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Bank Management, 6th edition.
                Management
           Timothy W. Koch and S. Scott MacDonald
           Copyright © 2006 by South-Western, a division of Thomson Learning




             Managing Interest Rate Risk:
             GAP and Earnings Sensitivity



                  Chapter 5

William Chittenden edited and updated the PowerPoint slides for this edition.
Interest Rate Risk

 Interest Rate Risk
    The potential loss from unexpected
     changes in interest rates which can
     significantly alter a bank’s profitability
     and market value of equity.
Interest Rate Risk: GAP & Earnings
Sensitivity
 When a bank’s assets and liabilities do
  not reprice at the same time, the result
  is a change in net interest income.
   The  change in the value of assets and
    the change in the value of liabilities will
    also differ, causing a change in the
    value of stockholder’s equity
Interest Rate Risk

 Banks typically focus on either:
   Net interest income or
   The market value of stockholders' equity
 GAP Analysis
   A static measure of risk that is commonly
    associated with net interest income (margin)
    targeting
 Earnings Sensitivity Analysis
   Earnings sensitivity analysis extends GAP
    analysis by focusing on changes in bank
    earnings due to changes in interest rates and
    balance sheet composition
Asset and Liability Management
Committee (ALCO)

 The ALCO’s primary responsibility is
  interest rate risk management.
 The ALCO coordinates the bank’s
  strategies to achieve the optimal
  risk/reward trade-off.
Two Types of Interest Rate Risk

 Spread Risk (reinvestment rate risk)
   Changes in interest rates will change
    the bank’s cost of funds as well as the
    return on their invested assets. They
    may change by different amounts.
 Price Risk
   Changes in interest rates may change
    the market values of the bank’s assets
    and liabilities by different amounts.
Interest Rate Risk:
 Spread (Reinvestment Rate) Risk
 If interest rates change, the bank will have
  to reinvest the cash flows from assets or
  refinance rolled-over liabilities at a different
  interest rate in the future.
     An increase in rates, ceteris paribus,
      increases a bank’s interest income but also
      increases the bank’s interest expense.
 Static GAP Analysis considers the impact of
  changing rates on the bank’s net interest
  income.
Interest Rate Risk:
 Price Risk
 If interest rates change, the market
  values of assets and liabilities also
  change.
   The  longer is duration, the larger is the
    change in value for a given change in
    interest rates.
 Duration GAP considers the impact of
  changing rates on the market value of
  equity.
Measuring Interest Rate Risk with GAP

 Example:
  A  bank makes a $10,000 four-year car
   loan to a customer at fixed rate of
   8.5%. The bank initially funds the car
   loan with a one-year $10,000 CD at a
   cost of 4.5%. The bank’s initial spread
   is 4%.
       4 year Car Loan       8.50%
       1 Year CD             4.50%
                             4.00%
   What   is the bank’s risk?
Measuring Interest Rate Risk with GAP

 Traditional Static GAP Analysis
    GAPt = RSAt -RSLt
   RSAt
       Rate Sensitive Assets
          Those assets that will mature or reprice in
           a given time period (t)
   RSLt
       Rate Sensitive Liabilities
          Those liabilities that will mature or reprice
           in a given time period (t)
Measuring Interest Rate Risk with GAP

 Traditional Static GAP Analysis
   What is the bank’s 1-year GAP with the
    auto loan?
      RSA1yr = $0

      RSL1yr = $10,000

      GAP1yr = $0 - $10,000 = -$10,000

        The bank’s one year funding GAP is -10,000
        If interest rates rise (fall) in 1 year, the
         bank’s margin will fall (rise)
Measuring Interest Rate Risk with GAP

 Traditional Static GAP Analysis
   Funding GAP
      Focuses on managing net interest

       income in the short-run
      Assumes a ‘parallel shift in the yield

       curve,’ or that all rates change at the
       same time, in the same direction and by
       the same amount.
       Does this ever happen?
Traditional Static GAP Analysis
 Steps in GAP Analysis
 Develop an interest rate forecast
 Select a series of “time buckets” or
  intervals for determining when assets
  and liabilities will reprice
 Group assets and liabilities into these
  “buckets ”
 Calculate the GAP for each “bucket ”
 Forecast the change in net interest
  income given an assumed change in
  interest rates
What Determines Rate Sensitivity (Ignoring
Embedded Options)?
 An asset or liability is considered rate
  sensitivity if during the time interval:
   It matures
   It represents and interim, or partial, principal
    payment
   It can be repriced
         The interest rate applied to the outstanding
          principal changes contractually during the
          interval
         The outstanding principal can be repriced
          when some base rate of index changes and
          management expects the base rate / index to
          change during the interval
What are RSAs and RSLs?
 Considering a 0-90 day “time bucket,” RSAs and
  RSLs include:
   Maturing instruments or principal payments
      If an asset or liability matures within 90 days,
       the principal amount will be repriced
      Any full or partial principal payments within

       90 days will be repriced
   Floating and variable rate instruments
      If the index will contractually change within
       90 days, the asset or liability is rate sensitive
      The rate may change daily if their base rate

       changes.
          Issue: do you expect the base rate to
           change?
Factors Affecting Net Interest Income

 Changes in the level of interest rates
 Changes in the composition of assets
  and liabilities
 Changes in the volume of earning
  assets and interest-bearing liabilities
  outstanding
 Changes in the relationship between
  the yields on earning assets and rates
  paid on interest-bearing liabilities
Factors Affecting Net Interest Income:
 An Example
 Consider the following balance sheet:
        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         $ 1,000               $ 1,000

    NII = (0.08 x 500 + 0.11 x 350) - (0.04 x 600 + 0.06 x 220)
    NII = 78.5 - 37.2 = 41.3
    NIM = 41.3 / 850 = 4.86%
    GAP = 500 - 600 = -100
Examine the impact of the following changes

 A 1% increase in the level of all short-term
  rates?
 A 1% decrease in the spread between
  assets yields and interest costs such that
  the rate on RSAs increases to 8.5% and the
  rate on RSLs increase to 5.5%?
 Changes in the relationship between short-
  term asset yields and liability costs
 A proportionate doubling in size of the
  bank?
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         $ 1,000                $    1,000

 NII = (0.09 x 500 + 0.11 x 350) - (0.05 x 600 + 0.06 x 220)
 NII = 83.5 - 43.2 = 40.3
 NIM = 40.3 / 850 = 4.74%      With a negative GAP, more
 GAP = 500 - 600 = -100        liabilities than assets reprice
                            higher; hence NII and NIM fall
1% decrease in the spread
      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        $ 1,000                  $ 1,000

 NII = (0.085 x 500 + 0.11 x 350) - (0.055 x 600 + 0.06 x 220)
 NII = 81 - 46.2 = 34.8
 NIM = 34.8 / 850 = 4.09%       NII and NIM fall (rise) with a
 GAP = 500 - 600 = -100         decrease (increase) in the
                               spread.
                               Why the larger change?
Changes in the Slope of the Yield Curve

 If liabilities are short-term and assets
 are long-term, the spread will
   widen   as the yield curve increases in
    slope
   narrow when the yield curve
    decreases in slope and/or inverts
Proportionate doubling in size
       Expected Balance   Sheet for Hypothetical Bank
               Assets     Yield        Liabilities  Cost
Rate sensitive $ 1,000    8.0%         $ 1,200      4.0%
Fixed rate     $ 700      11.0%        $      440   6.0%
Non earning    $ 300                   $      200
                                       $ 1,840
                                       Equity
                                       $      160
 Total         $ 2,000                 $ 2,000

 NII = (0.08 x 1000 + 0.11 x 700) - (0.04 x 1200 + 0.06 x 440)
 NII = 157 - 74.4 = 82.6
 NIM = 82.6 / 1700 = 4.86%       NII and GAP double, but         NIM
 GAP = 1000 - 1200 = -200        stays the same.
                               What has happened to risk?
Changes in the Volume of Earning Assets and
Interest-Bearing Liabilities

 Net interest income varies directly with
 changes in the volume of earning
 assets and interest-bearing liabilities,
 regardless of the level of interest rates
RSAs increase to $540 while fixed-rate assets
decrease to $310 and RSLs decrease to $560
while fixed-rate liabilities increase to $260
     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         $ 1,000               $ 1,000

  NII = (0.08 x 540 + 0.11 x 310) - (0.04 x 560 + 0.06 x 260)
  NII = 77.3 - 38 = 39.3
  NIM = 39.3 / 850 = 4.62%
                                    Although the bank’s GAP
  GAP = 540 - 560 = -20             (and hence risk) is lower,
                                NII is also lower.
Changes in Portfolio Composition and Risk

 To reduce risk, a bank with a negative
  GAP would try to increase RSAs
  (variable rate loans or shorter
  maturities on loans and investments)
  and decrease RSLs (issue relatively
  more longer-term CDs and fewer fed
  funds purchased)
 Changes in portfolio composition also
  raise or lower interest income and
  expense based on the type of change
Changes in Net Interest Income are directly
proportional to the size of the GAP
 If there is a parallel shift in the yield
  curve:
         ÄNIIexp  GAP  iexp
 It is rare, however, when the yield
  curve shifts parallel
   Ifrates do not change by the same
    amount and at the same time, then net
    interest income may change by more
    or less.
Summary of GAP and the Change in NII

                            GAP Summary
           Change in   Change in          Change in   Change in
 GAP        Interest    Interest           Interest   Net Interest
            Income      Income             Expense      Income
Positive    Increase    Increase    >      Increase    Increase
Positive    Decrease    Decrease    >      Decrease    Decrease

Negative   Increase    Increase     <     Increase     Decrease
Negative   Decrease    Decrease     <     Decrease     Increase

 Zero      Increase    Increase     =     Increase       None
 Zero      Decrease    Decrease     =     Decrease       None
Rate, Volume, and Mix Analysis

 Banks often publish a summary of how net
 interest income has changed over time.
     They separate changes over time to:
        shifts in assets and liability
         composition and volume
        changes associated with movements in

         interest rates.
     The purpose is to assess what factors
      influence shifts in net interest income over
      time.
Measuring Interest Rate Risk: Synovus

                                                 2004 Compared to 2003          2003 Compared to 2002
                                                    Change Due to *                 Change Due to *
             Interest earned on:            Volume Yield/Rate Net Change Volume Yield/Rate Net Change
 Taxable loans, net                        $ 149,423 (117,147)       32,276 161,222    36,390       197,612
 Tax-exempt loans, net†                        1,373      (586)         787   1,108      (450)          658
 Taxable investment securities                (5,313)     (916)      (6,229)  4,507     2,570         7,077
 Tax-exempt investment securities†             2,548        74        2,622   2,026      (206)        1,820
 Interest earning deposits with banks            223      (176)          47      28        48            76
 Federal funds sold and securities
                                                406      (1,745)    (1,339)     1,447     1,410       2,857
   purchased under resale agreements
 Mortgage loans held for sale                 7,801      (1,680)     6,121       (113)      549         436
   Total interest income                    156,461    (122,176)    34,285    170,225    40,311     210,536

Interest paid on:
  Interest bearing demand deposits            6,074     (12,517)    (6,443)     1,537     5,433       6,970
  Money market accounts                      21,380     (36,244)   (14,864)     4,654    13,888      18,542
  Savings deposits                             (369)     (3,307)    (3,676)      (660)      (67)       (727)
  Time deposits                              32,015     (22,545)     9,470     38,824    32,812      71,636
  Federal funds purchased and securities
                                             (6,165)    (29,744)   (35,909)    23,148    15,870      39,018
    sold under repurchase agreements
  Other borrowed funds                       21,318      (4,272)    17,046     21,960      3,361     25,321
    Total interest expense                   74,253    (108,629)   (34,376)    89,463     71,297    160,760
      Net interest income                    82,208     (13,547)    68,661     80,762    (30,986)    49,776
Interest Rate-Sensitivity Reports
Classifies a bank’s assets and liabilities into time intervals
according to the minimum number of days until each
instrument is expected to be repriced.
 GAP values are reported a periodic and
 cumulative basis for each time interval.
   Periodic GAP
      Is the Gap for each time bucket and

       measures the timing of potential income
       effects from interest rate changes
   Cumulative GAP
      It is the sum of periodic GAP's and

       measures aggregate interest rate risk over
       the entire period
      Cumulative GAP is important since it

       directly measures a bank’s net interest
       sensitivity throughout the time interval.
Measuring Interest Rate Risk with GAP
                    1-7      8-30    31-90    91-180 181-365 Over Not Rate
                   Days      Days    Days      Days   Days   1 year Sensitive    Total
Assets
U.S. Treas & ag               0.7      3.6       1.2     0.3     3.7              9.5
MM Inv                                 1.2       1.8                              3.0
Municipals                             0.7       1.0     2.2     7.6             11.5
FF & Repo's           5.0                                                         5.0
Comm loans            1.0    13.8      2.9       4.7     4.6    15.5             42.5
Install loans         0.3     0.5      1.6       1.3     1.9     8.2             13.8
Cash                                                                      9.0     9.0
Other assets                                                              5.7     5.7
  Total Assets        6.3     15.0    10.0      10.0      9.0   35.0      14.7   100.0
Liabilities and Equity
MMDA                          5.0     12.3                                       17.3
Super NOW             2.2                                                         2.2
CD's < 100,000        0.9     2.0      5.1       6.9     1.8     2.9             19.6
CD's > 100,000        1.9     4.0     12.9       7.9     1.2                     27.9
FF purchased                                                                      -
NOW                                              9.6                              9.6
Savings                                                          1.9              1.9
DD                                                                       13.5    13.5
Other liabilities                                                         1.0     1.0
Equity                                                                    7.0     7.0
 Total Liab & Eq.      5.0    11.0    30.3      24.4      3.0    4.8      21.5   100.0
Periodic GAP          1.3      4.0    -20.3     -14.4     6.0   30.2
Cumulative GAP        1.3      5.3    -15.0     -29.4   -23.4    6.8
Advantages and Disadvantages of
Static GAP Analysis
 Advantages
   Easy to understand
   Works well with small changes in interest
    rates
 Disadvantages
   Ex-post measurement errors
   Ignores the time value of money
   Ignores the cumulative impact of interest rate
    changes
   Typically considers demand deposits to be
    non-rate sensitive
   Ignores embedded options in the bank’s
    assets and liabilities
Measuring Interest Rate Risk with
the GAP Ratio
 GAP Ratio = RSAs/RSLs
   A GAP ratio greater than 1 indicates a
    positive GAP
   A GAP ratio less than 1 indicates a
    negative GAP
What is the ‘Optimal GAP’

 There is no general optimal value for a
  bank's GAP in all environments.
 Generally, the farther a bank's GAP is
  from zero, the greater is the bank's
  risk.
 A bank must evaluate its overall risk
  and return profile and objectives to
  determine its optimal GAP
GAP and Variability in Earnings
 Neither the GAP nor GAP ratio provide
 direct information on the potential variability
 in earnings when rates change.
     Consider two banks, both with $500 million
      in total assets.
          Bank A: $3 mil in RSAs and $2 mil in RSLs.
                GAP = $1 mil and GAP ratio = 1.5 mil
          Bank B: $300 mil in RSAs and $200 mil RSLs.
                GAP equals $100 mill and 1.5 GAP ratio.
          Clearly, the second bank assumes greater
           interest rate risk because its net interest
           income will change more when interest rates
           change.
Link Between GAP and Net Interest Margin



 Many banks will specify a target GAP
 to earning asset ratio in the ALCO
 policy statements

 Target Gap      (Allowable % Change in NIM)(Expected NIM)
Earning assets        Expected % change in interest rates
               
Establishing a Target GAP: An Example

 Consider a bank with $50 million in
  earning assets that expects to
  generate a 5% NIM.
 The bank will risk changes in NIM
  equal to plus or minus 20% during the
  year
   Hence,   NIM should fall between 4% and
    6%.
Establishing a Target GAP: An Example
(continued)
 If management expects interest rates to vary
  up to 4 percent during the upcoming year,
  the bank’s ratio of its 1-year cumulative
  GAP (absolute value) to earning assets
  should not exceed 25 percent.
       Target GAP/Earning assets

            = (.20)(0.05) / 0.04 = 0.25
 Management’s willingness to allow only a 20
  percent variation in NIM sets limits on the
  GAP, which would be allowed to vary from
  $12.5 million to $12.5 million, based on $50
  million in earning assets.
Speculating on the GAP

 Many bank managers attempt to adjust
  the interest rate risk exposure of a
  bank in anticipation of changes in
  interest rates.
 This is speculative because it assumes
  that management can forecast rates
  better than the market.
Can a Bank Effectively Speculate on the GAP?

 Difficult to vary the GAP and win as
  this requires consistently accurate
  interest rate forecasts
 A bank has limited flexibility in
  adjusting its GAP; e.g., loan and
  deposit terms
 There is no adjustment for the timing
  of cash flows or dynamics of the
  changing GAP position
Earnings Sensitivity Analysis
 Allows management to incorporate the
 impact of different spreads between
 asset yields and liability interest costs
 when rates change by different
 amounts.
Steps to Earnings Sensitivity Analysis

 Forecast future interest rates
 Identify changes in the composition of
  assets and liabilities in different rate
  environments
 Forecast when embedded options will be
  exercised
 Identify when specific assets and liabilities
  will reprice given the rate environment
 Estimate net interest income and net
  income
 Repeat the process to compare forecasts of
  net interest income and net income across
  different interest rate environments.
Earnings Sensitivity Analysis and the
Exercise of Embedded Options
 Many bank assets and liabilities
 contain different types of options, both
 explicit and implicit:
   Option  to refinance a loan
   Call option on a federal agency bond
    the bank owns
   Depositors have the option to withdraw
    funds prior to maturity
   Cap (maximum) rate on a floating-rate
    loan
Earnings Sensitivity Analysis
Recognizes that Different Interest
Rates Change by Different Amounts
at Different Times
 It is well recognized that banks are
 quick to increase base loan rates but
 are slow to lower base loan rates when
 rates fall.
Recall the our example from before:
         4 year Car Loan            8.50%
         1 Year CD                  4.50%
                                    4.00%
        GAP1Yr = $0 - $10,000 = -$10,000
        What if rates increased?
                    1 year GAP Position
   Change in Rates          Base      Change in Rates
  -3       -2        -1     GAP1yr   +1       +2        +3
-1,000   -2,000   -8,000 -10,000 -10,000 -10,000 -10,000
Re-finance the auto loans             All CD’s will mature
What about the 3 Month GAP Position?

 Base GAP3m = $10,000 - $10,000 = 0



               3 Month GAP Position
   Change in Rates   Base     Change in Rates
  -3     -2      -1  GAP3m   +1     +2      +3
+8,000 +6,000 +2,000   0   -1,000 -3,000 -6,000
Re-finance auto loans, and     People will “pull” the
 less likely to “pull” CD’s   CD’s for higher returns
The implications of embedded options

 Does the bank or the customer determine
 when the option is exercised?
     How and by what amount is the bank being
      compensated for selling the option, or how
      much must it pay to buy the option?
     When will the option be exercised?
         This is often determined by the
          economic and interest rate environment
 Static GAP analysis ignores these
 embedded options
Earnings Sensitivity Analysis (Base Case)
  Example
   Assets
                                    3 Months  >3-6   >6-12       >1-3     >3-5     >5-10    >10-20     >20
                         Total       or Less Months Months       Years    Years    Years     Years    Years
Loans
  Prime Based            100,000     100,000
  Equity Credit Lines     25,000      25,000
  Fixed Rate >1 yr       170,000      18,000   18,000   36,000   96,000    2,000
  Var Rate Mtg I Yr       55,000      13,750   13,750   27,500
  30-Yr Fix Mortgage     250,000       5,127    5,129    9,329   32,792   28,916 116,789     51,918
  Consumer               100,000       6,000    6,000   12,000   48,000   28,000
  Credit Card             25,000       3,000    3,000    6,000   13,000
Investments
  Eurodollars             80,000      80,000
  CMOs FixRate            35,000       2,871    2,872    5,224   13,790    5,284    4,959
  US Treasury             75,000                5,000    5,000   25,000   40,000
  Fed Funds Sold          25,000      25,000

Cash & Due From Banks      15,000                                                                      15,000
Loan Loss Reserve         -15,000                                                                     -15,000
Non-earning Assets         60,000                                                                      60,000
 Total Assets           1,000,000    278,748   53,751 101,053 228,582 104,200 121,748        51,918    60,000
Earnings Sensitivity Analysis (Base Case)
  Example
   Liabilities and GAP Measures
                                 3 Months  >3-6   >6-12        >1-3      >3-5      >5-10    >10-20    >20
                      Total       or Less Months Months        Years     Years     Years     Years   Years
Deposits
 MMDAs                240,000     240,000
 Retail CDs           400,000      60,000   60,000   90,000 160,000      30,000
 Savings               35,000                                                                         35,000
 NOW                   40,000                                                                         40,000
 DDA Personal          55,000                                                                         55,000
 Comm'l DDA            60,000      24,000                                                             36,000
Borrowings
 TT&L                  25,000      25,000
 L-T notes FR          50,000                                                      50,000
 Fed Funds Purch                                                                        0
NIR Liabilities         30,000                                                                        30,000
Capital                 65,000                                                                        65,000
 Tot Liab & Equity   1,000,000    349,000   60,000   90,000 160,000      30,000    50,000        0   261,000

Swaps- Pay Fixed                   50,000                      -25,000   -25,000
GAP                                -20,252 -6,249     11,053   43,582    49,200 71,748 51,918 -201,000
CUMULATIVE GAP                     -20,252 -26,501   -15,448   28,134    77,334 149,082 201,000      0
Fed Funds Forecast vs. Implied Forward Rates
                                            4.50
         Interest Rate                                               Market Implied Rates
                                            4.25
         Forecasts




                                        %
                                        e
                                                    Most LikelyForecast




                                        t
                                            4.00




                                        a
                                        R
                                        s
                                            3.75




                                        d
                                        n
                                        u
                                        F
                                            3.50




                                        d
                                        e
                                        F
                                            3.25

                                            3.00
                                                1   3 5 7 9 11 13 15 17 19 21 23
                                                           Time (month)
    Most LikelyForecast and Rate Ramps Dec. 2005
     6
     5
t
n
    4
e
c
r
e
     3
P
     2
     0
      11 1 3 5 7 9 11 1 3 5 7 9 12
           2006           2007
1.0
                                                                                         Sensitivity of Earnings: Year One
                                                                    .5
Earnings sensitivity over one and two
                                                                    2
years versus most likely rate scenario

                                         Change in NII ($MM)
                                                                   (.5)
                                                                                             ALCO Guideline
                                                                  (1.0)
                                                                                             Board Limit
                                                                  (1.5)
                                                                  (2.0)
                                                                  (2.5)
                                                                  (3.0)
                                                                  (3.5)
                                                                     - 300       -200        -100         ML           +100        +200   +300
                                                                             Ramped Change in Rates from Most Likely (Basis Point)
                                                                   1.0
                                                                                        Sensitivity of Earnings: Year Two
                                                                     .5
                                            Change in NII ($MM)




                                                                    2
                                                                   (.5)
                                                                                             ALCO Guideline
                                                                  (1.0)
                                                                                             Boar Limit
                                                                                                d
                                                                  (1.5)
                                                                  (2.0)
                                                                  (2.5)
                                                                  (3.0)
                                                                     - 300       -200       -100          ML           +100        +200   +300
                                                                              Ramped Change in Rates from Most Likely (Basis Points)
Earnings Sensitivity Analysis Results

 For the bank:
   The embedded options can potentially
    alter the bank’s cash flows
   Interest rates change by different
    amounts at different times
 Summary results are known as
 Earnings-at-Risk or Net Interest
 Income Simulation
Earnings Sensitivity Analysis
 Earnings-at-Risk
     The potential variation in net interest income
      across different interest rate environments,
      given different assumptions about balance
      sheet composition, when embedded options
      will be exercised, and the timing of repricings.
        Demonstrates the potential volatility in

         earnings across these environments
        The greater is the potential variation in

         earnings (earnings at risk), the greater is
         the amount of risk assumed by a bank , or
        The greater is the maximum loss, the

         greater is risk
Income Statement GAP

 Income Statement GAP
    Forecasts the change in net interest
     income given a 1% rise or fall in the
     bank’s benchmark rate over the next
     year.
    It converts contractual GAP data to
     figures evidencing the impact of a 1%
     rate movement.
    Income statement GAP is also know in
     the industry as Beta GAP analysis
Income Statement GAP Adjusts the
Balance Sheet GAP to Incorporate the
Earnings Change Ratio

 The Earnings Change Ratio
   This ratio indicates how the yield on
   each asset and rate paid on each
   liability is assumed to change relative
   to a 1 percent move in the benchmark
   rate.
Amounts In Thousands                Prime Down 100bp        Prime Up 100bp
                                                       Balance         Income Balance         Income
                                                        Sheet        Statement Sheet         Statement
                                                                   t                       t
                                                        GAP* ECR        GAP    GAP* ECR         GAP
                       Rate-Sensitive Assets              A      B      AXB      C      D      CxD
Income Statement GAP

                       Loans
                            Fixed Rate                   $5,661   100%    $5,661     $5,661   100%    $5,661
                            Floating Rate                 3,678   100%     3,678      3,678   100%     3,678
                       Securities
                            Principal Cash Flows
                            Agencies                        200   71%        142        200   71%        142
                            Agy Callables                 2,940   71%      2,087        300   60%        180
                            CMO Fixed                       315   58%        183         41   51%         21
                            Fed Funds Sold                2,700   96%      2,592      2,700   96%      2,592
                            Floating Rate
                       Total Rate-Sensitive Assets      $15,494          $14,343    $12,580          $12,274
                       Rate-Sensitive Liabilities
                             Savings                     $1,925   75%      $1,444    $1,925    5%        $96
                             Money Mkt Accts             11,001   60%       6,601    11,001   40%      4,400
                             NOW                          2,196   80%       1,757     2,196   20%        439
                             Fed Funds Purch/Repo             0   96%           0         0   96%          0
                             CDs - IOOM                   3,468   85%       2,948     3,468   85%      2,948
                             CDs < 100M                   4,370   84%       3,671     4,370   84%      3,671
                       Total Rate-Sensitive             $22,960          $16,420 $22,960             $11,554
                       Rate Sensitivity Gap (Assets-   ($7,466)          ($2,077) ($10,380)            $719
                       Liab) Assets
                       Total                            $29,909          $29,909 $29,909             $29,909
                       GAP as a Percent of Total       -24.96%            -6.94% -34.71%              2.40%
                       Assets in Net Interest
                       Change                                             ($20.8)                       $7.2
                       Change in Net Interest                              0.07%                      0.02%
                       Net Interest Margin                                 5.20%                      5.20%
                       Percentage Change in Net                            1.34%                      0.46%
Managing the GAP and Earnings Sensitivity
Risk
 Steps to reduce risk
   Calculate periodic GAPs over short
    time intervals.
   Fund repriceable assets with matching
    repriceable liabilities so that periodic
    GAPs approach zero.
   Fund long-term assets with matching
    noninterest-bearing liabilities.
   Use off-balance sheet transactions to
    hedge.
Adjust the Effective Rate Sensitivity of a
Bank’s Assets and Liabilities

Objective            Approaches
                     Buy longer-term securities.
Reduce asset
                     Lengthen the maturities of loans.
  sensitivity
                     Move from floating-rate loans to term loans.

Increase asset       Buy short-term securities.
   sensitivity       Shorten loan maturities.
                     Make more loans on a floating-rate basis.
                     Pay premiums to attract longer-term deposit
Reduce liability
                        instruments.
  sensitivity
                     Issue long-term subordinated debt.
                     Pay premiums to attract short-term deposit
Increase liability     instruments.
   sensitivity       Borrow more via non-core purchased
                       liabilities.
Bank Management, 6th edition.
                Management
           Timothy W. Koch and S. Scott MacDonald
           Copyright © 2006 by South-Western, a division of Thomson Learning




             Managing Interest Rate Risk:
             GAP and Earnings Sensitivity



                  Chapter 5

William Chittenden edited and updated the PowerPoint slides for this edition.

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Session7 Koch5

  • 1. Bank Management, 6th edition. Management Timothy W. Koch and S. Scott MacDonald Copyright © 2006 by South-Western, a division of Thomson Learning Managing Interest Rate Risk: GAP and Earnings Sensitivity Chapter 5 William Chittenden edited and updated the PowerPoint slides for this edition.
  • 2. Interest Rate Risk  Interest Rate Risk  The potential loss from unexpected changes in interest rates which can significantly alter a bank’s profitability and market value of equity.
  • 3. Interest Rate Risk: GAP & Earnings Sensitivity  When a bank’s assets and liabilities do not reprice at the same time, the result is a change in net interest income.  The change in the value of assets and the change in the value of liabilities will also differ, causing a change in the value of stockholder’s equity
  • 4. Interest Rate Risk  Banks typically focus on either:  Net interest income or  The market value of stockholders' equity  GAP Analysis  A static measure of risk that is commonly associated with net interest income (margin) targeting  Earnings Sensitivity Analysis  Earnings sensitivity analysis extends GAP analysis by focusing on changes in bank earnings due to changes in interest rates and balance sheet composition
  • 5. Asset and Liability Management Committee (ALCO)  The ALCO’s primary responsibility is interest rate risk management.  The ALCO coordinates the bank’s strategies to achieve the optimal risk/reward trade-off.
  • 6. Two Types of Interest Rate Risk  Spread Risk (reinvestment rate risk)  Changes in interest rates will change the bank’s cost of funds as well as the return on their invested assets. They may change by different amounts.  Price Risk  Changes in interest rates may change the market values of the bank’s assets and liabilities by different amounts.
  • 7. Interest Rate Risk: Spread (Reinvestment Rate) Risk  If interest rates change, the bank will have to reinvest the cash flows from assets or refinance rolled-over liabilities at a different interest rate in the future.  An increase in rates, ceteris paribus, increases a bank’s interest income but also increases the bank’s interest expense.  Static GAP Analysis considers the impact of changing rates on the bank’s net interest income.
  • 8. Interest Rate Risk: Price Risk  If interest rates change, the market values of assets and liabilities also change.  The longer is duration, the larger is the change in value for a given change in interest rates.  Duration GAP considers the impact of changing rates on the market value of equity.
  • 9. Measuring Interest Rate Risk with GAP  Example: A bank makes a $10,000 four-year car loan to a customer at fixed rate of 8.5%. The bank initially funds the car loan with a one-year $10,000 CD at a cost of 4.5%. The bank’s initial spread is 4%. 4 year Car Loan 8.50% 1 Year CD 4.50% 4.00%  What is the bank’s risk?
  • 10. Measuring Interest Rate Risk with GAP  Traditional Static GAP Analysis GAPt = RSAt -RSLt  RSAt  Rate Sensitive Assets  Those assets that will mature or reprice in a given time period (t)  RSLt  Rate Sensitive Liabilities  Those liabilities that will mature or reprice in a given time period (t)
  • 11. Measuring Interest Rate Risk with GAP  Traditional Static GAP Analysis  What is the bank’s 1-year GAP with the auto loan?  RSA1yr = $0  RSL1yr = $10,000  GAP1yr = $0 - $10,000 = -$10,000  The bank’s one year funding GAP is -10,000  If interest rates rise (fall) in 1 year, the bank’s margin will fall (rise)
  • 12. Measuring Interest Rate Risk with GAP  Traditional Static GAP Analysis  Funding GAP  Focuses on managing net interest income in the short-run  Assumes a ‘parallel shift in the yield curve,’ or that all rates change at the same time, in the same direction and by the same amount. Does this ever happen?
  • 13. Traditional Static GAP Analysis Steps in GAP Analysis  Develop an interest rate forecast  Select a series of “time buckets” or intervals for determining when assets and liabilities will reprice  Group assets and liabilities into these “buckets ”  Calculate the GAP for each “bucket ”  Forecast the change in net interest income given an assumed change in interest rates
  • 14. What Determines Rate Sensitivity (Ignoring Embedded Options)?  An asset or liability is considered rate sensitivity if during the time interval:  It matures  It represents and interim, or partial, principal payment  It can be repriced  The interest rate applied to the outstanding principal changes contractually during the interval  The outstanding principal can be repriced when some base rate of index changes and management expects the base rate / index to change during the interval
  • 15. What are RSAs and RSLs?  Considering a 0-90 day “time bucket,” RSAs and RSLs include:  Maturing instruments or principal payments  If an asset or liability matures within 90 days, the principal amount will be repriced  Any full or partial principal payments within 90 days will be repriced  Floating and variable rate instruments  If the index will contractually change within 90 days, the asset or liability is rate sensitive  The rate may change daily if their base rate changes.  Issue: do you expect the base rate to change?
  • 16. Factors Affecting Net Interest Income  Changes in the level of interest rates  Changes in the composition of assets and liabilities  Changes in the volume of earning assets and interest-bearing liabilities outstanding  Changes in the relationship between the yields on earning assets and rates paid on interest-bearing liabilities
  • 17. Factors Affecting Net Interest Income: An Example  Consider the following balance sheet: 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 $ 1,000 $ 1,000 NII = (0.08 x 500 + 0.11 x 350) - (0.04 x 600 + 0.06 x 220) NII = 78.5 - 37.2 = 41.3 NIM = 41.3 / 850 = 4.86% GAP = 500 - 600 = -100
  • 18. Examine the impact of the following changes  A 1% increase in the level of all short-term rates?  A 1% decrease in the spread between assets yields and interest costs such that the rate on RSAs increases to 8.5% and the rate on RSLs increase to 5.5%?  Changes in the relationship between short- term asset yields and liability costs  A proportionate doubling in size of the bank?
  • 19. 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 $ 1,000 $ 1,000 NII = (0.09 x 500 + 0.11 x 350) - (0.05 x 600 + 0.06 x 220) NII = 83.5 - 43.2 = 40.3 NIM = 40.3 / 850 = 4.74% With a negative GAP, more GAP = 500 - 600 = -100 liabilities than assets reprice higher; hence NII and NIM fall
  • 20. 1% decrease in the spread 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 $ 1,000 $ 1,000 NII = (0.085 x 500 + 0.11 x 350) - (0.055 x 600 + 0.06 x 220) NII = 81 - 46.2 = 34.8 NIM = 34.8 / 850 = 4.09% NII and NIM fall (rise) with a GAP = 500 - 600 = -100 decrease (increase) in the spread. Why the larger change?
  • 21. Changes in the Slope of the Yield Curve  If liabilities are short-term and assets are long-term, the spread will  widen as the yield curve increases in slope  narrow when the yield curve decreases in slope and/or inverts
  • 22. Proportionate doubling in size Expected Balance Sheet for Hypothetical Bank Assets Yield Liabilities Cost Rate sensitive $ 1,000 8.0% $ 1,200 4.0% Fixed rate $ 700 11.0% $ 440 6.0% Non earning $ 300 $ 200 $ 1,840 Equity $ 160 Total $ 2,000 $ 2,000 NII = (0.08 x 1000 + 0.11 x 700) - (0.04 x 1200 + 0.06 x 440) NII = 157 - 74.4 = 82.6 NIM = 82.6 / 1700 = 4.86% NII and GAP double, but NIM GAP = 1000 - 1200 = -200 stays the same. What has happened to risk?
  • 23. Changes in the Volume of Earning Assets and Interest-Bearing Liabilities  Net interest income varies directly with changes in the volume of earning assets and interest-bearing liabilities, regardless of the level of interest rates
  • 24. RSAs increase to $540 while fixed-rate assets decrease to $310 and RSLs decrease to $560 while fixed-rate liabilities increase to $260 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 $ 1,000 $ 1,000 NII = (0.08 x 540 + 0.11 x 310) - (0.04 x 560 + 0.06 x 260) NII = 77.3 - 38 = 39.3 NIM = 39.3 / 850 = 4.62% Although the bank’s GAP GAP = 540 - 560 = -20 (and hence risk) is lower, NII is also lower.
  • 25. Changes in Portfolio Composition and Risk  To reduce risk, a bank with a negative GAP would try to increase RSAs (variable rate loans or shorter maturities on loans and investments) and decrease RSLs (issue relatively more longer-term CDs and fewer fed funds purchased)  Changes in portfolio composition also raise or lower interest income and expense based on the type of change
  • 26. Changes in Net Interest Income are directly proportional to the size of the GAP  If there is a parallel shift in the yield curve: ÄNIIexp  GAP  iexp  It is rare, however, when the yield curve shifts parallel  Ifrates do not change by the same amount and at the same time, then net interest income may change by more or less.
  • 27. Summary of GAP and the Change in NII GAP Summary Change in Change in Change in Change in GAP Interest Interest Interest Net Interest Income Income Expense Income Positive Increase Increase > Increase Increase Positive Decrease Decrease > Decrease Decrease Negative Increase Increase < Increase Decrease Negative Decrease Decrease < Decrease Increase Zero Increase Increase = Increase None Zero Decrease Decrease = Decrease None
  • 28. Rate, Volume, and Mix Analysis  Banks often publish a summary of how net interest income has changed over time.  They separate changes over time to:  shifts in assets and liability composition and volume  changes associated with movements in interest rates.  The purpose is to assess what factors influence shifts in net interest income over time.
  • 29. Measuring Interest Rate Risk: Synovus 2004 Compared to 2003 2003 Compared to 2002 Change Due to * Change Due to * Interest earned on: Volume Yield/Rate Net Change Volume Yield/Rate Net Change Taxable loans, net $ 149,423 (117,147) 32,276 161,222 36,390 197,612 Tax-exempt loans, net† 1,373 (586) 787 1,108 (450) 658 Taxable investment securities (5,313) (916) (6,229) 4,507 2,570 7,077 Tax-exempt investment securities† 2,548 74 2,622 2,026 (206) 1,820 Interest earning deposits with banks 223 (176) 47 28 48 76 Federal funds sold and securities 406 (1,745) (1,339) 1,447 1,410 2,857 purchased under resale agreements Mortgage loans held for sale 7,801 (1,680) 6,121 (113) 549 436 Total interest income 156,461 (122,176) 34,285 170,225 40,311 210,536 Interest paid on: Interest bearing demand deposits 6,074 (12,517) (6,443) 1,537 5,433 6,970 Money market accounts 21,380 (36,244) (14,864) 4,654 13,888 18,542 Savings deposits (369) (3,307) (3,676) (660) (67) (727) Time deposits 32,015 (22,545) 9,470 38,824 32,812 71,636 Federal funds purchased and securities (6,165) (29,744) (35,909) 23,148 15,870 39,018 sold under repurchase agreements Other borrowed funds 21,318 (4,272) 17,046 21,960 3,361 25,321 Total interest expense 74,253 (108,629) (34,376) 89,463 71,297 160,760 Net interest income 82,208 (13,547) 68,661 80,762 (30,986) 49,776
  • 30. Interest Rate-Sensitivity Reports Classifies a bank’s assets and liabilities into time intervals according to the minimum number of days until each instrument is expected to be repriced.  GAP values are reported a periodic and cumulative basis for each time interval.  Periodic GAP  Is the Gap for each time bucket and measures the timing of potential income effects from interest rate changes  Cumulative GAP  It is the sum of periodic GAP's and measures aggregate interest rate risk over the entire period  Cumulative GAP is important since it directly measures a bank’s net interest sensitivity throughout the time interval.
  • 31. Measuring Interest Rate Risk with GAP 1-7 8-30 31-90 91-180 181-365 Over Not Rate Days Days Days Days Days 1 year Sensitive Total Assets U.S. Treas & ag 0.7 3.6 1.2 0.3 3.7 9.5 MM Inv 1.2 1.8 3.0 Municipals 0.7 1.0 2.2 7.6 11.5 FF & Repo's 5.0 5.0 Comm loans 1.0 13.8 2.9 4.7 4.6 15.5 42.5 Install loans 0.3 0.5 1.6 1.3 1.9 8.2 13.8 Cash 9.0 9.0 Other assets 5.7 5.7 Total Assets 6.3 15.0 10.0 10.0 9.0 35.0 14.7 100.0 Liabilities and Equity MMDA 5.0 12.3 17.3 Super NOW 2.2 2.2 CD's < 100,000 0.9 2.0 5.1 6.9 1.8 2.9 19.6 CD's > 100,000 1.9 4.0 12.9 7.9 1.2 27.9 FF purchased - NOW 9.6 9.6 Savings 1.9 1.9 DD 13.5 13.5 Other liabilities 1.0 1.0 Equity 7.0 7.0 Total Liab & Eq. 5.0 11.0 30.3 24.4 3.0 4.8 21.5 100.0 Periodic GAP 1.3 4.0 -20.3 -14.4 6.0 30.2 Cumulative GAP 1.3 5.3 -15.0 -29.4 -23.4 6.8
  • 32. Advantages and Disadvantages of Static GAP Analysis  Advantages  Easy to understand  Works well with small changes in interest rates  Disadvantages  Ex-post measurement errors  Ignores the time value of money  Ignores the cumulative impact of interest rate changes  Typically considers demand deposits to be non-rate sensitive  Ignores embedded options in the bank’s assets and liabilities
  • 33. Measuring Interest Rate Risk with the GAP Ratio  GAP Ratio = RSAs/RSLs  A GAP ratio greater than 1 indicates a positive GAP  A GAP ratio less than 1 indicates a negative GAP
  • 34. What is the ‘Optimal GAP’  There is no general optimal value for a bank's GAP in all environments.  Generally, the farther a bank's GAP is from zero, the greater is the bank's risk.  A bank must evaluate its overall risk and return profile and objectives to determine its optimal GAP
  • 35. GAP and Variability in Earnings  Neither the GAP nor GAP ratio provide direct information on the potential variability in earnings when rates change.  Consider two banks, both with $500 million in total assets.  Bank A: $3 mil in RSAs and $2 mil in RSLs. GAP = $1 mil and GAP ratio = 1.5 mil  Bank B: $300 mil in RSAs and $200 mil RSLs. GAP equals $100 mill and 1.5 GAP ratio.  Clearly, the second bank assumes greater interest rate risk because its net interest income will change more when interest rates change.
  • 36. Link Between GAP and Net Interest Margin  Many banks will specify a target GAP to earning asset ratio in the ALCO policy statements Target Gap (Allowable % Change in NIM)(Expected NIM) Earning assets Expected % change in interest rates 
  • 37. Establishing a Target GAP: An Example  Consider a bank with $50 million in earning assets that expects to generate a 5% NIM.  The bank will risk changes in NIM equal to plus or minus 20% during the year  Hence, NIM should fall between 4% and 6%.
  • 38. Establishing a Target GAP: An Example (continued)  If management expects interest rates to vary up to 4 percent during the upcoming year, the bank’s ratio of its 1-year cumulative GAP (absolute value) to earning assets should not exceed 25 percent.  Target GAP/Earning assets = (.20)(0.05) / 0.04 = 0.25  Management’s willingness to allow only a 20 percent variation in NIM sets limits on the GAP, which would be allowed to vary from $12.5 million to $12.5 million, based on $50 million in earning assets.
  • 39. Speculating on the GAP  Many bank managers attempt to adjust the interest rate risk exposure of a bank in anticipation of changes in interest rates.  This is speculative because it assumes that management can forecast rates better than the market.
  • 40. Can a Bank Effectively Speculate on the GAP?  Difficult to vary the GAP and win as this requires consistently accurate interest rate forecasts  A bank has limited flexibility in adjusting its GAP; e.g., loan and deposit terms  There is no adjustment for the timing of cash flows or dynamics of the changing GAP position
  • 41. Earnings Sensitivity Analysis  Allows management to incorporate the impact of different spreads between asset yields and liability interest costs when rates change by different amounts.
  • 42. Steps to Earnings Sensitivity Analysis  Forecast future interest rates  Identify changes in the composition of assets and liabilities in different rate environments  Forecast when embedded options will be exercised  Identify when specific assets and liabilities will reprice given the rate environment  Estimate net interest income and net income  Repeat the process to compare forecasts of net interest income and net income across different interest rate environments.
  • 43. Earnings Sensitivity Analysis and the Exercise of Embedded Options  Many bank assets and liabilities contain different types of options, both explicit and implicit:  Option to refinance a loan  Call option on a federal agency bond the bank owns  Depositors have the option to withdraw funds prior to maturity  Cap (maximum) rate on a floating-rate loan
  • 44. Earnings Sensitivity Analysis Recognizes that Different Interest Rates Change by Different Amounts at Different Times  It is well recognized that banks are quick to increase base loan rates but are slow to lower base loan rates when rates fall.
  • 45. Recall the our example from before: 4 year Car Loan 8.50% 1 Year CD 4.50% 4.00%  GAP1Yr = $0 - $10,000 = -$10,000  What if rates increased? 1 year GAP Position Change in Rates Base Change in Rates -3 -2 -1 GAP1yr +1 +2 +3 -1,000 -2,000 -8,000 -10,000 -10,000 -10,000 -10,000 Re-finance the auto loans All CD’s will mature
  • 46. What about the 3 Month GAP Position?  Base GAP3m = $10,000 - $10,000 = 0 3 Month GAP Position Change in Rates Base Change in Rates -3 -2 -1 GAP3m +1 +2 +3 +8,000 +6,000 +2,000 0 -1,000 -3,000 -6,000 Re-finance auto loans, and People will “pull” the less likely to “pull” CD’s CD’s for higher returns
  • 47. The implications of embedded options  Does the bank or the customer determine when the option is exercised?  How and by what amount is the bank being compensated for selling the option, or how much must it pay to buy the option?  When will the option be exercised?  This is often determined by the economic and interest rate environment  Static GAP analysis ignores these embedded options
  • 48. Earnings Sensitivity Analysis (Base Case) Example  Assets 3 Months >3-6 >6-12 >1-3 >3-5 >5-10 >10-20 >20 Total or Less Months Months Years Years Years Years Years Loans Prime Based 100,000 100,000 Equity Credit Lines 25,000 25,000 Fixed Rate >1 yr 170,000 18,000 18,000 36,000 96,000 2,000 Var Rate Mtg I Yr 55,000 13,750 13,750 27,500 30-Yr Fix Mortgage 250,000 5,127 5,129 9,329 32,792 28,916 116,789 51,918 Consumer 100,000 6,000 6,000 12,000 48,000 28,000 Credit Card 25,000 3,000 3,000 6,000 13,000 Investments Eurodollars 80,000 80,000 CMOs FixRate 35,000 2,871 2,872 5,224 13,790 5,284 4,959 US Treasury 75,000 5,000 5,000 25,000 40,000 Fed Funds Sold 25,000 25,000 Cash & Due From Banks 15,000 15,000 Loan Loss Reserve -15,000 -15,000 Non-earning Assets 60,000 60,000 Total Assets 1,000,000 278,748 53,751 101,053 228,582 104,200 121,748 51,918 60,000
  • 49. Earnings Sensitivity Analysis (Base Case) Example  Liabilities and GAP Measures 3 Months >3-6 >6-12 >1-3 >3-5 >5-10 >10-20 >20 Total or Less Months Months Years Years Years Years Years Deposits MMDAs 240,000 240,000 Retail CDs 400,000 60,000 60,000 90,000 160,000 30,000 Savings 35,000 35,000 NOW 40,000 40,000 DDA Personal 55,000 55,000 Comm'l DDA 60,000 24,000 36,000 Borrowings TT&L 25,000 25,000 L-T notes FR 50,000 50,000 Fed Funds Purch 0 NIR Liabilities 30,000 30,000 Capital 65,000 65,000 Tot Liab & Equity 1,000,000 349,000 60,000 90,000 160,000 30,000 50,000 0 261,000 Swaps- Pay Fixed 50,000 -25,000 -25,000 GAP -20,252 -6,249 11,053 43,582 49,200 71,748 51,918 -201,000 CUMULATIVE GAP -20,252 -26,501 -15,448 28,134 77,334 149,082 201,000 0
  • 50. Fed Funds Forecast vs. Implied Forward Rates 4.50 Interest Rate Market Implied Rates 4.25 Forecasts % e Most LikelyForecast t 4.00 a R s 3.75 d n u F 3.50 d e F 3.25 3.00 1 3 5 7 9 11 13 15 17 19 21 23 Time (month) Most LikelyForecast and Rate Ramps Dec. 2005 6 5 t n 4 e c r e 3 P 2 0 11 1 3 5 7 9 11 1 3 5 7 9 12 2006 2007
  • 51. 1.0 Sensitivity of Earnings: Year One .5 Earnings sensitivity over one and two 2 years versus most likely rate scenario Change in NII ($MM) (.5) ALCO Guideline (1.0) Board Limit (1.5) (2.0) (2.5) (3.0) (3.5) - 300 -200 -100 ML +100 +200 +300 Ramped Change in Rates from Most Likely (Basis Point) 1.0 Sensitivity of Earnings: Year Two .5 Change in NII ($MM) 2 (.5) ALCO Guideline (1.0) Boar Limit d (1.5) (2.0) (2.5) (3.0) - 300 -200 -100 ML +100 +200 +300 Ramped Change in Rates from Most Likely (Basis Points)
  • 52. Earnings Sensitivity Analysis Results  For the bank:  The embedded options can potentially alter the bank’s cash flows  Interest rates change by different amounts at different times  Summary results are known as Earnings-at-Risk or Net Interest Income Simulation
  • 53. Earnings Sensitivity Analysis  Earnings-at-Risk  The potential variation in net interest income across different interest rate environments, given different assumptions about balance sheet composition, when embedded options will be exercised, and the timing of repricings.  Demonstrates the potential volatility in earnings across these environments  The greater is the potential variation in earnings (earnings at risk), the greater is the amount of risk assumed by a bank , or  The greater is the maximum loss, the greater is risk
  • 54. Income Statement GAP  Income Statement GAP  Forecasts the change in net interest income given a 1% rise or fall in the bank’s benchmark rate over the next year.  It converts contractual GAP data to figures evidencing the impact of a 1% rate movement.  Income statement GAP is also know in the industry as Beta GAP analysis
  • 55. Income Statement GAP Adjusts the Balance Sheet GAP to Incorporate the Earnings Change Ratio  The Earnings Change Ratio  This ratio indicates how the yield on each asset and rate paid on each liability is assumed to change relative to a 1 percent move in the benchmark rate.
  • 56. Amounts In Thousands Prime Down 100bp Prime Up 100bp Balance Income Balance Income Sheet Statement Sheet Statement t t GAP* ECR GAP GAP* ECR GAP Rate-Sensitive Assets A B AXB C D CxD Income Statement GAP Loans Fixed Rate $5,661 100% $5,661 $5,661 100% $5,661 Floating Rate 3,678 100% 3,678 3,678 100% 3,678 Securities Principal Cash Flows Agencies 200 71% 142 200 71% 142 Agy Callables 2,940 71% 2,087 300 60% 180 CMO Fixed 315 58% 183 41 51% 21 Fed Funds Sold 2,700 96% 2,592 2,700 96% 2,592 Floating Rate Total Rate-Sensitive Assets $15,494 $14,343 $12,580 $12,274 Rate-Sensitive Liabilities Savings $1,925 75% $1,444 $1,925 5% $96 Money Mkt Accts 11,001 60% 6,601 11,001 40% 4,400 NOW 2,196 80% 1,757 2,196 20% 439 Fed Funds Purch/Repo 0 96% 0 0 96% 0 CDs - IOOM 3,468 85% 2,948 3,468 85% 2,948 CDs < 100M 4,370 84% 3,671 4,370 84% 3,671 Total Rate-Sensitive $22,960 $16,420 $22,960 $11,554 Rate Sensitivity Gap (Assets- ($7,466) ($2,077) ($10,380) $719 Liab) Assets Total $29,909 $29,909 $29,909 $29,909 GAP as a Percent of Total -24.96% -6.94% -34.71% 2.40% Assets in Net Interest Change ($20.8) $7.2 Change in Net Interest 0.07% 0.02% Net Interest Margin 5.20% 5.20% Percentage Change in Net 1.34% 0.46%
  • 57. Managing the GAP and Earnings Sensitivity Risk  Steps to reduce risk  Calculate periodic GAPs over short time intervals.  Fund repriceable assets with matching repriceable liabilities so that periodic GAPs approach zero.  Fund long-term assets with matching noninterest-bearing liabilities.  Use off-balance sheet transactions to hedge.
  • 58. Adjust the Effective Rate Sensitivity of a Bank’s Assets and Liabilities Objective Approaches Buy longer-term securities. Reduce asset Lengthen the maturities of loans. sensitivity Move from floating-rate loans to term loans. Increase asset Buy short-term securities. sensitivity Shorten loan maturities. Make more loans on a floating-rate basis. Pay premiums to attract longer-term deposit Reduce liability instruments. sensitivity Issue long-term subordinated debt. Pay premiums to attract short-term deposit Increase liability instruments. sensitivity Borrow more via non-core purchased liabilities.
  • 59. Bank Management, 6th edition. Management Timothy W. Koch and S. Scott MacDonald Copyright © 2006 by South-Western, a division of Thomson Learning Managing Interest Rate Risk: GAP and Earnings Sensitivity Chapter 5 William Chittenden edited and updated the PowerPoint slides for this edition.