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**CFA Practice Question**

A bond's price increases by 1.25% of par when interest rates drop by 10 basis points (bp). Its price declines by 1.08% of par when rates increase by 10 bp. The current bond price is $98.85 and the prevailing yield to maturity is 8%. What is the duration of this bond?

A. 10.93

B. 11.65

C. 11.79

**Explanation:**Duration is calculated by, ignoring the negative sign, D = (ΔP / P) x (1 / P)

ΔP is averaged for the up and the down move. In this case, Avg. ΔP = (1.25 + 1.08) / 2 = 1.165.

Thus, D = (1.165 / 98.85) x (1 / 0.001) = 11.79. One basis point equals 0.0001.

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**User Contributed Comments**
11

User |
Comment |
---|---|

eddeb |
What about this method: (100.085-97.78)/(2*98.85*0.001) = 11.65 Looks good to me. |

jayjunk |
D = (delta P / P) x (1 / delta r) not D = (delta P / P) x (1 / P) At least that's what I think, correct me if I am wrong. |

amak |
Read the question carefully, it is 1.25% of PAR, meaning 1.25% of $100. So you must add $1.25 to 98.85, NOT 1.0125x98.85 |

MUSK |
Good point amak, thanks |

Kuki |
Price if yields decrease: 98.85+(1.25%*100)=100.10 Price if yields increase: 98.85-(1.08%*100)=97.77 Therefore Duration = (100.10-97.77)/(2*98.85*0.001) = 11.79 (2 dp) |

malawyer |
the PAR got me too, good and tricky question! |

StanleyMo |
we are too tire to handle tricky questions after fighting war with 90 questions++ lol |

cfahitman |
thanks amak! yours is straight to the point and explain the trick. it said delta P is average = (1.25+1.08)/2... which confused me even more. the trick is simply 1.25% of par, not of 98.85! we can use the same formula by doing difference between two prices: 101.25 and 98.92 to get the answer. |

ddrmax |
tricky |

mary11 |
man,they make easy questions confusing. |

madelinee |
Arrrgggghhhhh PAR!!! |