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**CFA Practice Question**

Assume that you hold a portfolio of bonds as follows:

$5,000,000 par value of 10-year bonds with a duration of 8.047 priced at 84.6275

$1,000,000 par value of 30-year bonds with a duration of 9.168 priced at 137.8586

$6,000,000 of 5-year bonds with a duration of 3.861 priced at 100 (par)

$5,000,000 par value of 10-year bonds with a duration of 8.047 priced at 84.6275

$1,000,000 par value of 30-year bonds with a duration of 9.168 priced at 137.8586

Calculate the duration of the portfolio.

A. 6.0168

B. 5.5683

C. 7.0253

**Explanation:**The duration of the portfolio is simply the weighted average of the components. Each bond segment is first multiplied by its % of value (par, discount, premium) and then multiplied by its duration. Ultimately each segment is divided by the total % of par portfolio value. In this case, duration = ($6,000,000 x 3.861) / $11,609,961 + ($4,231,375 x 8.047) / $11,609,961 + (1,378,586 x 9.168) / $11,609,961 = 6.0168.

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**User Contributed Comments**
11

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

Figo |
How was the $11,609,961 computed? |

masha |
11,609,961 = 6,000,000+,4,231,375,1,378,586 (and the latter two are calculated as par value adjusted for discount / premium) |

eddeb |
Portfolio is measured at PV |

babaj |
weighted average |

jerepast |
discount or premium / par |

twotwo |
$11,609,961 = 6,000,000+4,231,375+1,378,586 first value at per $4,231,375 =84.6275*5,000,000 $1,378,586 =137.8586*1,000,000 |

apiccion |
Weigh each bond in the portfolio by its price * par value. Remember duration tells you the % change of the PRICE, so any calculation would need to incorporate price. |

AUAU |
just don't know the discount & premium! |

mixer |
Discount is when price of bond is below par while premuim is when price is above par value |

shiva5555 |
I hate these 3 or 4 trick problems. I always miss one of the tricks. |

egypt |
i think that we have 2 multiply weight by the duration i made this but i have got a difference answer |