Interest rate risk
duration gap model
Res$, Sironi (2008) Koch, MacDonald (2003) 1 2 3 4 5 6 7 Un esercizio
1.) 1000 loan, principal + interest paid in 20 years (10%).
2.) 1000 loan, 900 principal in 1 year,
100 principal in 20 years (10%).
1000 + int
|-------------------|-----------------|
0
10
20
900+int
100 + int
|----|--------------|-----------------|
0 1
10
20
What is the maturity of each? 20 years
What is the "effective" maturity? H: yield rate10%
8 9 10 11 12 There are four steps in duration gap
analysis.
1. 
2. 
3. 
Management develops an interest rate forecast.
Management estimates the market value of bank
assets, liabilities and stockholders’ equity.
Management estimates the weighted duration of assets
and weighted duration of liabilities.
– 
4. 
The effects of both on- and off-balance sheet
items are incorporated. These estimates are
used to calculate duration gap.
Management forecasts changes in the market value of
stockholders’ equity across different interest rate
environments.
Esercizio: calcolate Duration gap
1
Par
$1,000 % Coup
Assets
Cash
Earning assets
3-yr Commercial loan
6-yr Treasury bond
Total Earning Assets
Non-cash earning assets
Total assets
700
200
900
0
1000
12.00%
8.00%
Liabilities
Interest bearing liabs.
1-yr Time deposit
3-yr Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
620
300
920
0
920
80
1000
5.00%
7.00%
Years
Mat.
YTM
100
Market
Value
Dur.
100
3
6
12.00%
8.00%
11.11%
10.00%
1
3
5.00%
7.00%
5.65%
5.65%
700
200
900
0
1000
2.69
4.99
620
300
920
0
920
80
1000
1.00
2.81
2.88
1.59
14 Positive and negative DGAPs
•  Positive DGAP
…indicates that assets are more price sensitive
than liabilities, on average.
–  Thus, when interest rates rise (fall), assets will fall
proportionately more (less) in value than liabilities
and the MVE will fall (rise) accordingly.
•  Negative DGAP
…indicates that weighted liabilities are more price
sensitive than assets.
–  Thus, when interest rates rise (fall), assets will fall
proportionately less (more) in value that liabilities
and the MVE will rise (fall).
16 Torniamo all’esercizio iniziale
17 18 19 20 1 percent increase in all rates.
1
Par
$1,000 % Coup
Years
Mat.
Assets
Cash
Earning assets
3-yr Commercial loan
6-yr Treasury bond
Total Earning Assets
Non-cash earning assets
Total assets
700 12.00%
200
8.00%
900
0
10003
3
6
Liabilities
Interest bearing liabs.
1-yr Time deposit
3-yr Certificate of deposit
Tot. Int Bearing Liabs.
Tot. non-int. bearing
Total liabilities
Total equity
Total liabs & equity
620
300
920
0
920
80
1000
1
3
YTM
100
Market
Value
Dur.
100
13.00%
9.00%
12.13%
84
700
10.88%
PV = ∑t =1
+
t
3
1.13 1.13
5.00%
7.00%
6.00%
8.00%
6.64%
6.64%
683.47
191.03
874.5
0
974.5
2.69
4.97
614.15
292.27
906.42
0
906.42
68.08
974.5
1.00
2.81
2.86
1.58
Calculating DGAP
•  DA = (683 / 974) * 2.68 + (191 / 974) * 4.97
= 2.86 yrs
•  DA = (614 / 906) * 1.00 + (292 / 906) * 2.80
= 1.58 yrs
–  DGAP = 2.86 - (906 / 974) * 1.58
= 1.36 years
•  What does 1.36 mean?
The average duration of assets > liabilities, hence
asset values change by more than liability values.
Approssimare VM banca Alfa
con duration gap (segue)
23 24 25 26 Esercizi/ 1
Input Area:
Expected Cash Flows
Discount Rate
Input Area:
Original interest rate
Interest rate after change (1)
Interest rate after change(2)
Total assets
Total liabilities
Time
Expected Cash Expected Cash
Receipts
Payments
1,500,675
1,595,786
1
746,872
831,454
2
341,555
123,897
3
62,482
1,005
4
9,871
0
5
5.00%
Calcolate: 1) Dura8on gap 2) Leverage adjusted DG 3) EffeDo sul patrimonio discendente dalla variazione dei tassi ipo8zzata 5.00%
5.75%
4.50%
$5,000,000
$4,500,000
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