### 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 8-1
Interest Rate (Percent)
20
19
18
Fed Funds
10-Year Treasury
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1980 1981
1982
1983
1984
1985
1986 1987 1988 1989
Monthly Average Rates
1990
1991
1992
1993
1994
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
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.




DNII = (GAP) * (Diexp.)
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 8.3
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
500
8.0%
600
4.0%
Fixed rate
350
11.0%
220
6.0%
Non earning
150
100
920
Equity
80
Total
1000
1000
NII = (0.08x500+0.11x350) 78.5
NIM = 41.3 / 850
GAP =
500
-
(0.04x600+0.06x220)
37.2
=
41.3
=
4.86%
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 Rates
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
500
9.0%
600
5.0%
Fixed rate
350
11.0%
220
6.0%
Non earning
150
100
920
Equity
80
Total
1000
1000
NII = (0.09x500+0.11x350) 83.5
NIM = 40.3 / 850
GAP =
500
-
(0.05x600+0.06x220)
43.2
=
40.3
=
4.74%
600
=
-100
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
500
8.5%
600
5.5%
Fixed rate
350
11.0%
220
6.0%
Non earning
150
100
920
Equity
80
Total
1000
1000
NII = (0.085x500+0.11x350) 81
NIM = 34.8 / 850
GAP =
500
-
(0.055x600+0.06x220)
46.2
=
34.8
=
4.09%
600
=
-100
Proportionate Doubling in Size
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
1000
8.0%
1200
4.0%
Fixed rate
700
11.0%
440
6.0%
Non earning
300
200
1840
Equity
160
Total
2000
2000
NII = (0.08x1000+0.11x700) 157
NIM = 82.6 / 1700
GAP =
1000
-
(0.04x1200+0.06x440)
74.4
=
82.6
=
4.86%
1200
=
-200
Increase in RSAs and Decrease
in RSLs
Expected Balance Sheet for Hypothetical Bank
Assets
Yield
Liabilities Cost
Rate sensitive
540
8.0%
560
4.0%
Fixed rate
310
11.0%
260
6.0%
Non earning
150
100
920
Equity
80
Total
1000
1000
NII = (0.08x540+0.11x310) 77.3
NIM = 39.3 / 850
GAP =
540
-
(0.04x560+0.06x260)
38
=
39.3
=
4.62%
560
=
-20
Rate Sensitivity Reports

Periodic GAP



Cumulative GAP



Gap for each time bucket.
Measures the timing of potential income effects from
interest rate changes.
Sum of periodic GAP's.
Measures aggregate interest rate risk over the entire
period.
Examine Exhibit 8.5:
Assets
U.S. Treasury
MM Inv
Municipals
FF & Repo's
Comm loans
Install loans
Cash
Other assets
Total Assets
1-7
5
1
0.3
6.3
Liabilities and Equity
MMDA
17.3
Super NOW
2.2
CD's < 100,000
0.9
CD's > 100,000
1.9
FF purchased
NOW
Savings
DD
Other liabilities
Equity
Total Liab & Eq.
22.3
GAP
Periodic GAP
-16
Cumulative GAP
-16
Time Frame for Rate Sensitivity
8-30 31-90 91-180 181-365 > 1 yr Not RS Total
0.7
3.6
1.2
0.3
3.7
9.5
1.2
1.8
3
0.7
1
2.2
7.6
11.5
5
13.8
2.9
4.7
4.6
15.5
42.5
0.5
1.6
1.3
1.9
8.2
13.8
9
9
5.7
5.7
15
10
10
9
35
14.7
100
2
4
5.1
12.9
6.9
7.9
1.8
1.2
2.9
9.6
1.9
6
18
24.4
3
4.8
9
-7
-8
-15
-14.4
-29.4
6
-23.4
30.2
6.8
13.5
1
7
21.5
17.3
2.2
19.6
27.9
0
9.6
1.9
13.5
1
7
100
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 assets
5. 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
Break Even Analysis (Cont.)
Annualized
Calculate Break Even Asset Yield
Average Rate
Rollover of RSA and RSL's
Rates Unchanged
Repriceable assets
Repriceable liabilities
GAP
Interest income (next 30 days)
Interest expense (next 30days)
Net interest return
\$ amount
21,300,000 14.10%
28,300,000
9.50%
(7,000,000)
246,847 =21.3mx0.141x(30/360)
220,973 =28.3mx0.095x(30/360)
25,874
Forecasted Break-even Yield on Assets
"New" Int exp. on existing RSL
-2.00%
Int exp on new money
1.00 mill
Required interest income
Break even asset yield (annualied)
216,321
9.30%
8,548 10.40%
25,874
250,742
250,742x(30/365) =
21300000+1000000(1-0.03)
13.70%
Speculating on the GAP.


DNII = (GAP) * (D 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
vrsprincipal
maturity
1.) 1000 loan,
+ 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
|---|--------------------------|---------------------------
Duration
Approximate measure of the market value of
interest elasticity
 DV 

 %DV
DUR   V  
Di
 Di


 1+i 

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.
Calculate Duration
nn
nn
Ctt(t)
Ctt(t)
 (1 + r)tt  (1 + r)tt
t=1
t=1
t=1
DUR = t=1

nn
Ctt
PV of the Sec.
 (1 + r)tt
t=1
t=1
Examples:
1000 face value, 10% coupon, 3 year,
12% YTM
Calculate Duration
nn
nn
Ctt(t)
Ctt(t)
 (1 + r)tt  (1 + r)tt
t=1
t=1
t=1
DUR = t=1

nn
Ctt
PV of the Sec.
 (1 + r)tt
t=1
t=1
Examples:
100 * 1 100 * 2
100 * 3
1000 * 3
+ face
+value,33 10%
+
1000
coupon,
3 year,
11
22
2597.6
(1.12)
(1.12)
(1.12)
(1.12)33
D

= 2.73 years
33
12% YTM
100
1000
951.96
 (1.12)
tt
t=1
t=1
+
(1.12)33
If YTM = 5%
1000 face value, 10% coupon, 3 year, 5% YTM
100 * 1 100 * 2
100 * 3
1000 * 3
+
+
+
11
22
33
(1.05)
(1.05)
(1.05)
(1.05)33
D
1136.16
3127.31
D
= 2.75 years
1136.16
If YTM = 20%
1000 face value, 10% coupon, 3 year, 20%
YTM
2131.95
D
= 2.68 years
789.35
If YTM = 12% and Coupon = 0
1000 face value, 0% coupon, 3 year, 12% YTM
1000
|-------|-------|-------|
0
1
2
3
If YTM = 12% and Coupon = 0
1000 face value, 0% coupon, 3 year, 12% YTM
1000
|-------|-------|-------|
0 10001* 3 2
3
(1.12)33
D
1000
(1.12)33
= 3 by definition
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,
1
click for other
examples
Exhibit 8.8
Par
Years
\$1,000 % Coup Mat.
Assets
Cash
100
Earning assets
Commercial loan
700 14.00%
Treasury bond
200 12.00%
Total Earning Assets
900
Non-cash earning assets
0
Total assets
1000
Liabilities
Interest bearing liabs.
Time deposit
Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
520 9.00%
400 10.00%
920
0
920
80
1000
YTM
Market
Value
Dur.
100
3
9
14.00%
12.00%
13.56%
12.20%
1
4
9.00%
10.00%
9.43%
9.43%
700
200
900
0
1000
2.65
5.97
520
400
920
0
920
80
1000
1.00
3.49
3.05
2.08
1
Exhibit 8.8
Par
Years
\$1,000 % Coup Mat.
Assets
Cash
100
Earning assets
Commercial loan
700 14.00%
3
Treasury bond
200 12.00%
9
Total Earning
98Assets
 1 98900
 1 98  3

Non-cash earning assets
02 
1
3
(
1
.
14
)
(
1
.
14
)
(
1
.
14
)
Total dur
assets
1000

Liabilities
Interest bearing liabs.
Time deposit
Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
YTM
Market
Value
Dur.
100

14.00%
12.00%
13.56%
700
3
(12.20%
1.14)3
700
200
900
0
1000
2.65
5.97
520
400
920
0
920
80
1000
1.00
3.49
3.05
700
520 9.00%
400 10.00%
920
0
920
80
1000
1
4
9.00%
10.00%
9.43%
9.43%
2.08
Calculating DGAP


In exhibit 8.8:
DA = (700 / 1000) * 2.65 + (200 / 1000) *
5.97 = 3.05
DA = (520 / 920) * 1.00 + (400 / 920) * 3.48
= 2.08
DGAP = 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
1
Exhibit 8.9
Par
Years
\$1,000 % Coup Mat.
Assets
Cash
100
Earning assets
Commercial loan
700 14.00%
Treasury bond
200 12.00%
Total Earning Assets
900
Non-cash earning assets
0
Total assets
1000
Liabilities
Interest bearing liabs.
Time deposit
Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
520 9.00%
400 10.00%
920
0
920
80
1000
YTM
Market
Value
Dur.
100
3
9
15.00%
13.00%
14.57%
13.07%
1
4
10.00%
11.00%
10.43%
10.43%
684.02
189.74
873.75
0
973.75
2.64
5.89
515.27
387.59
902.86
0
902.86
70.891
973.75
1.00
3.48
3.00
2.06
1
Exhibit 8.9
Par
Years
\$1,000 % Coup Mat.
Assets
Cash
100
Earning assets
Commercial loan
700 14.00%
Treasury bond
200 12.00%
Total Earning Assets
900
Non-cash earning
0
3 assets
98 1000700
Total assets
PV  
t
(
1
.
15
)
t1
Liabilities
Interest bearing liabs.
Time deposit
Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity

YTM
Market
Value
Dur.
100
3
9
15.00%
13.00%
14.57%
13.07%
684.02
189.74
873.75
0
973.75
2.64
5.89
515.27
387.59
902.86
0
902.86
70.891
973.75
1.00
3.48
3.00
(1.15)3
520 9.00%
400 10.00%
920
0
920
80
1000
1
4
10.00%
11.00%
10.43%
10.43%
2.06
Calculating DGAP


In exhibit 8.9:
DA = (684 / 974) * 2.64 + (189 / 974) * 5.89 =
3.00
DA = (515 / 903) * 1.00 + (387 / 903) * 3.48
= 2.06
DGAP = 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:
 DV 
 V  %DV
DUR  

Di   Di


 1+i 
Change in the Market Value of
Equity

Using the relationship:
 DV 

We can define the change
as:
 in Dthe

i MVE

In our case:
DMVE = (-1.14) x [+0.01 / (1.1356)] x 1,000
= -\$10.04

 %DV
DUR   V  
Di
 Di


 1+i 
DMVE  ( DGAP)  
  TA
 (1  iearnassets ) 
```