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Duration and Interest Rate Risk. Why Study Duration. Duration: measures the sensitivity of bond price change on interest rate change Objective: to see how much price change in bond value due to interest rate changes – a way to gauge interest rate risk. What is Duration?

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Presentation Transcript
why study duration
Why Study Duration
  • Duration: measures the sensitivity of bond price change on interest rate change
  • Objective: to see how much price change in bond value due to interest rate changes – a way to gauge interest rate risk
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What is Duration?

A measurement of the life of the bond on a present value basis

Formula for Duration

How to Calculation Duration

- find bond price

- find discounted cash flow in each period

- go through the worksheet

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Everything else equal,
    • 1. When the maturity of a bond lengthens, the duration rises as well.
    • 2. When interest rates rise, the duration of a coupon bond falls.
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3. The higher is the coupon rate on the bond, the shorter is the duration of the bond.
  • 4. Duration is additive: the duration of a portfolio of securities is the weighted-average of the durations of the individual securities, with the weights equaling the proportion of the portfolio invested in each.
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Exercise

Calculating duration for an 11-year 20% coupon bond when current interest rate is 10%

duration and interest rate risk
Duration and Interest-Rate Risk
  • %ΔP - DUR x Δi/(1+i)
  • i 10% to 11%:
  • For a coupon bond with coupon rate of 10%, DUR = 6.76 Yrs
  • %ΔP =
  • ΔP =
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For a 10 year, 20% coupon bond, DUR = 5.72 Yrs, if interest rate increases from 10% to 11%

%ΔP =

ΔP =

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Duration and Interest-Rate Risk

  • The greater is the duration of a security, the greater is the percentage change in the market value of the security for a given change in interest rates. Therefore, the greater is the duration of a security, the greater is its interest-rate risk.
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