CFA CFA Level 1 Convexity Adjustment

Convexity Adjustment

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    • Avatar of NaidenBNaidenB
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        The following question:
        Corp. bond s.a pay
        N=8 years @5.75 coupon is priced at 108.32. Duration: 6.4; Convexity: 0.5. Credit spread narrows with 75 basis points. Estimate return impact with/without convexity adjustment.

        So without convexity is simple: -Duration*change in spread = -6.4*-0.0075 = 4.8%

        I don’t get the logic with convex. adjustment.

        -duration*change in spread + 1/2 convexity*(change in spread)^2

        -6.4*-0.0075 + 1/2 (50) *(-0.0075)^2 = 4.94%

        How did we get the convexity from 0.5 to 50? What’s the reasoning behind this adjustment. Help would be appreciated 🙂

      • Avatar of NaidenBNaidenB
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          Thanks @vincentt‌ Makes sense now.

        • Avatar of vincenttvincentt
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            no problem at all.

          • Avatar of vincenttvincentt
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              Basically, you can use 50 or 0.5 it’s up to you because the formula can be as such:

              (-effective duration * change in yield * 100) + (1/2 * convexity * (change in yield) ^ 2 * 100)
              = (-6.4 * -0.75%) + (1/2 * 0.5 * -0.75%^2 )
              = 4.8% + 0.25 * 0.5625%
              = 4.8% + 0.1406%
              = 4.94%

              It’s the same on whether you want to use the *100 on 0.5 (to make it 50) or on 0.0075 (to make it 0.75%).

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              @NaidenB Schweser tells you to use the same scale as duration for convexity…. basically multiply convexity by 100

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