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### Asset-Liability Management:Determining and Measuring Interest Rates and Controlling Interest Sensitive and Duration Gaps

### Part I. Interest-Sensitive GAP Analysis

Chapter 6

The Definition ofAsset-Liability Management

Asset-Liability Management (ALM) broadly defined is the coordinated decision-making process which views the balance sheet as an integrated whole and results in strategies and actions that contribute to the management of risk and the creation of value for the bank’s shareholders. ALM in the broadest sense involves all aspects of bank management.

ALM and Interest Rate Risk

- The management of interest rate risk is central to ALM.
- Unexpected interest rate changes cause the Net Interest Margin to change if the repricing of assets and liabilities do not match.
- Unexpected interest rate changes cause the value of the bank’s equity to change if the duration of assets and liabilities do not match.
- ALM defined in a narrow sense is the management of interest rate risk.

The rates at which banks can reinvest cash flows from assets and rates they pay on rolled over or new liabilities are not known with certainty in the future.

Cost of Funds vs. Return on Assets

Interest Sensitive GAP, impact on NII and NIM

Price Risk

Change in interest rates will cause a change in the value (price) of assets and liabilities.

Duration GAP, impact on market value of equity

Interest Rate RiskThe Goals of ALM

The Principal Goals of ALM are

- Maximize, or stabilize, Net Interest Margin (Manage Reinvestment Risk)
- Achieved by Controlling the Bank’s Interest-Sensitive Gap

- Maximize, or stabilize, the Market Value of the Owner’s Equity (Manage Price Risk)
- Achieved by Controlling the Bank’s Duration Gap

The two goals may be incompatible. The bank probably cannot achieve both goals at the same time.

Asset and Liability Management Committee (ALCO)

- A bank's asset and liability management committee (ALCO) coordinates all policy decisions and strategies that determine a bank's risk and profit objectives.
- Interest rate risk management is the primary responsibility of this committee.
- The senior managers of the bank comprise the committee.

On 1-1-1999, loan officer Mike Redd makes a $1,000 loan due in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

Charlie Greene, the funding manager, issues in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

a $1,000 CD to acquire the deposits to fund Mike Redd’s loan. Deposit customers did not want long term CD’s so Charlie issues a CD due in one year at a rate of 3%.

Fund in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

the

loan

with

a

CD

On 1-1-1999 we make

$1,000 Loan

due in 5 years on

1-1-2004 with a

Fixed Rate 6%

$1,000 CD

due 1 year

1-1-2000

Fixed Rate 3%

Notice mismatch

of repricing

opportunities. We

will be required to

replace the funding

next year.

Year 1 (1999)

Interest Income $60

Interest Expense$30

NII $30

NIM = 30/1,000 = 3%

$1,000 CD in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

due 1 year

1-1-2001

Fixed Rate 5%

$1,000 Loan

due in 4 years

1-1-2004

Fixed Rate 6%

Year 2000: 1 yr

rates go up 2%

Interest Income $60

Interest Expense$50

NII $10

NIM = 10/1,000 = 1%

The original CD used

to fund the loan matures

and must be replaced

with another 1 year CD but

it carries a 5% rate.

$1,000 Loan in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

due in 3 years

1-1-2004

Fixed Rate 6%

$1,000 CD

due 1 year

1-1-2002

Fixed Rate 2%

Year 2001: 1 yr

rates go down 3%

Interest Income $60

Interest Expense$20

NII $40

NIM = 40/1,000 = 4%

The second CD used

to fund the loan matures

and must be replaced

with another 1 year CD but

it carries a 2% rate.

“Charlie, in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

why don’t we

hedge our bets

with a 2 year CD”

“President Redd,

our NIM has been

very volatile.”

NIM

3%

1%

4%

Rates*

3%

5%

2%

* 1 Year CD

$1,000 CD in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

due in 2 years

1-1-2004

Fixed Rate 3.5%

$1,000 Loan

due in 2 years

1-1-2004

Fixed Rate 6%

Year 2002: 1 yr Rates go up 1%

Interest Income $60

Interest Expense$35

NII $25

NIM = 25/1,000 = 2.5%

The third CD used

to fund the loan matures

and must be replaced BUT

is replaced with a 2 year CD

which carries a 3.5% rate.

$1,000 Loan in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

due in 5 years

Fixed Rate 6%

$1,000 CD

due 2 years

Fixed Rate 3.5%

Year 2003: Rates

go up 3%

Interest Income $60

Interest Expense $35

NII $25

NIM = 25/1,000 = 2.5%

The CD with a two year

maturity has not matured

yet so our funding costs are

still 3.5%, not the current 6%

on 1 yr CD’s

Interest-Sensitivity Analysis in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually. (for 1-1-1999)

Interest-Sensitivity Analysis in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually. (for 1-1-2002)

Interest Sensitivity Analysis: in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually. Rate Sensitivity Reports

Rate Sensitivity Reports in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

A rate sensitivity report classifies a bank’s assets and liabilities into time intervals according to the minimum number of days until each instrument can be repriced.

It then reports GAP values on a periodic and cumulative basis through each time interval.

Definition of Repriceable in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually. Assets and Liabilities

- A repriceable asset or liability is any asset or liability on which the bank has the discretion of changing the interest rate during the next time period.
- The time period chosen determines if an asset or liability is repriceable.
- The legal contract for the item will determine when it can be repriced, for example, at maturity or at various intervals for adjustable rate instruments.

Interest-Sensitive Gap Measurement in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

Interest-Sensitive Gap =

Interest-Sensitive Assets

MINUS Interest-Sensitive Liabilities

Remember Interest-Sensitive is the same as Repriceable.

Periodic GAP vs. in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually. Cumulative GAP

The periodic GAP indicates whether more assets or liabilities can be repriced within a specific time interval or maturity bucket. The periodic GAP is not very meaningful because it ignores whether assets and liabilities in other periods can be repriced.

The cumulative GAP is the most important because it directly measures a bank’s net interest sensitivity from the present to the last day of the time interval. The cumulative GAP measures the sum of the periodic GAPS from time 0, the present, to the end of the time interval under consideration.

Positive Gap: Asset Sensitive in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

- Interest Rates Increase
More assets reprice at the higher rates than liabilities. So, interest income goes up more that interest expense causing

NII and NIM to go UP.

- Interest Rates Fall
More assets reprice at the lower rates than liabilities. So, interest incomes decreases more than interest expense causing

NII and NIM to go DOWN.

Negative Gap: Liability Sensitive in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

- Interest Rates Increase
More liabilities reprice at the higher rates than assets. So, interest expense goes up more than interest income causing

NII and NIM to go DOWN.

- Interest Rates Fall
More liabilities reprice at the lower rates than assets. So, interest expense decreases more than interest income causing

NII and NIM to go UP.

Zero Gap in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

When Interest Rates Change in Either Direction, NIM does not change.

This happens because interest income and interest expense increase or decrease in the same amount causing NII and NIM to remain constant.

Speculating on the GAP in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

- Many bank managers attempt to adjust the interest rate risk exposure of a bank in anticipation of changes in interest rates.
- This activity is speculative because it assumes that management can forecast rates better than forward rates embedded in the yield curve.

- Speculating on the GAP
- Difficult to vary the GAP and win – requires accurate interest rate forecast on a consistent basis.
- Usually only look short term.
- Only limited flexibility in adjusting the GAP because customers and depositors preferences..

Advantages and Disadvantages of GAP in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

- The primary advantage of GAP analysis is its simplicity.
- The primary weakness is that it ignores the time value of money and the market value of the owner’s equity.
- Assumes that interest rate changes on assets occur at the same time as liabilities. This is probably not the case.
- GAP ignores the impact of embedded options.
- For this reason, most banks conduct earnings sensitivity analysis, or pro forma analysis, to project earnings and the variation in earnings under different interest rate environments.

Part II. in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

The Concept of Duration and Managing a Bank’s Duration Gap

The Definition of Duration in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

Duration is the weighted average number of years until

the cash flows from an investment are received.

Duration is the “effective” time until maturity.

Notice that duration is a more descriptive measure of the

repricing opportunities than maturity.

Duration is a better description of the structure of the time

pattern of the cash flows of a financial instrument than

maturity.

Duration versus Maturity in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

1.) 1,000 loan, principal + interest paid in 20 years.

2.) 1,000 loan, 900 principal in 1 year, 100 principal in 20 years.

1000|-------------------|-----------------|0 10 20

900100|----|--------------|-----------------| 0 1 10 20

What is the maturity of each? 20 years

What is the "effective“ or average maturity?

2.) = [(900/1000) x 1]+[(100/1000) x 20] = 2.9 yrs

1

2

Duration, however, uses a weighted average of the present values.

Macaulay’s Duration in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

Formula:

Market Price

Market Price of the Security =

Present Value of all Cash Flows (CF)

y = Yield to Maturity

t = Time Period

Macaulay’s Duration in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

Example:

y = 12%

Coupon Rate = 10%

Par Value = $1,000

Maturity = 3 Years

Calculation of in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

Macaulay’s Duration

Duration of a Discount Bond or Zero Coupon Bond in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

If YTM = 12%, 1000 face, 0% coupon, 3 year maturity$711.78 1000|-------|-------|-------|0 1 2 3

Duration = Maturity

Modified Duration in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

Modified duration is an indication of the percentage change

in the price of a fixed income financial instrument for a given

change in interest rates.

D* = Modified Duration = D/(1 + i)

D = Macaulay’s Duration

P/P = -D*( i) or

P/P = -D{ i/(1 + i)}

Duration and Risk Management in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

The important feature of duration from a risk management

point of view is that it measures the sensitivity of the market

value of financial instruments to changes in interest rates.

Assume we own a bond with D = 4 years, current market price =

$1,000, and a yield to maturity of 10%. What percentage change

in the price of our bond will occur if market interest rates increase

by 1% to 11%.

P/P = -D{ i/(1 + i)} = -4(.01/1.10) = -0.0364 = -3.64%

The price of our bond will go down by 3.64% if interest rates go

up 1%.

The Purpose of Duration Gap Analysis in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

The purpose of DGAP analysis is to provide a measure of

the impact of unexpected interest rate changes on the

market value of a bank’s owners’ equity, i.e. net worth.

Interest sensitive GAP analysis does not consider the impact

of changing interest rates on the market value of a bank’s

owners’ equity.

Two Interest Rate Theorems in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually. Central to DGAP Analysis

I. Market yields and market prices move in opposite directions.

A rise in market rates of interest will cause the market value

of both fixed-rate assets and liabilities to decline.

II. The longer the maturity of a fixed rate financial instrument,

the greater will be the change in market value for a given

change in market interest rates.

The longer the duration of a bank’s assets and liabilities, the

more they will decline in market value when market interest

rates rise.

The Duration Gap in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

DGAP = DA - {DL (TL\TA)}

DGAP = Duration Gap

DA= Dollar Weighted Duration of theAsset Portfolio

DL = Dollar Weighted Duration of the Bank’s Liabilities

TL = Total Market Value of the Bank’s Liabilities

TA = Total Market Value of the Bank’s Assets

DGAP is measured in years and is a measure of the mismatch

in the average duration of the assets and the liabilities. The larger

the mismatch, the greater the impact of unexpected interest rate

changes on the market value of the net worth of the bank.

DGAP = Leverage Adjusted Duration GAP in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

When I refer to the DGAP or Duration GAP I mean the Leverage Adjusted DGAP.

DGAP = DA - {DL (TL\TA)}

Disregard the concept

DGAP = DA - DL(Equation 20 Text)

The Duration of a Portfolio in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

The duration of a portfolio of bank assets or

liabilities is the value weighted average of

the duration of each instrument in the portfolio.

The Calculation of the Duration of a Portfolio in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually. of Assets

DA = 3.047 years

Computation of the DGAP in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

Positive Duration GAP in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

- Interest Rates Increase
Assets have a higher duration so they will decrease more in value than liabilities. This causes the Net Worth to decrease.

- Interest Rates Fall
Assets have a higher duration so they will increase more in value than liabilities. This causes the Net Worth to increase.

Negative Duration GAP in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

- Interest Rates Increase
Assets have a lower duration so they will decrease less in value than liabilities. This causes the Net Worth to increase.

- Interest Rates Fall
Assets have a lower duration so they will increase less in value than liabilities. This causes the Net Worth to decrease.

Zero Duration GAP in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

If the DGAP = 0 over the planning period,

the bank is immunized against changes in the

value of its net worth.

In other words, the market value of the bank’s

equity will be stable in the event of unexpected

interest rate changes, either up or down.

Change in the $Value of a Bank’s Net Worth in 5 years (1-1-2004) at a fixed rate of 6% per year. Principal is due at maturity and interest is payable annually.

NW = TA - TL

Using P/P = -D[ i/(1 + i)] =

P = -D[ i/(1 + i)] P

NW = {-DA[i/(1+i)] TA} - {-DL[i/(1+i)] TL}

or

NW = {-DGAP [i/(1+i)] TA}

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