March 6

1
March 6

• Stock Project
• Current Events
• Interest rate risk Chapter 8-9
• Duration

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What does Duration give us?

• interest rate sensitivityor, bond prices move
  inversely proportional to size of duration

PriceChanges
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Properties of Duration

• Greater duration-greater interest rate risk
• decreases as market interest rates increase
• increases with maturity
• always less than or equal to maturity
• decreases as coupon rate increases

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For a portfolio (balance sheet)

• Duration of a portfolio is the weighted average
  of the durations of the individual assets in the
  portfolio.
• Weights are the shares of the portfolio market
  value each asset (liability) has

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Duration Gap

• DAduration of assets
• DLduration of liabilitiesapproximates the
  sensitivity of net worth to interest rate changes

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Value of Change

• Supposethen,what happens
• change DA
• change DL
• change k

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Duration Gap

• If duration gap 0, means balance sheet is
  hedged or immunized.
• The market value of equity will not change as
  interest rates change in either direction

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Problem

• Balance SheetT-bonds 5 yrs to maturity
  paying 6 semi-annually and selling at par
• What is duration assets?
• What is duration of liabilities?
• What is leveraged adjusted duration gap?What is
  interest rate risk exposure?
• If yield curve shifted - r / (1 r) 0.005
  what is impact on equity?
• If yield curve shifted - r / (1 r) -0.0025
  what is impact on equity?

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Criticisms of Duration to Immunization

• dynamic problem
• difficult to implement on a balance sheet
• convexity
• flat yield curve assumption
• uniform yield curve shift
• default risk

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Properties of Convexity

• Larger convexity results in larger errors when
  using duration
• Increases with bond maturity
• vary with coupon
• For same duration
• 0 coupon bonds less convex than coupon bonds
• May be desirable
• protection from interest rate increases
• gains following interest rate decreases

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Convexity Measurement

• duration is slope (first derivative)
• convexity is change in slope (second derivative)

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Convexity Measurement

• Calculationbecause you already have

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Sample problems

• Suppose you purchase a 5 yr 13.76 (annual pay)
  bond that is priced to yield 10
• Duration?
• If interest rates rise to 11 within the next
  year and your investment horizon is 4 years from
  today, what will you yield on your investment?
• You have discovered that the price of a bond rose
  from 975 to 995 when the YTM fell from 9.75 to
  9.25. What is the duration of the bond?

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Convexity Measurement

• duration is slope (first derivative)
• convexity is change in slope (second derivative)

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Convexity Measurement Book

• Scaling factor 108

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Convexity Measurement method 2

• Calculationbecause you already have

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Convexity vs. Price Changes

• Remembercorrection for convexitywhere CX
  is convexity

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Simple Example

• 2 year bond, 1,000 face value
• annual coupon 10
• YTM 14
• Duration?, Convexity?
• What is expected change if interest rates
  increase 50 basis points?

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You try

• 3 year bond
• 5 coupon
• YTM 6
• Duration, convexity
• Effect of rate change from 6 to 8
• Components
• Duration
• Convexity
• True

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Repricing

• Duration
• Equity (net worth) measure
• When it a cash flow measure?

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Summary Interest Rate Risk Measurment

• Repricing Gap
• Duration and convexity for an instrument
• Duration measurement for a firms B/S
• Duration GAP
• Chapter 8 questions
• 3, 6, 7, 9, 13, 14
• Chapter 9
• 1-9, 12-23, 28

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Repricing Gap

• Repricing or Maturity Buckets
• one day
• 1 day to 3 months
• 3 months to 6 months
• more than 6 months to 12 months
• more than 1 year to 5 years
• over 5 years
• Rate sensitive assets (RSA) in each category
• Rate sensitive liabilities (RSL) in each category
• Difference (RSA - RSL) is termed GAP
• GAP x r net interest income (NII)
• Estimate (NII) for different buckets
• less than 3 months
• less than 1 year
• less than 5 years

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Duration Gap

• Identify assets and liabilities
• Calculate duration for each component
• Weight the durations by total assets and total
  liabilities respectively