Calculate Interest Earning Asset - PowerPoint by zmw59708

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									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
    17                                                                          10-Year Treasury
    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     1990   1991   1992   1993   1994
                                                 Monthly Average Rates
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) -    (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 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) -    (0.05x600+0.06x220)
                    83.5          -          43.2   =      40.3
       NIM = 40.3 / 850                             =   4.74%
       GAP =         500          -           600   =      -100
 1% Decrease in 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              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 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) -   (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 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) -    (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 Sensitivity
Assets              1-7      8-30 31-90 91-180 181-365 > 1 yr Not RS Total
U.S. Treasury                   0.7   3.6    1.2    0.3       3.7        9.5
MM Inv                                1.2    1.8                           3
Municipals                            0.7      1    2.2       7.6      11.5
FF & Repo's             5                                                  5
Comm loans              1     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     9
Other assets                                                       5.7   5.7
 Total Assets         6.3       15    10      10       9       35 14.7  100

Liabilities and Equity
MMDA                 17.3                                                 17.3
Super NOW              2.2                                                 2.2
CD's < 100,000         0.9      2     5.1     6.9    1.8     2.9          19.6
CD's > 100,000         1.9      4    12.9     7.9    1.2                  27.9
FF purchased                                                                 0
NOW                                           9.6                          9.6
Savings                                                      1.9           1.9
DD                                                                 13.5   13.5
Other liabilities                                                     1      1
Equity                                                                7      7
 Total Liab & Eq.    22.3       6     18    24.4       3     4.8   21.5   100
GAP
Periodic GAP           -16       9     -8   -14.4       6   30.2
Cumulative 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 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                        $ 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.
   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 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
        |---|--------------------------|---------------------------
Duration
Approximate measure of the market value of
interest elasticity

            DV 
            V  %DV
     DUR         
              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

                    n                         n
                          C t (t)                   C t (t)
                    (1 + r)        t         (1 + r)        t
           DUR =   t =1
                     n
                                            t =1
                           Ct
                    (1 + r)
                                            PV of theSec.
                                    t
                   t =1




Examples:
    1000 face value, 10% coupon, 3 year,
 12% YTM
 Calculate Duration
                  n
                  n        n
                           n
               Ctt(t)         Ctt(t)
            (1 + r)tt  (1 + r)tt
     DUR = t=1
           t=1
            n
            n           t=1
                          t=1
                Ctt
            (1 + r)tt  PV of the Sec.
           t=1
           t=1




 Examples:
    100 * 1 100 * 2     100 * 3    1000 * 3
        1000 face+value, 10% coupon, 3 year,
    (1.12)11
             +
               (1.12)22
                        (1.12)33
                                 +
                                    (1.12)3
                                          3   2597.6
D  12% YTM    3
               3                                    = 2.73 years
                   100      1000
             (1.12)  tt
                           +
                               (1.12)3
                                     3
                                              951.96
            t=1
            t=1
If YTM = 5%
1000 face value, 10% coupon, 3 year, 5%
YTM



         100 * 1 100 * 2        100 * 3    1000 * 3
               1
                  +       2
                             +         3
                                         +
         (1.05) 1
                    (1.05) 2
                                (1.05) 3
                                            (1.05)3
                                                  3
      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
 |-------|-------|-------|
          1
 0 1000 * 3 2              3
     (1.12)3
           3
  D
      1000
     (1.12)3
           3


                         = 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,
            click for other
1   Exhibit 8.8
            examples
                                    Par      Years
                                $1,000 % Coup Mat.    YTM
                                                              Market
                                                              Value    Dur.
Assets
 Cash                       100                                 100
 Earning assets
   Commercial loan          700 14.00%         3     14.00%     700    2.65
   Treasury bond            200 12.00%         9     12.00%     200    5.97
     Total Earning Assets   900                      13.56%     900
   Non-cash earning assets    0                                   0
  Total assets             1000                      12.20%    1000    3.05

Liabilities
  Interest bearing liabs.
    Time deposit                  520 9.00%    1      9.00%     520    1.00
    Certificate of deposit        400 10.00%   4     10.00%     400    3.49
      Tot. Int Bearing Liabs.     920                 9.43%     920
    Tot. non-int. bearing           0                             0
    Total liabilities             920                9.43%      920    2.08
  Total equity                     80                            80
    Total liabs & equity         1000                          1000
1   Exhibit 8.8                     Par      Years
                                $1,000 % Coup Mat.    YTM
                                                               Market
                                                               Value    Dur.
Assets
 Cash                        100                                 100
 Earning assets
   Commercial loan           700 14.00% 3            14.00%      700    2.65
   Treasury bond             200 12.00% 9            12.00%      200    5.97
                 98  1        1 98  3
     Total Earning Assets 98900                      700  3
                                                     13.56%      900
                        
   Non-cash earning assets
                      1        02      3
                                                                  0
  Total dur  (1.14)
        assets            (1.14) (1.14)
                            1000                     (1.14)3
                                                     12.20%     1000    3.05

Liabilities
                                      700
  Interest bearing liabs.
    Time deposit                  520 9.00%    1      9.00%      520    1.00
    Certificate of deposit        400 10.00%   4     10.00%      400    3.49
      Tot. Int Bearing Liabs.     920                 9.43%      920
    Tot. non-int. bearing           0                              0
    Total liabilities             920                 9.43%      920    2.08
  Total equity                     80                             80
    Total liabs & equity         1000                           1000
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                                   Par      Years            Market
    Exhibit 8.9                 $1,000 % Coup Mat.    YTM     Value    Dur.
Assets
  Cash                       100                                100
  Earning assets
    Commercial loan          700 14.00%        3     15.00%   684.02   2.64
    Treasury bond            200 12.00%        9     13.00%   189.74   5.89
     Total Earning Assets    900                     14.57%   873.75
    Non-cash earning assets    0                                   0
   Total assets             1000                     13.07%   973.75   3.00

Liabilities
  Interest bearing liabs.
     Time deposit                 520 9.00%    1     10.00%   515.27   1.00
     Certificate of deposit       400 10.00%   4     11.00%   387.59   3.48
      Tot. Int Bearing Liabs.     920                10.43%   902.86
     Tot. non-int. bearing          0                              0
     Total liabilities            920                10.43%   902.86   2.06
  Total equity                     80                         70.891
     Total liabs & equity        1000                         973.75
1                                   Par      Years             Market
    Exhibit 8.9                 $1,000 % Coup Mat.     YTM     Value    Dur.
Assets
  Cash                        100                                100
  Earning assets
    Commercial loan           700 14.00%          3   15.00%   684.02   2.64
    Treasury bond             200 12.00%          9   13.00%   189.74   5.89
     Total Earning Assets     900                     14.57%   873.75
    Non-cash earning assets
                   3            0                                   0
                       98 1000  700
   Total assets 
           PV       (1.15)    t
                                     (1.15)3
                                                      13.07%   973.75   3.00

Liabilities           t1

  Interest bearing liabs.
     Time deposit                    520 9.00%    1   10.00%   515.27   1.00
     Certificate of deposit          400 10.00%   4   11.00%   387.59   3.48
      Tot. Int Bearing Liabs.        920              10.43%   902.86
     Tot. non-int. bearing             0                            0
     Total liabilities               920              10.43%   902.86   2.06
  Total equity                        80                       70.891
     Total liabs & equity           1000                       973.75
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
                    DV 
    Using the relationship:
                     V  %DV
              DUR         
                       Di   Di
                         
                     1+i 


                               the 
    We can define the change in Di MVE as:
                          
          DMVE  ( DGAP)                        TA
                             (1  iearnassets ) 


   In our case:
    DMVE = (-1.14) x [+0.01 / (1.1356)] x 1,000
               = -$10.04

								
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