# Measuring Interest Rate Risk

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```					Measuring Interest Rate Risk
Static Gap Analysis
• Calculate the gap between rate sensitive assets
and rate sensitive liabilities over a given horizon
(i.e. 0-90 days, 1 year)
• Assets or Liabilities are rate sensitive if:
– It is an interest paying demand deposit.
– It matures within the horizon or there is partial or
interim principal payment
– Interest Rate changes by contractual terms
– Interest Rate changes according to some base rate
Static GAP
• Difference between dollar value of risk
sensitive assets and risk sensitive
liabilities within some time bucket.
• Cumulative GAP measures the GAP for a
time horizon of today until the end of some
date.
• Cumulative GAP measures the effect of a
permanent change in interest rates on
income over that horizon.
∆NII = GAP*∆i
Example
Assets    Yield               Liabilities Yield
Rate Sensitive         500     8.00%                   600     4.00%
Fixed Rate             350   11.00%                    220     6.00%
Nonearning             150                             100
/Nonpaying                                  Equity
80
1000                            1000
GAP                   -100
NII                   41.3
NIM                 4.86%

Assets       Yield             Liabilities Yield
Rate Sensitive            500     9.00%                 600     5.00%
∆NII =             Fixed Rate                350    11.00%                 220     6.00%
GAP*∆I             Nonearning/               150                           100
Nonpaying                                  Equity
80
=-100*.01                               1000                             1000
GAP                   -100
=1                 NII                   40.3
NIM                 4.74%
Steps for GAP Analysis
• Make Interest Rate Forecast
• Select a series of Time Buckets – Specific
periods of time in the future
• Allocate all rate sensitive assets and
liabilities into time buckets
• Calculate periodic GAP and cumulative
GAP for each time bucket.
• Calculate effect of change in interest rate
on net income.
Rate sensitivity reports
…classifies a bank’s assets and liabilities into time
intervals according to the minimum number of
days until each instrument can be repriced.
Hang Seng Bank 2005
Less than 3-6 Months6Months- More than Nonearning/ Trading
Assets                          3 months            1 Year    1 Year     Nonpaying Book       Total
Cash& Short-term Funds              56807                3505                5539       2347      68198
Placings w/ Banks                   11211      3101      1919                                     16231
CD's Held                           20539      2366      4318      6348                    19     33590
Investment Securities               63977      7027     11253     53821      1947       1866     139891
Advances to Customers              222916     14781      6182      5349      2546          99    251873
Other Assets                         1857       896        97        313    33984       1695      38842
Total Assets                       377307     28171     27274     65831     44016       6026     548625

Liabilities & Equity
Deposit Accounts                    417652     5617      3242      7476     29429               463416
Deposts from Banks                    8018                                    514         99      8631
Other Liabilities                     3446       18                         21954       7123     32541
Minority Interests                                                            852                  852
Shareholders Funds                                                          43185                43185
Internal Funding of the Trading Book 1196                                              -1196         0
Total Liabilites                    430312     5635      3242      7476     95934       6026    548625

GAP                                -53005     22536     24032     58355     -51918
Cumulative GAP                     -53005    -30469     -6437     51918          0
Weakness of GAP
• Cannot capture interest rate risk within buckets.
• Focuses on small interest rate changes in short-
run.
• May be changes in spreads between different
base rates and asset/liability rates.
• Does not allow composition of assets and
liabilities to change
– Non-interest paying liabilities may disappear if rates
rise.
– Debtors typically have an option to repay funds early.
Earnings Sensitivity Analysis
• Forecast different interest rate scenarios.
• Forecast changes in volume and
composition effects of interest rate
scenarios.
Cumulative Gap only measures interest risk if
changes in interest rate have even effects across
assets and liabilities
• Because interest rates changes may be temporary, they may affect of
the shape of the yield curve. If rate sensitive assets and liabilities
have different maturity structures, cumulative gap may not
• Consider the case where short-term interest rates go up by 2% for 6
months and return to previous level for subsequent 6 months.

Assets         Yield        Liabilities Yield
Rate Sensitive            500                        600
Demand                    200      9.00%             600     5.00%
6 Months                  300      8.00%
Fixed Rate                350     11.00%              220   6.00%
Nonearning/               150                         100
Nonpaying                               Equity
80
1500                         1600
GAP                   -100
NII                   37.3
NIM                 2.76%
Managing the GAP
• Calculate periodic GAPs and match rate
sensitive assets and liabilities at certain
intervals.
• Match long-term assets with non-bearing
liabilities
• Use off-balance sheet transactions to
hedge interest risk.
Present Value of a Stream of Income is
equal to the sum of the present value of
each component
•   Examples
1. Coupon Bond                          C        C          C                   C     FACE
PRICE                                      ....          
C  BOND       (1  y ) (1  y ) 2 (1  y )3          (1  y)T (1  y)T

2. Fixed Payment Loan
PAY       PAY       PAY                PAY
                    .... 
(1  y ) (1  y ) (1  y )
2         3
(1  y )T
3. General
T
Xt
PVt  
1  y 
t
t 1
Changes in interest rates, change in
bond prices
• Bond prices are inverse to interest rates
which determine bond yields. A rise in
interest rates reduces bond prices. A fall in
interest rates increases bond prices.
• % effect of a permanent change in interest
rates results in a change in price/present
value proportional to T.
1     Par
log(1  y )  log(     )
T      P0
y     1
          log  P0 
1 y    T
How does a change in the discount
factor affect present value?
PV    T        1             
  Xt                   yt
y             1  y t     
t 1
               
T    
    Xt       1    
  t                   
1  y  1  y  
t
t 1 
                   
PV  T  PVX t  y                               Xt
   t                        PVX t 
PV    t 1  PV  1  y
                             1  y 
t
 T  PVX t 
duration    t     
A way to measure the maturity structure of                                    t 1  PV 
an income stream is to calculate what                             PV
PV   duration
percentage of the present value of an                              y
income stream comes from different                                    1 y
maturity dates
Duration also
To sum up this measure, calculate a                               measures the
weighted sum of the years until final                             sensitivity of the
maturity using these percentages as                               income stream to
weights.                                                          changes in the interest
This measure is called DURATION of the                            rate.
income stream.
Duration Gap
• Market Value of equity should be the gap
between the present value of assets and
the present value of liabilities
NWMV = APV – LPV
NW A L     A L L
NW  A  L                 
A   A   A     A   L A
• Use the duration of assets to calculate the
y
effect of a change in interest rates 1  y
NW                               L
   duration A  duration L     DGAP
A                                A
Immunization
• Banks may deal with interest rate risk by
structuring assets and liabilities so as to
close the duration gap as much as
possible.
• Firms conduct simulation series to
calculate the effect of different interest rate
scenarios on balance sheets.

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