Chapter 12 - Depository Institutions: Banks and Bank Management

Chapter 12
Depository Institutions: Banks and Bank Management
Conceptual and Analytical Problems

1. Explain how a bank manager uses Core Principles 1, 2 and 3 (Time Has Value, Risk
Requires Compensation, and Information Is the Basis for Decisions) to select assets
and issue liabilities consistent with shareholder preferences. (LO1)

Answer: The manager evaluates the return and risk of each asset and liability prior to
adding it to the balance sheet. These evaluations depend on the timing and risk
associated with the payments, using core principles 1and 2, and usually require
collection and processing of information, using core principle 3. On the asset side, for
example, does the interest rate on auto loans provide sufficient compensation for the
risk of default? To make this judgment, the loan officer must collect and process
information to judge whether prospective borrowers are able and willing to repay. On
the liability side, will the interest rate offered on certificates of deposit attract funds
sufficient to support the bank’s assets? The risk and return of the overall balance
sheet also should be evaluated according to the owners’ risk preferences. For
example, risk-averse shareholders may wish the manager to hold a relatively large
proportion of government securities and a relatively low proportion of loans.

2. Consider a bank with the following balance sheet. You read online that the bank’s
return on assets (ROA) was 1 percent. What were the bank’s after-tax profits? (LO2)

Bank Balance Sheet

(in thousands)
Assets Liabilities
Reserves $200 Deposits $2,000

Loans $950 Borrowing $0

Securities $950 Bank Capital $100

Answer: Since the return on assets is defined as

Net profit after taxes

ROA 
Bank assets
,

with ROA reported as 0.01 and assets of $2.1 billion, after-tax net profit would be

ROA × (Bank assets) = 0.01 × ($2,100, 000,000) = $21,000,000

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Chapter 12 - Depository Institutions: Banks and Bank Management

3. Based on the information provided below about banks A and B, compute for each
bank its return on assets (ROA), return on equity (ROE) and leverage ratio. (LO2)

a. Bank A has net profit after taxes of $1.8 million and the balance sheet below:

Bank A
(in millions)
Assets Liabilities
Reserves $5 Deposits $75
Loans $45 Borrowing $10
Securities $45 Bank Capital $10

b. Bank B has net profit after taxes of $1 million and the balance sheet below:

Bank B
(in millions)
Assets Liabilities
Reserves $8 Deposits $80
Loans $50 Borrowing $2
Securities $22 Bank Capital $8

Answer: For both banks, we will compute ROA as

Net profit after taxes

ROA 
Bank assets
and ROE as
Net profit after taxes
ROE 
Bank capital
As a check, we note that ROA × Leverage Ratio = ROE

 Bank Assets 
 
 Bank Capital 
where   is the leverage ratio, the value of assets divided by the
owner’s equity.

a. Bank A has net profit after taxes of $1.8 million. Given assets of $95 million, its
ROA was (1.8 / 95) = .0189 or 1.89%. Since bank capital is $10 million, its ROE
is (1.8 / 10) = .18 or 18%. Its leverage ratio is (95 / 10) = 9.5. As a check, we
should find that:

ROA × (Leverage Ratio) = ROE

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 Chapter 12 - Depository Institutions: Banks and Bank Management

In this case, with ROA of 1.89% and leverage of 9.5, ROE of 18% is correct.

b. Bank B had net profit after taxes of $1 million. Its ROA is (1 / 80) = .0125 or
1.25%; its ROE is (1 / 8) = .125 or 12.5%; and its leverage ratio is
(80 / 8) = 10.

4. Banks hold more liquid assets than do most businesses. Explain why. (LO1)

Answer: Banks are required to meet depositors’ demands for cash. In order to be
able to do this, they need to hold assets that are relatively liquid. Most businesses do
not need to be able to come up with cash on short notice, so they do not need to hold
as many liquid assets.

5. Explain why banks’ holdings of cash have increased significantly as a portion of their
balance sheets in recent times. (LO1)

Answer: Banks hold cash for liquidity purposes - to meet immediate withdrawal
requests from customers. Holding cash is costly for banks, however, due to the
interest foregone on holding alternative assets. With the onset of the financial crisis,
banks dramatically increased their cash holdings, as the possibility of bank runs rose
and other assets became less liquid. Falling interest rates also reduced the
opportunity cost of holding cash. Moreover, in October 2008, the Federal Reserve
began paying interest on bank reserves (one type of cash asset), further reducing the
opportunity cost of holding cash in this form.

6. Why are checking accounts not an important source of funds for commercial banks in
the United States? (LO2)

Answer: Financial innovation has reduced the importance of checkable deposits in

the day-to-day business of banking. The reason for their decline is that checking
accounts pay little to no interest; they are a low-cost source of funds for banks but a
low-return investment for depositors. As interest rates rose through the 1970s and
remained high into the 1990s, individuals and businesses realized the benefits of
reducing the balances in their checking accounts and began to look for ways to earn
higher interest rates. Banks obliged by offering innovative accounts whose balances
could be shifted automatically when the customers’ checking accounts ran low.

7. The volume of commercial and industrial loans made by banks has declined over the
past few decades, while the volume of real estate loans has risen. Explain why this
trend occurred and how it contributed to banks’ difficulties during the financial crisis
of 2007-2009. (LO2)

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Chapter 12 - Depository Institutions: Banks and Bank Management

Answer: The rise of the commercial paper market enabled businesses to raise funds
directly, diminishing their need to borrow from banks. The creation of mortgage-
backed securities meant that banks did not have to hold the relatively illiquid
mortgage loans they originated on their balance sheets. However, banks purchased a
large amount of these mortgage-backed securities and so suffered a significant
decline in the value of their assets when MBS prices plummeted.

8. *Why do you think that U.S. banks are prohibited from holding equity as part of their
own portfolios? (LO3)

Answer: If a bank owns equity in a company to which it extends a loan, the fact that
it is a part owner of the company can give rise to a conflict of interest. If the
company were to run into trouble with the loan, the bank may be tempted to treat that
company differently. Any perceived financial trouble for the company may reduce
the value of its stock and so adversely impact the value of the bank’s equity
investment.

9. Explain how a bank uses liability management to respond to a deposit outflow. Why
do banks prefer liability management to asset management in this circumstance?
(LO1)

Answer: Banks can respond to a deposit outflow by borrowing from another bank or
from the Federal Reserve or by issuing large-denomination time deposits. During the
financial crisis of 2007-2009, banks found it difficult to raise funds through many of
the usual channels and the Federal Reserve introduced additional lending programs to
help banks manage their liquidity. Banks prefer liability management to asset
management because asset management shrinks the size of a bank’s balance sheet,
while liability management does not.

10. A bank with a two-year horizon has issued a one-year certificate of deposit for $50
million at an interest rate of 2 percent. With the proceeds, the bank has purchased a
two-year Treasury note that pays 4 percent interest. What risk does the bank face in
entering into these transactions? What would happen if all interest rates were to rise
by 1 percent? (LO3)

Answer: The bank faces the risk that the short-term interest rate will rise before the
second year, increasing the amount of interest the bank has to pay on the CD, but
leaving the interest income that the bank receives from the Treasury note unchanged.
With an interest rate of 2 percent for the CD and 4 percent for the Treasury note, the
bank’s annual interest income is (.04) × $50 million = $2 million and the bank’s
annual interest expenses are (.02) × $50 million = $1 million. The bank makes a
profit of $2 million – $1 million = $1 million. If the interest rate rises 1 percent, the
bank’s profit falls to [(.04 × $50 million) – (.03 × $50 million)] = $500,000.

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Chapter 12 - Depository Institutions: Banks and Bank Management

11. *In response to changes in banking legislation, recent decades have seen a significant
increase in interstate branching by banks in the United States. How do you think a
development of this type would affect the level of risk in banking business? (LO3)

Answer: The increase in interstate branching increases the ability of banks to

diversify their loans across different geographic areas and often different industries.
This would reduce the credit risk banks face.

12. Consider the partial balance sheets of Bank A and Bank B. Suppose that reserve
requirements are 10 percent of transaction deposits and both banks have equal access
to the interbank market and funds from the Federal Reserve.
a.) Which bank appears to face a greater liquidity risk?
b.) Which bank appears to face a greater risk of default? What other information
might you use to assess the risk of default of these banks?
Explain your answers. (LO3)

Answer:
i) On the basis of the information given, Bank B has the greater liquidity risk. The
liability sides of the balance sheets are the same, so the analysis should focus on
the asset side.

Bank A has a higher level of excess reserves and is therefore better able to meet
unexpected withdrawals by depositors. In addition, Bank A has a higher level of
securities which are generally more liquid than loans. Bank A could sell these
securities in the market place if funds were needed immediately.

ii) Bank A has net worth (bank capital) of $320 million while Bank B has net worth
of $100 million. Bank A has more of a cushion against interest rate movements
and so, on the basis of the information available, Bank B runs the greater risk of
default. More information on the interest-rate sensitivity of the assets and
liabilities of the two banks would be helpful in further assessing their default risk,
as would information on each bank’s off-balance sheet commitments.

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Chapter 12 - Depository Institutions: Banks and Bank Management

13. Bank Y and Bank Z both have assets of $1 billion. The return on assets for both banks
is the same. Bank Y has liabilities of $800 million while Bank Z’s liabilities are $900
million. In which bank would you prefer to hold an equity stake? Explain your
choice. (LO2)

Answer: Your choice will depend on your preference for return versus risk.
If the two banks have $1 billion in assets and have the same return on assets, then net
profit after taxes must be the same for both banks.

Bank Y has bank or equity capital of $200 million while Bank Z has equity capital of
$100 million, so the return on equity is higher for Bank Z.

Bank Z has a higher leverage ratio than Bank Y, however, as a higher portion of its
assets is financed from borrowed funds. Therefore, Bank Z represents a riskier
investment.

14. *You are a bank manager and have been approached by a swap dealer about
participating in fixed for floating interest rate swaps. If your bank has the typical
maturity structure, which side of the swap might you be interested in paying and
which side would you want to receive? (LO3)

Answer: A typical bank has liabilities that are shorter-term than its assets – or has
floating rate liabilities and fixed rate assets. Because the bank receives fixed interest
payments and has to make floating interest payments, it is at risk when interest rates
rise. To hedge against this risk, the bank should pay fixed and receive floating in the
interest rate swap. That way, when interest rates rise, the receipts from the swap will
increase to offset the higher rates the bank must pay its depositors.

15. If lines of credit and other off-balance sheet activities do not, by definition, appear on
the bank’s balance sheet, how can they influence the level of liquidity risk to which
the bank is exposed? (LO3)

Answer: With lines of credit, customers pay a fee to the bank for the right to borrow
at their behest. It is the customer, not the bank that determines when the loan is made
and becomes an asset on the bank’s balance sheet. The bank is obligated to honor its
commitment whenever the customer requests the loan and will need to finance that
loan regardless of its liquidity situation at that point in time. This increases the
liquidity risk faced by the bank.

16. Suppose a bank faces a gap of -20 between its interest-sensitive assets and its interest-
sensitive liabilities. What would happen to bank profits if interest rates were to fall
by 1 percentage point? You should report your answer in terms of the change in
profit per $100 in assets. (LO2)

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Chapter 12 - Depository Institutions: Banks and Bank Management

Answer: A gap of -20 means that the bank has more interest-sensitive liabilities than
assets. When interest rates fall, therefore, its profits will rise as it gains more on
paying less on its liabilities than it loses in receiving less on its assets. The gap of -20
implies that profits will rise by 20 cents per $100 of assets.

17. *Duration analysis is an alternative to gap analysis for measuring interest rate risk.
(See footnote 8 on page 313.) The duration of an asset or liability measures how
sensitive its market value is to a change in the interest rate: the more sensitive, the
longer the duration. In Chapter 6, you saw that the longer the term of a bond, the
larger the price change for a given change in the interest rate.

Using this information and the knowledge that interest rates increases tend to hurt
banks, would you say that the average duration of a bank’s assets is longer or shorter
than that of its liabilities? (LO1)

Answer: When interest rates increase, the market value of assets such as bonds fall.
If interest rate increases hurt banks, then the average value of assets must fall by more
than the average value of liabilities. Given that duration is a measure of the
sensitivity of the market value to a change in interest rates, this implies that the
average duration of bank assets is longer than that of its liabilities.

18. Suppose you were the manager of a bank with the following balance sheet.

Bank Balance Sheet

(in millions)
Assets Liabilities
Reserves $30 Checkable Deposits $200
Securities $150 Time Deposits $600
Loans $820 Borrowings $100

You are required to hold 10 percent of checkable deposits as reserves. If you were
faced with unexpected withdrawals of $30 million from time deposits, would you
rather:
a. Draw down $10 million of excess reserves and borrow $20 million from other
banks?
b. Draw down $10 million of excess reserves and sell securities of $20 million?
Explain your choice. (LO1)

Answer: Option (a) is preferable to option (b) because it doesn’t shrink the size of the
balance sheet. In normal market conditions, banks would prefer not to reduce the size
of their balance sheets as that lowers their profits.

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Chapter 12 - Depository Institutions: Banks and Bank Management

19. Suppose you are advising a bank on the management of its balance sheet. In light of
the financial crisis of 2007-2009, what arguments might you make to convince the
bank to hold additional capital? (LO2)

Answer: The financial crisis of 2007-2009 resulted in projected losses of nearly $1

trillion in US bank assets. In the absence of substantial government support, many
banks would have become insolvent. Holding sufficient capital (the difference
between the value of a bank’s assets and liabilities) is crucial for maintaining the
bank’s solvency. While holding capital is costly, there is a trade-off between
securing the solvency of the bank and that cost.

20. The financial crisis compelled banks to reduce their leverage sharply. Consider the
following two views of the balance sheet of a bank before and after the financial
crisis. Which balance sheet view is more likely to be that of the bank after the
financial crisis? Support your choice with calculations. (LO2)

Bank Balance Sheet – View 1

(in millions)
Assets Liabilities

Reserves $30 Deposits $800

Securities $150 Other Borrowed Funds $90

Loans $820 Bank Capital $110

Bank Balance Sheet View 2

(in millions)
Assets Liabilities

Reserves $30 Deposits $800

Securities $150 Other Borrowed Funds $110

Loans $820 Bank Capital $90

Answer: We can calculate the leverage ratio for each of the views:

Leverage Ratio = Total Assets / Bank Capital.

For View 1, we get 1,000/110 = 9.09
For View 2, we get 1,000/90 = 11.1

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Chapter 12 - Depository Institutions: Banks and Bank Management

If banks reduced their leverage after the crisis, it is more likely that View 1 represents
the post-crisis balance sheet.

Note, you could also calculate the leverage ratio as Debt / Equity + 1.
For View 1, we get 890/110 = 8.09 + 1 = 9.09
For View 2, we get 910/90 = 10.1 + 1 = 11.1

21. Suppose you operate a bank in a country where the central bank is expected to
embark on a series of interest rate increases. Based on gap analysis, would this
scenario be more likely to hurt or help your bank’s profitability, assuming your
bank’s liabilities are more interest sensitive than its assets? What steps might your
bank take to prepare for this scenario? (LO3)

Answer: Given your bank has a negative gap—i.e. more interest sensitive liabilities
than assets, it is more likely that a series of interest rate hikes would hurt profits. This
is because the additional interest the bank would have to pay on its interest sensitive
liabilities would be greater than the additional interest it would earn on its assets.
The bank could try to reduce the gap between the interest sensitivity of its assets and
liabilities as this would lessen the impact on profits, everything else being equal.
The bank also could engage in hedging activities to manage this interest rate risk,
such as engaging in interest rate swaps.

22. Cyber risk has been recognized as a growing source of operational risk for financial
institutions. Why might managing this risk at an individual firm level not be
adequate? (LO3)

Answer: The costs associated with a cyber attack are usually not borne by a single
institution, as data breaches involve spillovers that create systemic risk. While good
operational practices at a firm level are a crucial part of protecting against cyber
attacks, decisions by individual firms weighing only the private costs and benefits of
decisions are not likely to lead to optimal outcomes due to these externalities.

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