# 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
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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