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

###
**CFA Practice Question**

What is the interest rate risk, in percentage price change, of a 7% semi-annual-pay bond with a maturity of seven years, yielding 8%, if interest rates change by 60 basis points?

B. -3.18%

C. 3.18%

A. -3.28

B. -3.18%

C. 3.18%

Correct Answer: B

Current Price = 94.72, Full Valuation = 91.71, % change = -3.18%

###
**User Contributed Comments**
26

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

Sheikh |
change: drop or rise? |

John1965 |
The direction of change does not matter, Sheikh. |

jamiejamie |
when I subtract 60 points, i get 97.84, when i add 6 points, i get 91.71. am i doing something wrong? |

kalps |
the direction of the change does matter - you get the wrong answer if you assume a drop - jamiejamie is correct - you are doing nothing wrong it is just that the question is not complete |

shasha |
agree. for interest changes less than 50 bp (up or down), bond price volatilities are almost equal; however, for "big" changes > 50bp, direction matters quite a lot. not surprising that a bigger price percentage change was found when jamiemie cut the interest rate to 7.4%. |

hcliv |
Your risk is calculated if rates go up because of the inverse relationship of prices and yield. If yield goes down, that means the price of the bond went up, hence a profit opportunity. |

haarlemmer |
I assumed that when the price of the bond goes up is not a risk I am facing. As a matter of fact, it is examing the downward risk. |

myanmar |
risk is negative so i assumed a rate increas of 60bp! |

dlo1 |
The direction of the interest rate "change" does matter. The positive convexity in the bond means a yield decrease results in a larger % change in the bond price than a yield increase. If it is implicitly assumed that you are "holding" the bond, the interest rate risk is for yields to rise and the correct answer is obtained. |

steved333 |
Risk is only assumed if the rate increases. It's only risk if it devalues your investment. |

MFTIOA |
can't risk decrease? |

johnowens |
tough question |

NavdeepS |
good observation myanmar. But I would say the question needs to be a bit more specific. It wont be "risk" if you were short on the bond. |

zactompson |
it will be a risk if you short or long the bond. Risk is not about losing money. Risk is about price volatility. |

seankang |
agree with myanmar, if interest drops then theres no risk since bond becomes more valuable |

charmaineho |
Assuming interest rate chg to 8.6% Orig: n=14,FV=100,I/Y=4,PMT=3.5, CPT PV=-94.7184 New: n=14,FV=100,I/Y=4.3,PMT-3.5, CPT PV=-91.7144 %chg= (-91.7144-(-94.7184))/(-94.7481)*100 = -3.17 |

shamsi12 |
charmaineho!!! I m not understanding how u r calculating %chg how r u placing negative signs to it. |

Jurrens |
Shamis12: PVs are negative for a TVM calculations, because you are having a negative cash outflow (such as buying a bond). You could convert them to positive and get the same answer |

JohnnyWu |
The question needs to specify direction. |

endurance |
Direction does not matter. If yields increase you get a negative change of 3.18 percent. If yields decrease the change is plus 3.3 percent. Pure math, nothing else - B is correct. |

johntan1979 |
Yup, B is the correct answer. Either -3.18% or +3.3% |

gill15 |
Yup Johntan is right. Either of those answers but only -3.18% is one of the choices. Nice little trick. |

gill15 |
That's interesting though...for the same basis change -- One going up and one down --- the percentage changes' in price are different.... still nice pickup johntan1979 |

HolzGe1 |
gill: the percentage price changes must be different due to the convexity of the price-yield-curve, I assume. So the percentage price change of PV+ vs. PV0 will always be less than the percentage price change of PV- vs. PV0. |

ascruggs92 |
Kalps will probably argue to the CFA institute that their questions were wrong or incomplete if he/she fails the test |

aparmar |
why is it only assuming the interest rate increased |