Bond duration and convexity

Discussion in 'P1.T3. Financial Markets & Products (30%)' started by sleepybird, May 8, 2012.

  1. sleepybird

    sleepybird Active Member

    Hi David,
    Why "short a coupon bond is equivalent to long effect duration and short effective convexity?" I think bonds have positive durations, so shorting bond = shorting duration?

    Also, for the below question, why am I getting 2 different duration and convexity using different method? What did I do wrong?

    What are the duration and convexity of a two-year bond that pays an annual coupon of 10% and whose current yield to maturity is 14%? Use 1,000 as the face value.

    Method 1:
    BV0​
    BV+​
    BV-​
    N 2 2 2
    PMT 100 100 100
    I/Y 14% 15% 13%
    FV 1,000 1,000 1,000
    PV $934.13 $918.71 $949.96

    Duration 1.6723 =(949.96-918.71)/(2*1%*934.13)
    Convexity 4.3283 =(949.96+918.71-2*934.13)/(934.13*1%^2)

    Method 2:
    t CF PV Wt t*wt t^2*wt
    1 100 87.71929825 0.093904448 0.093904448 0.093904448
    2 1100 846.4142813 0.906095552 1.812191104 3.624382208
    934.1335796​
    1.000000​
    1.906095552​
    3.718286656
    Duration
    Convexity​

    Thank you very much for your help.
    Sleepybird
  2. sleepybird

    sleepybird Active Member

    Sorry the table was copied from excel. For method 2, using the weighted average of time method, I get duration of 1.9061 and convexity of 3.7183, which differ from duration of 1.6723 and convexity of 4.3283 calculated in method 1. Thanks.
  3. Krivetka

    Krivetka New Member

    No one have ideas?
    To calculate the price impact on a bond (currently priced 60.00) with modified duration of 5.7 and convexity 55.65 if the yield change in basis points is 23.
  4. sl

    sl Active Member

    change in price = -price*mod.duration*change in yield

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