Measuring Interest Rate Risk with Duration GAP

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Measuring Interest Rate Risk with Duration GAP

• Economic Value of Equity Analysis
• Focuses on changes in stockholders equity given
  potential changes in interest rates
• Duration GAP Analysis
• Compares the price sensitivity of a banks total
  assets with the price sensitivity of its total
  liabilities to assess the impact of potential
  changes in interest rates on stockholders equity.

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Duration GAP

• Duration GAP Model
• Focuses on either managing the market value of
  stockholders equity
• The bank can protect EITHER the market value of
  equity or net interest income, but not both
• Duration GAP analysis emphasizes the impact on
  equity

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The Concept of Duration

• Duration is the Weighted Average Maturity of a
  Promised Stream of Future Cash Flows

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To Calculate Duration
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Price Sensitivity of a Security
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Duration and Modified Duration

• The greater the duration, the greater the price
  sensitivity
• Modified Duration gives an estimate of price
  volatility

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Convexity

• The Rate of Change in an Assets Price or Value
  Varies with the Level of Interest Rates or Yields

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Duration of an Asset portfolio
Where
wi the dollar amount of the ith asset divided
by total assets DAi the duration of the ith
asset in the portfolio
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Duration of a Liability Portfolio
Where
wi the dollar amount of the ith liability
divided by total liabilities DLi the duration
of the ith liability in the portfolio
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Steps in Duration GAP Analysis

• Forecast interest rates.
• Estimate the market values of bank assets,
  liabilities and stockholders equity.
• Estimate the weighted average duration of assets
  and the weighted average duration of liabilities.
  
• Incorporate the effects of both on- and
  off-balance sheet items. These estimates are used
  to calculate duration gap.
• Forecasts changes in the market value of
  stockholders equity across different interest
  rate environments.

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Duration Gap
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Change in the Value of a Banks Equity
Where i overall ytm of assets
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Duration GAP and Value of Equity

• To protect the value of equity against any change
  when rates change , the bank could set the
  duration gap to zero

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Hypothetical Bank Balance Sheet
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Calculating DGAP

• DA
• (700/1000)2.69 (200/1000)4.99 2.88
• DL
• (620/920)1.00 (300/920)2.81 1.59
• DGAP
• 2.88 - (920/1000)1.59 1.42 years
• What does this tell us?
• The average duration of assets is greater than
  the average duration of liabilities thus asset
  values change by more than liability values.

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1 percent increase in all rates.
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Calculating DGAP

• DA
• (683/974)2.68 (191/974)4.97 2.86
• DA
• (614/906)1.00 (292/906)2.80 1.58
• DGAP
• 2.86 - (906/974) 1.58 1.36 years
• What does 1.36 mean?
• The average duration of assets is greater than
  the average duration of liabilities, thus asset
  values change by more than liability values.

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Change in the Market Value of Equity

• In this case

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Positive and Negative Duration GAPs

• Positive DGAP
• Indicates that assets are more price sensitive
  than liabilities, on average.
• Thus, when interest rates rise (fall), assets
  will fall proportionately more (less) in value
  than liabilities and equity will fall (rise)
  accordingly.
• Negative DGAP
• Indicates that weighted liabilities are more
  price sensitive than weighted assets.
• Thus, when interest rates rise (fall), assets
  will fall proportionately less (more) in value
  that liabilities and the equity will rise (fall).

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Impact of Changing Interest Rates on a Banks
Equity