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Basic Question 6 of 17
A 6% coupon bond with semi-annual coupons has a convexity (in years) of 120, sells for 80% of par, and is priced at a yield to maturity of 8%. If the ytm increases to 9.5%, the predicted contribution to the percentage change in price, due to convexity, would be ______.
B. 1.35%
C. 2.7%
A. 1.08%
B. 1.35%
C. 2.7%
User Contributed Comments 24
| User | Comment |
|---|---|
| virginia | How do you compute it? |
| Aimy | The answer should be 13.5 percent. |
| kevin | Come on Aimy, the total change is only 1.5%! |
| Gina | convexity adjustment formula: (estim convexity on seminann.basis)(delta r^2)x100 =60(0.015)^2(100) =1.35 |
| mm04 | Where is the 60 from? I never see convexity adjusted for semi-annual? |
| stefdunk | convexity is 120, but the bond has a semi-annual coupon, therefore adjust 120/2=60 |
| natali | if convexity is adjusted for semi-annual, shouldn't the change in yield also be adjusted - 0.015/2? |
| tengo | If you calculate the convexity for a 20bp shock you get about 84 not 120. I do not know what a convexity of 120 measured in years is sinc econvexity it has totally different units that a duration. the answer appaear to be 2.7%. There are no sample problems were the convexity is ever divided by 2 for a semi annual pay bond!! |
| BADGUY | tengo i had 2.7 too and agree with you! |
| tanyak | so are we dividing annual convexity by 2 or not??? |
| thekapila | nopes convexity is not adjusted for semiannual basis. |
| mountaingoat | appears change in yld is not adjusted semi-annual only convexity. when you calculate convexity the change in yield is not divided by 2. |
| MFTIOA | This problem is flawed: if the annual convexity is 120, the semi-annual convexity should be n^2 (n = number of payments), or 2^2=4 times as much, or 480. |
| sam95 | No the problem is not flawed. 2x [(120)(0.015/2)^2x100] =1.35 don't forget to change the yld in to semi annual and then after using the formula change it back to the annual to get the % change in price annually. |
| panvino | I also agree with Tengo - I calculated the convexity and got 84, though I got 1.89 for convexity adjustment. |
| rocyang | sam95: since convexity adjustment from calculation is given in decimal, the end result 1.35 should stand for 135% change! |
| Jurrens | Rocyang: that's not factoring convexity which causes the curvature in the yield/price relationship. Good question to exemplify this extreme adjustment |
| dipu617 | Thanks to sam95. @Gina : convexity doesn't change to semi-annual, rather change in interest rate is semi-annual.... The solution provided by sam95 is correct. :-) |
| johntan1979 | No no no no no... it is NEVER stated in the question that the change in YTM is semi-annual... We always assume the basis point change, which, in this case, is 150 basis points or in decimals, 0.015. 2.7% is the right answer, not half of that. |
| gill15 | Sometimes I read these posts and I think i'm wrong when I'm right. Listen to Johntan... When you change the basis points you are changing the ANNUAL yield up and down. Do NOT do any other way. |
| Callie2 | Hmmm..I thought this was a pretty straight forward question. Convexity Adj = est. convexity * (change in r)^2 * 100 = 120*(.015)^2*100 =2.7 |
| CJPerugini | Convexity Effect = 0.5*Annual Convexity*(Change in YTM)^2 =0.5*120*(0.015^2) =0.0135 |
| CJPerugini | To prove this we can also calculate the effect on price based on a semi-annual basis, where Semi-Annual Convexity = Annual Convexity * 2^2 =0.5*120*4*(0.0075^2) =0.0135 |
| sarasyed5 | where does the 0.015 come from? |
I used your notes and passed ... highly recommended!
Lauren
Learning Outcome Statements
calculate and interpret convexity and describe the convexity adjustment
calculate the percentage price change of a bond for a specified change in yield, given the bond's duration and convexity
CFA® 2024 Level I Curriculum, Volume 4, Module 12.