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Convexity and Duration

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  • Convexity and Duration

    Hi, I've heard that if you are asked you find "Duration" without any specification during the exam, it means "Macaulay Duration". So, how about "Convexity"? If I am asked to find the Convexity, am I supposed to get the Macaulay convexity as well ?
    Thanks

  • #2
    Thats a good question but from what I have gathered from the ASM study manual and past exam questions on the SOA website it will specifically ask for the Macaulay Duration (MAC D).

    If a question asks for the modified duration (MOD D) it can be easily calculated one way by first calculating MAC D and using the relation


    MOD D= v*( MAC D) at the effective interest rate i.

    As far as your question regarding convexity I would assume that they are the same, but hopefully someone will have definite knowledge on this one.

    Hope this helps.

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    • #3
      I believe convexity is strictly a function of i. I suppose they can throw some dark material, such that you'll have to transform the continous rate into i and so on and so forth.
      "As far as I'm concerned, I prefer silent vice to ostentatious virtue." Albert Einstein
      "It is hard to tell if a man is telling the truth when you know you would lie if you were in his place." H. L. Mencken

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      • #4
        Originally posted by Stoneking View Post
        Hi, I've heard that if you are asked you find "Duration" without any specification during the exam, it means "Macaulay Duration". So, how about "Convexity"? If I am asked to find the Convexity, am I supposed to get the Macaulay convexity as well ?
        Thanks
        I ve seen a problem where they ask for regular convexity meaning C and also Mac Convexity.So i believe they will specify in one way or the other.

        But,is effective duration the same as modified one?

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        • #5
          I am using the Actex manual and I was also really furious when the sample problems were not specifying which kind of duration. From the answers it seems that if they just say duration that means Macaulay duration and they specify for modified duration.

          Also what is this Macaulay Convexity? The only Convexity they talk about in the Actex book is this: P''(i)/P(i).
          Last edited by Y2A; November 1 2008, 11:24 PM.

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          • #6
            As a general rule of thumb, anytime they say just "duration" they mean macaulay duration, if they ever want modified duration they will specify it.

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            • #7
              Originally posted by Y2A View Post
              I am using the Actex manual and I was also really furious when the sample problems were not specifying which kind of duration. From the answers it seems that if they just say duration that means Macaulay duration and they specify for modified duration.

              Also what is this Macaulay Convexity? The only Convexity they talk about in the Actex book is this: P''(i)/P(i).
              If you start from the general formula for convexity:
              c=[sum of t(t+1)*CF*V^t/PV]/(1+i)^2=[sum of t^2*CF*V^t/PV(1+i)^2]+[sum of t*CF*V^t/PV(1+i)^2].
              Now ,if look at the second sum you will see Dm/(1+i)^2,Dm-Mac duration,whereas the first part is Cm/(1+i)^2,Cm-mac convexity
              C=Cm/(1+i)^2+Dm/(1+i)^2

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