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**CFA Practice Question**

A portfolio manager has bought $10 million market value of a bond issue that has a duration of 5. Estimate the change in market value for this bond if interest rates change by 50 basis points.

A. $500,000

B. $50,000

C. $250,000

**Explanation:**Duration is an estimate of the percentage price change of a bond if interest rates change by 100 basis points or 1%. The formula is Approximate Percentage Price Change = - Duration * Change in Yield * 100. In this case, the formula is (-5) * (+/-.005) *100 = +/- 2.5%. Taking 2.5% of $10,000,000 is $250,0000 and adding / subtracting that from the original price gives $10,250,000 / $9,750,000. The reason for the negative sign on the right-hand side of the original formula is the inverse relationship between price change and yield change. A duration of 5 means that for every 100 basis point change in rates, we estimate the price of the bonds will change in the opposite direction by 5%.

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**User Contributed Comments**
7

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

steved333 |
Duration is 100 bp. 5 is for 100 bp, so 2.5 is for 50 bp. $250k is a multiple of that. |

Xocrevilo |
D = ((change in P)/(P)) x (1/BPM) 5 = ((change in P)/(10m)) x (1/0.005) change in P = 5 x 50,000 = 250,000 |

steved333 |
5*5 is 25. Then it's just a matter of decimal places and multiply by FV |

mekc |
50 bp = 0.005 = 0.5% 100bp = 1% |

dipu617 |
I don't get it. In the duration formula, there is "2" in denominator!!! That makes the result 500,000. Anybody with an explanation??!! |

dand1 |
You're not asked to use the formula for this one, you are already given the result of it which is 5. |

mbuenafe |
right on xocrevilo. |