s the FSLIC went bankrupt (and the FDIC came close) because book
value accounting allowed institutions to build large losses which the insurer eventually had to
pay. There is also an implicit assumption in their argument that an interest rate change will
be reversed in time to restore profitability to the institution. I doubt the validity of that
argument, but more importantly, I would counter that if a short term interest rate move can
put an institution under then the regulators need to bring about a change in management at
that institution anyway.
3. FIs also maintain that they would be less likely to engage in long term lending and investing
if these accounts were regularly marked to market. This statement itself is very revealing as it
indicates that FI managers recognize that the current accounting rules allow managers to
take on more risk than they could otherwise. There might be disruptions in the short run,
but in a free capital system, other new lenders would emerge if banks refused to make these
loans. They may not make as many, or they may increase the price of the loans, or they may
simply hedge more. This appears to be a disingenuous argument.
4. The industry argues the lack of liquidity in the recent crisis led to unrealistically low market
values of assets and marking to market imposed excessive losses on institutions.
Consequently the Financial Accounting Standards Board (FASB) allows management to rely
on internal estimates of cash flows to estimate fair value. This is referred to as ‘marking to
model’ rather than ‘marking to market.’ This makes sense in a non-functioning market
environment but it still allows FIs to not update the value of assets and liabilities to current
market conditions and adds subjectivity that is likely to be manipulated by management.
4 Alternatively managers may be implicitly implying that the maturity of their investments is the
proper time horizon over which value should be measured, but equity does not mature when their
investments do so they are ignoring reinvestment risk over the longer time horizon, the value of
which is better captured by current market values.
5. As of April 2009 FASB allows DIs to not recognize losses in earnings and regulatory capital
on accounts that are a) designated as held for investment rather than sale and b) temporarily
impaired in value due to market conditions rather than underlying credit deterioration. The
losses must be accounted for and revealed separately. This again adds subjectivity that can
be used to hide losses. The new rules imply that regulators will be able to evaluate these
issues and will be willing to do so.
This discussion is part of a larger debate between accountants and bankers who favor book value
and rules based measures and financial economists who favor letting the market determine value.
Accounting rules are designed to provide a stable measure of historical value that minimizes
managerial manipulations and preserves management accountability. However, in a dynamic
world where value is determined as the present worth of expected future firm prospects, book
value cannot possibly accurately measure daily fluctuations in economic firm value. If you
believe that firm value is the aggregation of the past and current decisions of the firm’s
management, then you will probably prefer book value measures of equity. If you instead
believe that firm value is properly an estimate of the value of the current and future prospects of
the firm then you should prefer market value.
1.1.1.1 VI. Web Links
http://www.federalreserve.gov/ Website of the Board of Governors of the Federal Reserve
http://www.fdic.gov/ The Federal Deposit Insurance Corporation website has net
charge off rates for banks and thrifts.
http://www.fasb.org/ FASB webpage with full text and summaries of FASB
statements
http://www.americanbanker.com/ ABA website.
http://www.wsj.com/ Website of the Wall Street Journal Interactive edition. The
web version of the well known financial newspaper can be
personalized to meet your own needs. Instructors can also
receive via e-mail current events cases keyed to financial
market news complete with discussion questions.
1.1.1.1.1.1 VII. Student Learning Activities
1. Go to the FDIC website and find the Quarterly Banking Profile. How has the average
duration gap been changing at institutions? Are the banks currently more or less vulnerable to
rising or falling interest rates? Explain why.
2. Go to the FDIC website and find the Quarterly Banking Profile. What has been
happening to the book value of equity capital? Why have these changes occurred? Has the
number of problem banks increased or decreased recently? Ascertain why. Find an index of
bank stocks. What has been happening to the market value of equity capital? Are the changes
similar? Why or why not?
3. Go to http://www.fasb.org/ and find the summary of FASB statement No. 114,
“Accounting by Creditors for Impairment of a Loan.” According to this statement how should
lenders value problem loans? Why are all loans not valued this way? Explain.
Find the FDIC DOS Manual of Examination Policies: Market Risk, Section 7.1 on the web.
What are the primary goals of examiners when they evaluate a bank’s interest rate risk (IRR)?
What are the ‘earnings approach’ and EVE? How do they differ? What is the FDIC looking for
in its IRR