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

Duration and Interest Rate Risk


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


Duration and 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


Duration and interest rate risk

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


Duration and interest rate risk

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

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


Duration and interest rate risk

  • 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.


Duration and interest rate risk

  • 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.


Duration and interest rate risk

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 =


Duration and interest rate risk

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

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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