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**CFA Practice Question**

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%

Correct Answer: C

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**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? |