Financial Markets and Institutions (2-downloads)

First National Bank

Assets

Liabilities

Reserves and cash items

$5 million

Checkable deposits

$15 million

Securities

Money market 

deposit accounts

Less than 1 year

$5 million

$5 million

1 to 2 years

$5 million

Savings deposits

$15 million

Greater than 2 years

$10 million

CDs

Residential mortgages

Variable rate

$10 million

Variable rate

$10 million

Less than 1 year

$15 million

Fixed rate (30-year)

$10 million

1 to 2 years

$5 million

Commercial loans

Greater than 2 years

$5 million

Less than 1 year

$15 million

Fed funds

$5 million

1 to 2 years

$10 million

Borrowings

Greater than 2 years

$25 million

Less than 1 year

$10 million

Physical capital

$5 million

1 to 2 years

$5 million

Greater than 2 years

$5 million

Bank capital

$5 million

Total

$100 million

Total

$100 million

The first step in assessing interest-rate risk is for the bank manager to decide which

assets and liabilities are rate-sensitive, that is, which have interest rates that will be reset

(repriced) within the year. Note that rate-sensitive assets or liabilities can have inter-

est rates repriced within the year either because the debt instrument matures within

the year or because the repricing is done automatically, as with variable-rate mortgages.

For many assets and liabilities, deciding whether they are rate-sensitive is

straightforward. In our example, the obviously rate-sensitive assets are securities with

maturities of less than one year ($5 million), variable-rate mortgages ($10 million),

and commercial loans with maturities less than one year ($15 million), for a total

of $30 million. However, some assets that look like fixed-rate assets whose interest

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rates are not repriced within the year actually have a component that is rate-sensitive.

For example, although fixed-rate residential mortgages may have a maturity of 

30 years, homeowners can repay their mortgages early by selling their homes or repay-

ing the mortgage in some other way. This means that within the year, a certain per-

centage of these fixed-rate mortgages will be paid off, and interest rates on this amount

will be repriced. From past experience the bank manager knows that 20% of the fixed-

rate residential mortgages are repaid within a year, which means that $2 million 

of these mortgages (20% of $10 million) must be considered rate-sensitive. The bank

manager adds this $2 million to the $30 million of rate-sensitive assets already 

calculated, for a total of $32 million in rate-sensitive assets.

The bank manager now goes through a similar procedure to determine the total

amount of rate-sensitive liabilities. The obviously rate-sensitive liabilities are money

market deposit accounts ($5 million), variable-rate CDs and CDs with less than one

year to maturity ($25 million), federal funds ($5 million), and borrowings with matu-

rities of less than one year ($10 million), for a total of $45 million. Checkable deposits

and savings deposits often have interest rates that can be changed at any time by

the bank, although banks often like to keep their rates fixed for substantial periods.

Thus, these liabilities are partially but not fully rate-sensitive. The bank manager

estimates that 10% of checkable deposits ($1.5 million) and 20% of savings deposits

($3 million) should be considered rate-sensitive. Adding the $1.5 million and $3 mil-

lion to the $45 million figure yields a total for rate-sensitive liabilities of $49.5 million.

Now the bank manager can analyze what will happen if interest rates rise by 

1 percentage point, say, on average from 10% to 11%. The income on the assets

rises by $320,000 (= 1% 

⫻ $32 million of rate-sensitive assets), while the payments

on the liabilities rise by $495,000 (= 1% 

⫻ $49.5 million of rate-sensitive liabili-

ties). The First National Bank’s profits now decline by $175,000 = ($320,000 –

$495,000). Another way of thinking about this situation is with the net interest

margin concept described in Chapter 17, which is interest income minus inter-

est expense divided by bank assets. In this case, the 1% rise in interest rates has

resulted in a decline of the net interest margin by 0.175% (= –$175,000/$100 mil-

lion). Conversely, if interest rates fall by 1%, similar reasoning tells us that the

First National Bank’s income rises by $175,000 and its net interest margin rises

by 0.175%. This example illustrates the following point: If a financial institution

has more rate-sensitive liabilities than assets, a rise in interest rates will reduce

the net interest margin and income, and a decline in interest rates will raise the

net interest margin and income.

Income Gap Analysis

One simple and quick approach to measuring the sensitivity of bank income to

changes in interest rates is gap analysis (also called income gap analysis), in

which the amount of rate-sensitive liabilities is subtracted from the amount of rate-

sensitive assets. This calculation, GAP, can be written as

(1)

where

RSA = rate-sensitive assets

RSL = rate-sensitive liabilities

GAP

⫽ RSA ⫺ RSL

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In our example, the bank manager calculates GAP to be

GAP = $32 million – $49.5 million = –$17.5 million

Multiplying GAP times the change in the interest rate immediately reveals the

effect on bank income:

(2)

where

= change in bank income

= change in interest rates

¢i

¢I

¢I ⫽ GAP ⫻ ¢i

Using the –$17.5 million gap calculated using Equation 1, what is the change in income

if interest rates rise by 1%?

Solution

The change in income is –$175,000.

where

GAP =

RSA – RSL

= –$17.5 million

=

change in interest rate 

= 0.01

Thus,

¢I ⫽ ⫺$17.5 million ⫻ 0.01 ⫽ ⫺$175,000

¢i

¢I ⫽ GAP ⫻ ¢i

E X A M P L E   2 3 . 1 Income Gap Analysis

The analysis we just conducted is known as basic gap analysis, and it suffers

from the problem that many of the assets and liabilities that are not classified as

rate-sensitive have different maturities. One refinement to deal with this problem, the

maturity bucket approach, is to measure the gap for several maturity subintervals,

called maturity buckets, so that effects of interest-rate changes over a multiyear period

can be calculated.

The manager of First National Bank notices that the bank balance sheet allows him to

put assets and liabilities into more refined maturity buckets that allow him to estimate the

potential change in income over the next one to two years. Rate-sensitive assets in this

period consist of $5 million of securities maturing in one to two years, $10 million of

commercial loans maturing in one to two years, and an additional $2 million (20% of fixed-

rate mortgages) that the bank expects to be repaid. Rate-sensitive liabilities in this period

consist of $5 million of one- to two-year CDs, $5 million of one- to two-year borrowings,

E X A M P L E   2 3 . 2 Income Gap Analysis

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By using the more refined maturity bucket approach, the bank manager can

figure out what will happen to bank income over the next several years when there

is a change in interest rates.

Duration Gap Analysis

The gap analysis we have examined so far focuses only on the effect of interest-

rate changes on income. Clearly, owners and managers of financial institutions care

not only about the effect of changes in interest rates on income but also about the

effect of changes in interest rates on the market value of the net worth of the finan-

cial institution.

1

An alternative method for measuring interest-rate risk, called duration gap