Duration and Interest Rate Risk
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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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Duration and Interest Rate Risk

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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?

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


Calculate Duration on a $1000 Ten-year 10% Coupon Bond When its interest rate is 10% (Table 4)


Calculate Duration on a $1000 Ten-year 10% Coupon Bond When its interest rate is 20% (Table 5)


Calculating Duration, i = 20% 10-yr 10% Coupon Bond


  • 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.


  • 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.


Exercise

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


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 =


For a 10 year, 20% coupon bond, DUR = 5.72 Yrs, if interest rate increases from 10% to 11%

%ΔP =

ΔP =


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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