- CFA Exams
- CFA Level I Exam
- Study Session 15. Fixed Income (2)
- Reading 46. Understanding Fixed-Income Risk and Return
- Subject 5. Money Duration of a Bond and the Price Value of a Basis Point

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**CFA Practice Question**

The PVBP of a 7%, 5-year option-free bond selling at 100 would be closest to ______.

B. 0.4148

C. 4.0554

A. 0.0416

B. 0.4148

C. 4.0554

Correct Answer: A

-.0001 Price = 100.0416

PVBP = (100.0416 - 99.9584)/2 = 0.0416

+.0001 Price = 99.9584

-.0001 Price = 100.0416

PVBP = (100.0416 - 99.9584)/2 = 0.0416

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**User Contributed Comments**
20

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

kalps |
It took me 20 mins to figure out what you have done here - perhaps i am thick but up till this section I have been impressed with the pacakge but this is really hacking me of for anyone with the same problem: calculat the prices with a one bp change 1bp = 0.01 i.e. What he failts to mention in the answer which is obvious now is that the fv+pv i.e. the YTM is 7% - if you mentioned this then there would not be a problem |

gruszewski |
YTM is mentioned. Bond is selling at par and they give cupon payment. |

Gina |
I/Y+= 7.01/2=3.5050 N=10 PMT=3.5 -> PV+ = 99.9584 etc. |

synner |
I/Y=(1+.07/2)^2 -1 annual pay yield of semi-annual bond |

Pieter |
It's actually quite easy to deduce without the maths. The duration of the bond is approx. 4. Now just realise that duration is the impact due to a 100 pbs yield change. Therefore, a 1 pbs change will have a price impact of 0,04% on a bond trading at par. |

ragingrazz |
This is only true if there is no options |

derektl2 |
if bond is selling at par ... % coupon payment = YTM |

tanyak |
how is the bond's duration approx 4? |

achu |
If you take the average cash flow from the coupons, that duration is 3. Those coupons are nominally $3.5*2*5= $35. The $100 end cash flow by itself would be duration 5; wtd average will be something above 4. Given the choices, only A would be of the right order of magnitude. |

steved333 |
'course, you can always plug it in the calc... |

cong |
I think the answer is pretty straight forward. |

bundy |
First step: find duration current yield to maturity is 7% as bond at par Find YTM for a rate shock of +1% and -1% Use those bond values to calculate duration second step multiply duration by .0001 x100 simple |

Louiedog |
very tricky. |

endurance |
thanks cong |

jonan203 |
kalps, we are all studying to be analysts, sometimes finding the answers to the AN questions involves a little analyzing and applying previous module concepts to current questions. |

johntan1979 |
$0.041603 |

Kevdharr |
PVBP means exactly what it stands for: "Price Value of a Basis Point". So, even though the question doesn't specify that there was any change in yield, the fact that it is asking for the PVBP tells you that you need to assume there is an increase and decrease in yield of 1 basis point. The formula is: Modified duration * 0.0001 * current price of the bond. You aren't given the modified duration, so you have to calculate it. To do that, you have to calculate the price of the bond assuming the yield increases and decreases by 1 basis point. Once you get modified duration (which is around 4.15835), multiply that by 0.0001 (this represent one basis point) then multiply that by the current price of 100.00. Remember to always assume semi-annual compounding unless told otherwise. |

CJPerugini |
$0.041603 is the average price change for a semi-annual period. Shouldn't this be annualized to $0.083206 if PVBP measures price change on an annual basis? |

ascruggs92 |
Kalps - perhaps you are thick. The problem gives you all the information you need. If a bond is selling at par (which is the case here) the YTM is equal to it's coupon rate for an option free bond. You don't even have to calculate the change in price like they did, you can just approximate using the formula given in this last section of the notes: (modified duration) x (1bp) x (price). For this problem, 100 x 5 x 0.0001 = 0.05, which A is closes to. |

marta4100 |
So, it took me a lot to understand, and im having a lot of issues with this fixed income topics. However I managed to fully understand this question, and understand it can be hard sometimes, so I will try to make things as clear as possible. On a texas BI: 1) FIRST THING: Find I/Y. In this case as bond is selling at par cupon payments and I/Y will be the same. So PMT will be 7%/2 (as its semianual). 2) Compute PV+ and PV+ -PV+: PMT= 3.5 I/Y: We said it was 7% = 0.07 + 0.0001 (1bpt)= 0.07010 = 7.01%. That divided by 2 as it is semianual = 3.505% (We put that number in the calculator). FV=100 N= 10 (5x2 as it is semianual) COMPUTE FOR PV+= 99.58 -PV- (We do the same) PMT= 3.5 I/Y: We said it was 7% = 0.07 - 0.0001 (1bpt)= 0.0699 = 6.99%. That divided by 2 as it is semianual = 3.495% (We put that number in the calculator). FV=100 N= 10 (5x2 as it is semianual) COMPUTE FOR PV-= 100.04 3) PV- PV+ = 100-4- 99.58= 0.0832 4)PVBP= 0,0832/2= 0,0416!! |