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  • Duration it is the measure of how long on an average the holder of the bond has to wait before he receives his payments on the bond
  • A coupon paying bond’s duration would be lower than n as the holder gets some of his payments in the form of coupons before n years
  • Macaulay’s duration: is the weighted average of the times when the payments are made. And the weights are a ratio of the coupon paid at time t to the present bond price

  • Where:
    • t = Respective time period
    • C = Periodic coupon payment
    • y = Periodic yield
    • n = Total no of periods
    • M = Maturity value
  • Macaulay duration is also used to measure how sensitive a bond or a bond portfolio's price is to changes in interest rates
  • A bond’s interest rate risk is affected by:
    • Yield to maturity
    • Term to maturity
    • Size of coupon
    • From Macaulay’s equation we get a key relationship:

  • In the case of a continuously compounded yield the duration used is modified duration given as:
  • Consider a bond trading at 96.54 with duration of 4.5 years. In this case:
    • ΔB = - 96.54* 4.5 Δy => ΔB = -434.43 Δy
    • If there is 10 basis points increase ( + Δy)  in the yield then the bond price would change by:
    • ΔB = -434.43 * ( 0.001)
    • ΔB = -0.43443
    • Hence, B = 96.54 – 0.43443 = 96.10

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