Alm interest rate risk management

Asset and Liability Management

Interest Rate Risk Management

Asset and Liability Management

Managing Interest Rate Risk Unexpected changes in interest rates can

significantly alter a bank’s profitability and market value of equity.

Figure 8-1Interest Rate (Percent)

Monthly Average Rates

Fed Funds 10-Year Treasury

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

Interest Rate Risk

Reinvestment rate risk- Cost of funds vrs return on assets.=> Funding GAP, impact on NII.

Price Risk - Change in interest rates will cause a change

in the value (price) of assets and liabilities.- Longer maturity (duration) -- > larger change

in value for a given change in interest rates.=> Duration GAP, impact on market value of

equity.

Funding GAP:Focus on managing NII in the short run.

Method Group assets and liabilities into time

"buckets" according to when they mature or re-price.

Calculate GAP for each time bucket

Funding GAPt = $ Value RSAt - $ Value or RSLt

where t = time bucket; e.g., 0-3 months.

Factors Affecting NII.

Changes in the level of i-rates. NII = (GAP) * (iexp.)

Changes in the volume of assets and liab. Change in the composition of assets and

liab. Changes in the relationship between asset

yields and liab. cost of funds.

Exhibit 8.3Expected Balance Sheet for Hypothetical Bank

Assets Yield Liabilities CostRate sensitive 500 8.0% 600 4.0%Fixed rate 350 11.0% 220 6.0%Non earning 150 100

920Equity

80 Total 1000 1000

NII = (0.08x500+0.11x350) - (0.04x600+0.06x220) 78.5 - 37.2 = 41.3

NIM = 41.3 / 850 = 4.86%GAP = 500 - 600 = -100

Exhibit 8.4

1% increase in the level of all short-term rates. 1% decrease in spread between assets yields

and interest cost. RSA increase to 8.5% RSL increase to 5.5%

Proportionate doubling in size. Increase in RSAs and decrease in RSL’s

RSA = 540, fixed rate = 310 RSL = 560, fixed rate = 260.

1% Increase in Short-Term RatesExpected Balance Sheet for Hypothetical Bank


920Equity

80 Total 1000 1000

NII = (0.09x500+0.11x350) - (0.05x600+0.06x220) 83.5 - 43.2 = 40.3

NIM = 40.3 / 850 = 4.74%GAP = 500 - 600 = -100

1% Decrease in SpreadExpected Balance Sheet for Hypothetical Bank


920Equity

80 Total 1000 1000

NII = (0.085x500+0.11x350) - (0.055x600+0.06x220) 81 - 46.2 = 34.8

NIM = 34.8 / 850 = 4.09%GAP = 500 - 600 = -100

Proportionate Doubling in SizeExpected Balance Sheet for Hypothetical Bank


1840Equity

160 Total 2000 2000

NII = (0.08x1000+0.11x700) - (0.04x1200+0.06x440) 157 - 74.4 = 82.6

NIM = 82.6 / 1700 = 4.86%GAP = 1000 - 1200 = -200

Increase in RSAs and Decrease in RSLs

Expected Balance Sheet for Hypothetical BankAssets Yield Liabilities Cost

Rate sensitive 540 8.0% 560 4.0%Fixed rate 310 11.0% 260 6.0%Non earning 150 100

920Equity

80 Total 1000 1000

NII = (0.08x540+0.11x310) - (0.04x560+0.06x260) 77.3 - 38 = 39.3

NIM = 39.3 / 850 = 4.62%GAP = 540 - 560 = -20

Rate Sensitivity Reports

Periodic GAP Gap for each time bucket. Measures the timing of potential income effects from

interest rate changes. Cumulative GAP

Sum of periodic GAP's. Measures aggregate interest rate risk over the entire

period. Examine Exhibit 8.5:

Time Frame for Rate SensitivityAssets 1-7 8-30 31-90 91-180 181-365 > 1 yr Not RS TotalU.S. Treasury 0.7 3.6 1.2 0.3 3.7 9.5MM Inv 1.2 1.8 3Municipals 0.7 1 2.2 7.6 11.5FF & Repo's 5 5Comm loans 1 13.8 2.9 4.7 4.6 15.5 42.5Install loans 0.3 0.5 1.6 1.3 1.9 8.2 13.8Cash 9 9Other assets 5.7 5.7 Total Assets 6.3 15 10 10 9 35 14.7 100

Liabilities and EquityMMDA 17.3 17.3Super NOW 2.2 2.2CD's < 100,000 0.9 2 5.1 6.9 1.8 2.9 19.6CD's > 100,000 1.9 4 12.9 7.9 1.2 27.9FF purchased 0NOW 9.6 9.6Savings 1.9 1.9DD 13.5 13.5Other liabilities 1 1Equity 7 7 Total Liab & Eq. 22.3 6 18 24.4 3 4.8 21.5 100GAPPeriodic GAP -16 9 -8 -14.4 6 30.2Cumulative GAP -16 -7 -15 -29.4 -23.4 6.8

Break Even Analysis

Focus on repriceable assets and calculate a break-even yield required to maintain stable NII after a rate change.

Method: 1. Calculate repriceable assets and liab. for the

desired period. 2. Calculate funding GAP for the period. 3. Calculate interest income for the period

Int Inc. = rRSA x (n/365) x $RSA 4. Calculate interest expense for the period. 5. Calculate NII.

Break Even Analysis (Cont.)

Forecast Break-Even yield on assets5. Calculate NII. 6. Calculate new interest expense on RSL that rolled over.

Int exp. = rRSL forcasted x (n/365) x $RSL 7. Calculate interest expense on "new money"

Int exp. on new money = rnew money x (n/365) x $amt of new money

8. Calculate required interest income = 5.) + 6.) + 7.) 9. Calculate break even asset yield for the use of new

money. Break even rate = [8.) net new money] x (365/n)

Break Even Analysis (Cont.)Calculate Break Even Asset Yield Annualized Average Rate

Rollover of RSA and RSL's $ amount Rates Unchanged

Repriceable assets 21,300,000 14.10%Repriceable liabilities 28,300,000 9.50% GAP (7,000,000) Interest income (next 30 days) 246,847 =21.3mx0.141x(30/360)Interest expense (next 30days) 220,973 =28.3mx0.095x(30/360) Net interest return 25,874

Forecasted Break-even Yield on Assets"New" Int exp. on existing RSL -2.00% 216,321 9.30%Int exp on new money 1.00 mill 8,548 10.40%Target net spread on repriceables 25,874 Required interest income 250,742

Break even asset yield (annualied) 250,742x(30/365) = 13.70%21300000+1000000(1-0.03)

Speculating on the GAP.

NII = (GAP) * ( iexp) Speculating on the GAP 1. Difficult to vary the GAP and win. 2. Requires accurate interest rate forecast on a

consistent basis. 3. Usually only look short term. 4. Only limited flexibility in adjusting the GAP,

customers and depositors. 5. No adjustment for timing of cash flows or

dynamics of the changing GAP position.

Duration GAP

Focus on managing NII or the market value of equity, recognizing the timing of cash flows

Interest rate risk is measured by comparing the weighted average duration of assets with liab.

Asset duration > Liability duration

interest rates

Market value of equity falls

Duration vrs maturity 1.) 1000 loan, principal + interest paid in 20 years. 2.) 1000 loan, 900 principal in 1 year, 100 principal in 20 years. 1000 + int

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

900+int 100 + int |---|--------------------------|----------------------------| 0 10 20

What is the maturity of each? What is the "effective" maturity?

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

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

DurationApproximate measure of the market value of interest elasticity

Price (value) changes Longer maturity/duration larger changes in price for a

given change in i-rates. Larger coupon smaller change in price for a given

change in i-rates.

DURV

i

VV

i1 + i

%DUR

V

i

VV

i1 + i

%

Calculate Duration

Examples: 1000 face value, 10% coupon, 3 year, 12% YTM

DUR =

C (t)(1 + r)

C(1 + r)

C (t)(1 + r)

tt

t=1

n

tt

t=1

n

tt

t=1

n

PV of the Sec.DUR =

C (t)(1 + r)

C(1 + r)

C (t)(1 + r)

tt

t=1

n

tt

t=1

n

tt

t=1

n

PV of the Sec.

Calculate Duration

Examples:1000 face value, 10% coupon, 3

year, 12% YTMD

100 * 1(1.12)

+100 * 2(1.12)

+ 100 * 3(1.12)

+ 1000 * 3(1.12)

100(1.12)

+ 1000

(1.12)

2597.6

951.96 = 2.73 years

1

2 3 3

t 3t=1

3D

100 * 1(1.12)

+100 * 2(1.12)

+ 100 * 3(1.12)

+ 1000 * 3(1.12)

100(1.12)

+ 1000

(1.12)

2597.6

951.96 = 2.73 years

1

2 3 3

t 3t=1

3

DUR =

C (t)(1 + r)

C(1 + r)

C (t)(1 + r)

tt

t=1

n

tt

t=1

n

tt

t=1

n

PV of the Sec.DUR =

C (t)(1 + r)

C(1 + r)

C (t)(1 + r)

tt

t=1

n

tt

t=1

n

tt

t=1

n

PV of the Sec.

If YTM = 5%1000 face value, 10% coupon, 3 year, 5% YTM

D

100 * 1(1.05)

+100 * 2(1.05)

+ 100 * 3(1.05)

+ 1000 * 3(1.05)

1136.16

1

2 3 3

D

100 * 1(1.05)

+100 * 2(1.05)

+ 100 * 3(1.05)

+ 1000 * 3(1.05)

1136.16

1

2 3 3

D 3127.31

11 36.16 = 2 .75 yearsD

3127.31

11 36.16 = 2 .75 years

If YTM = 20%1000 face value, 10% coupon, 3 year, 20% YTM

D 2131.95

789.35 = 2.68 yearsD

2131.95

789.35 = 2.68 years

If YTM = 12% and Coupon = 01000 face value, 0% coupon, 3 year, 12% YTM

1000|-------|-------|-------|0 1 2 3

If YTM = 12% and Coupon = 01000 face value, 0% coupon, 3 year, 12% YTM

1000|-------|-------|-------|0 1 2 3

= 3 by definition

D

1000 * 3(1.12)1000

(1.12)

3

3

D

1000 * 3(1.12)1000

(1.12)

3

3

Relate Two Types of Interest Rate Risk Reinvestment rate risk Price risk.

If i-rate YTM from reinvestment of the cash flows and holding period return (HPR) increases.

If you sell the security prior to maturity then the price or value falls , hence HPR falls.

Increases in i-rates will improve HPR from a higher reinvestment rate but reduce HPR from capital losses if the security is sold prior to maturity.

An immunized security is one in which the gain from the higher reinvestment rate is just offset by the capital loss. This point is where your holding period equals the duration of the security.

Duration GAP at the Bank The bank can protect either the market value

of equity (MVE) or the book value of NII, but not both.

To protect the MVE the bank would set DGAP to zero:

DGAP = DA - u x DL.whereDA = weighted average

duration of assets,DL = weighted average

duration of liabs,

Exhibit 8.8Exhibit 8.8

click for otherexamples1 Par Years Market

$1,000 % Coup Mat. YTM Value Dur.Assets

Cash 100 100Earning assets

Commercial loan 700 14.00% 3 14.00% 700 2.65Treasury bond 200 12.00% 9 12.00% 200 5.97 Total Earning Assets 900 13.56% 900Non-cash earning assets 0 0

Total assets 1000 12.20% 1000 3.05

LiabilitiesInterest bearing liabs.

Time deposit 520 9.00% 1 9.00% 520 1.00Certificate of deposit 400 10.00% 4 10.00% 400 3.49 Tot. Int Bearing Liabs. 920 9.43% 920Tot. non-int. bearing 0 0Total liabilities 920 9.43% 920 2.08

Total equity 80 80Total liabs & equity 1000 1000

Exhibit 8.81 Par Years Market$1,000 % Coup Mat. YTM Value Dur.

AssetsCash 100 100Earning assets

Commercial loan 700 14.00% 3 14.00% 700 2.65Treasury bond 200 12.00% 9 12.00% 200 5.97 Total Earning Assets 900 13.56% 900Non-cash earning assets 0 0

Total assets 1000 12.20% 1000 3.05


Time deposit 520 9.00% 1 9.00% 520 1.00Certificate of deposit 400 10.00% 4 10.00% 400 3.49 Tot. Int Bearing Liabs. 920 9.43% 920Tot. non-int. bearing 0 0Total liabilities 920 9.43% 920 2.08

Total equity 80 80Total liabs & equity 1000 1000

dur

981114

981114

983114

7003114

700

1 2 3 3(. ) (. ) (. ) (. )

Calculating DGAP

In exhibit 8.8:DA = (700 / 1000) * 2.65 + (200 / 1000) *

5.97 = 3.05DA = (520 / 920) * 1.00 + (400 / 920) *

3.48 = 2.08DGAP = 3.00 - (920 / 1000) * 2.06 = 1.14

years What does 1.14 mean?

The average duration of assets > liabilities, hence asset values change by more than liability values.

What is the minimum risk position?

To eliminate the risk of changes in the MVE, what do they have to change DA or DL by?

Change DA = -1.14

Change DL = +1.14/u = 1.24



Commercial loan 700 14.00% 3 15.00% 684.02 2.64Treasury bond 200 12.00% 9 13.00% 189.74 5.89 Total Earning Assets 900 14.57% 873.75Non-cash earning assets 0 0

Total assets 1000 13.07% 973.75 3.00


Time deposit 520 9.00% 1 10.00% 515.27 1.00Certificate of deposit 400 10.00% 4 11.00% 387.59 3.48 Tot. Int Bearing Liabs. 920 10.43% 902.86Tot. non-int. bearing 0 0Total liabilities 920 10.43% 902.86 2.06

Total equity 80 70.891Total liabs & equity 1000 973.75



Commercial loan 700 14.00% 3 15.00% 684.02 2.64Treasury bond 200 12.00% 9 13.00% 189.74 5.89 Total Earning Assets 900 14.57% 873.75Non-cash earning assets 0 0

Total assets 1000 13.07% 973.75 3.00


Time deposit 520 9.00% 1 10.00% 515.27 1.00Certificate of deposit 400 10.00% 4 11.00% 387.59 3.48 Tot. Int Bearing Liabs. 920 10.43% 902.86Tot. non-int. bearing 0 0Total liabilities 920 10.43% 902.86 2.06

Total equity 80 70.891Total liabs & equity 1000 973.75

PVt

t

98

115

700

1151

3

3(. ) (. )

Calculating DGAP

In exhibit 8.9:DA = (684 / 974) * 2.64 + (189 / 974) * 5.89

= 3.00DA = (515 / 903) * 1.00 + (387 / 903) *

3.48 = 2.06DGAP = 3.00 - (903 / 974) * 2.06 = 1.09

years What does 1.09 mean?

The average duration of assets > liabilities, hence asset values change by more than liability values.

Change in the Market Value of Equity

Using the relationship:

DURV

i

VV

i1 + i

%DUR

V

i

VV

i1 + i

%

Change in the Market Value of Equity

Using the relationship:

We can define the change in the MVE as:

In our case: MVE = (-1.14) x [+0.01 / (1.1356)] x 1,000

= -$10.04

DURV

i

VV

i1 + i

%DUR

V

i

VV

i1 + i

%

MVEDGAPi

iTA

earnassets

( )

( )1

Business

Alm interest rate risk management