Asset and Liability Management

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Asset and Liability Management

• Interest Rate Risk Management

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Asset and Liability Management

• Managing Interest Rate Risk
• Unexpected changes in interest rates can
  significantly alter a banks profitability and
  market value of equity.

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Figure 8-1
Interest Rate (Percent)
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Fed Funds
10-Year Treasury
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16
15
14
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12
11
10
9
8
7
6
5
4
3
2
Monthly Average Rates
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Interest Rate Risk

• Reinvestment rate risk
• - Cost of funds vrs return on assets.
• gt 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) -- gt larger change
  in value for a given change in interest rates.
• gt Duration GAP, impact on market value of
  equity.

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Funding GAPFocus on managing NII in the short
run.

• Method
• ¾ Group assets and liabilities into time
  "buckets" according to when they mature or
  re-price.
• ¾ Calculate GAP for each time bucket
• ¾ Funding GAPt Value RSAt - Value or RSLt
• where t time bucket e.g., 0-3 months.

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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.

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Exhibit 8.3
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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 RSLs
• RSA 540, fixed rate 310
• RSL 560, fixed rate 260.

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1 Increase in Short-Term Rates
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1 Decrease in Spread
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Proportionate Doubling in Size
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Increase in RSAs and Decrease in RSLs
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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

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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.

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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
  of new money.
• Break even rate 8.) net new money x
  (365/n)

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Break Even Analysis (Cont.)
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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.

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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 gt Liability duration
• interest rates
• Market value of equity falls

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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
• 900int 100
  int -----------------------------------------
  ---------------- 0
  10 20
• What is the maturity of each?
• What is the "effective" maturity?
• 1.) 20 years
• 2.) (900/100) x 1(100/1000) x 20 2.9 yrs
• Duration, however, uses a weighted average of the
  present values.

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DurationApproximate measure of the market value
of interest elasticity

• 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.

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Calculate Duration

• Examples 1000 face value, 10 coupon, 3 year,
  12 YTM

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Calculate Duration

• Examples 1000 face value, 10 coupon, 3 year,
  12 YTM

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If YTM 51000 face value, 10 coupon, 3 year,
5 YTM
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If YTM 201000 face value, 10 coupon, 3 year,
20 YTM

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If YTM 12 and Coupon 01000 face value, 0
coupon, 3 year, 12 YTM

• 
  1000---------------------0 1
  2 3

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If YTM 12 and Coupon 01000 face value, 0
coupon, 3 year, 12 YTM

• 
  1000---------------------0 1
  2 3
• 3 by definition

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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.

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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,

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Exhibit 8.8
click for otherexamples
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Exhibit 8.8
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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 gt liabilities, hence asset values change
  by more than liability values.

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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

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Exhibit 8.9
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Exhibit 8.9
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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 gt liabilities, hence asset values change
  by more than liability values.

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Change in the Market Value of Equity

• Using the relationship

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Change in the Market Value of Equity

• Using the relationship
• We can define the change in the MVE as
• In our case DMVE (-1.14) x 0.01 / (1.1356)
  x 1,000 -10.04