Financial Markets and Institutions (2-downloads)

579

TA B L E   2 3 . 1

Duration of the First National Bank’s Assets and Liabilities

Amount

($ millions)

Duration

(years)

Weighted

Duration (years)

Assets

Reserves and cash items

5

0.0

0.00

Securities

Less than 1 year

5

0.4

0.02

1 to 2 years

5

1.6

0.08

Greater than 2 years

10

7.0

0.70

Residential mortgages

Variable rate

10

0.5

0.05

Fixed rate (30-year)

10

6.0

0.60

Commercial loans

Less than 1 year

15

0.7

0.11

1 to 2 years

10

1.4

0.14

Greater than 2 years

25

4.0

1.00

Physical capital

5

0.0

0.00

Average duration

2.70

Liabilities

Checkable deposits

15

2.0

0.32

Money market deposit accounts

5

0.1

0.01

Savings deposits

15

1.0

0.16

CDs

Variable rate

10

0.5

0.05

Less than 1 year

15

0.2

0.03

1 to 2 years

5

1.2

0.06

Greater than 2 years

5

2.7

0.14

Fed funds

5

0.0

0.00

Borrowings

Less than 1 year

10

0.3

0.03

1 to 2 years

5

1.3

0.07

Greater than 2 years

5

3.1

0.16

Average duration

1.03

---

580

Part 7 The Management of Financial Institutions

Based on the information provided in Example 3, use Equation 4 to determine the dura-

tion gap for First National Bank.

Solution

The duration gap for First National Bank is 1.72 years.

where

DUR

a

=

average duration of assets 

= 2.70

L

=

market value of liabilities 

= 95

A

=

market value of assets 

= 100

DUR

l

=

average duration of liabilities 

= 1.03

Thus,

DUR

gap

⫽ 2.70 ⫺ a

95

100

⫻ 1.03 b ⫽ 1.72 years

DUR

gap

⫽ DUR

a

⫺ a

L

A

⫻ DUR

l

b

E X A M P L E   2 3 . 4 Duration Gap Analysis

What is the change in the market value of net worth as a percentage of assets if interest

rates rise from 10% to 11%? (Use Equation 5.)

Solution

A rise in interest rates from 10% to 11% would lead to a change in the market value of

net worth as a percentage of assets of –1.6%.

where

DUR

gap

=

duration gap 

= 1.72

=

change in interest rate 

= 0.11 – 0.10 = 0.01

i

=

interest rate 

= 0.10

Thus,

¢NW

A

⫽ ⫺1.72 ⫻

0.01

1

⫹ 0.10

⫽ ⫺0.016 ⫽ ⫺1.6%

¢i

¢NW

A

⫽ ⫺DUR

gap

⫻

¢i

1

⫹ i

E X A M P L E   2 3 . 5 Duration Gap Analysis

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Chapter 23 Risk Management in Financial Institutions

581

To estimate what will happen if interest rates change, the bank manager uses the

DUR

gap

calculation in Equation 4 to obtain the change in the market value of net

worth as a percentage of total assets. In other words, the change in the market value

of net worth as a percentage of assets is calculated as

(5)

With assets totaling $100 million, Example 23.5 indicates a fall in the market value

of net worth of $1.6 million, which is the same amount that we found in Example 23.3.

As our examples make clear, both income gap analysis and duration gap analysis

indicate that the First National Bank will suffer from a rise in interest rates. Indeed,

in this example, we have seen that a rise in interest rates from 10% to 11% will cause

the market value of net worth to fall by $1.6 million, which is one-third the initial amount

of bank capital. Thus, the bank manager realizes that the bank faces substantial 

interest-rate risk because a rise in interest rates could cause it to lose a lot of its cap-

ital. Clearly, income gap analysis and duration gap analysis are useful tools for telling

a financial institution manager the institution’s degree of exposure to interest-rate risk.

Example of a Nonbanking Financial Institution

So far we have focused on an example involving a banking institution that has bor-

rowed short and lent long so that when interest rates rise, both income and the net

worth of the institution fall. It is important to recognize that income gap and dura-

tion gap analyses apply equally to other financial institutions. Furthermore, it is

important for you to see that some financial institutions have income gaps and dura-

tion gaps that are opposite in sign to those of banks, so that when interest rates

rise, both income and net worth rise rather than fall. To get a more complete pic-

ture of income gap and duration gap analyses, let us look at a nonbank financial insti-

tution, the Friendly Finance Company, which specializes in making consumer loans.

The Friendly Finance Company has the following balance sheet:

¢NW

A

⬇ ⫺DUR

gap

⫻

¢i

1

⫹ i