- CFA Exams
- CFA Exam: Level I 2021
- Study Session 15. Fixed Income (2)
- Reading 46. Understanding Fixed-Income Risk and Return
- Subject 2. Macaulay, Modified and Effective Durations

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**CFA Practice Question**

What is the duration of a 10%, 12-year, option-free bond selling at 124.09? Use 50 bp.

B. -7.49

C. 7.49

A. 7.63

B. -7.49

C. 7.49

Correct Answer: C

New yields at 6.5 and 7.5%. V- = 128.85 and V+ = 119.56

Duration = (128.85 - 119.56)/[2 x 124.09 x 0.005] = 7.49

Current yield 7%, N=24, PV=-124.09, PMT = 5, FV = 100, I/YR =?= 3.499 (2) = 7%

New yields at 6.5 and 7.5%. V- = 128.85 and V+ = 119.56

Duration = (128.85 - 119.56)/[2 x 124.09 x 0.005] = 7.49

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**User Contributed Comments**
18

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

kalps |
1) Need to find current yield 2) Need to estimate prices using a 0.5% change in yield 3) Then apply duration formula This is another example of an incomplete question how are you meant to know what the change in yield is ?????????? Until you see the answer you cannot tell it is 1/2% |

Aimy |
you should calculate current yield at first. This is not an incomplete question. |

gruszewski |
You should assume a small yield change (not larger than 50 bp). Actually for 1% yield change answet is quite similar. |

quincy |
mark this one |

wldu |
yes, how can I assume 0.5%? By common sense? |

tomchen |
I used 25bp, v_=126.44, v+=121.7931, Duration= (126.44-121.7931)/2*124.09*.0025=7.49, same thing , ask common sense ? |

myanmar |
duration is the maesure of the price difference after a 100 bp change in yield. |

gaur |
i used 100 bp change (1%) and got 7.50...pretty close to the right answer. |

gullan |
what I feel is that 100 basis point change is achieved by 50 basis point change up and down. |

NinaB |
In the book 5 page 624 and forward there is info about the size of the yield change. The key here is that Duration is an approximation of price change; we use a linear curve to estimate a non linear price. To limit the error in the approximation we should use a small change in yield. The larger change in yield the further away from the actual price line we get. You can use any change smaller than 50 bp and should end up with the same answer. In the book they mostly use 10 or 20 bp. Duration (approx. % change in P) = actual %P change + error term. We want to limit the error term. Hope it helps even with my foreigner English :) |

sam95 |
It is clearly stated in the reading that duration is calculated for 1% change, otherwise it will be stated in the question.For a 1% change you have to add and subtract 50bp from the annual yield. |

CheeHong |
Duration is a straightline, percentage of change does not matter. |

mrushdi |
Is duration always POSITIVE. |

rm001 |
Its an option free bond => positive convexity => price at lower yield is greater than price at higher yield => duration will be positive => C is the only option !! |

dmfcrowe |
Yes duration is always positive. Easy peasy to spot. |

jpducros |
duration is always positive for option free bond only ! |

johntan1979 |
While that is the obvious truth, no harm knowing how to calculate the exact answer... just in case all the answers are positive. |

johntan1979 |
And to gaur, without rounding, exact answer is 7.50448 |