CFA CFA Level 1 Convexity Adjustment

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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.

-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 🙂

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Thanks @vincentt‌ Makes sense now.

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no problem at all.

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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