- CFA Exams
- 2021 Level I
- Study Session 15. Fixed Income (2)
- Reading 46. Understanding Fixed-Income Risk and Return
- Subject 4. Bond Portfolio Duration

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##### Subject 4. Bond Portfolio Duration PDF Download

There are two ways to calculate the duration of a bond portfolio:

*The weighted average of the time to receipt of aggregate cash flows.*This method is based on the**cash flow yield**, which is the internal rate of return on the aggregate cash flows.*The weighted average of the durations of individual bonds that compose the portfolio.*The weight is the proportion of the portfolio that a bond comprises.Portfolio Duration = w _{1}D_{1}+ w_{2}D_{2}+ w_{3}D_{3}+ ... + w_{k}D_{k}

w_{i}= the market value of bond i / market value of the portfolio

D_{i}= the duration of bond i

k = the number of bonds in the portfolio

To illustrate this calculation, consider the following three-bond portfolio in which all three bonds are option-free:

- 10% 5-year 100.0000 10 $4 million $4,000,000 3.861
- 8% 15-year 84.6275 10 $5 million $4,231,375 8.047
- 14% 30-year 137.8586 10 $1 million $1,378,586 9.168

In this illustration, it is assumed that the next coupon payment for each bond is exactly six months from now (i.e., there is no accrued interest). The market value for the portfolio is $9,609,961. Since each bond is option-free, modified duration can be used.

- w1 = $4,000,000/$9,609,961 = 0.416, D1 = 3.861
- w2 = $4,231,375/$9,609,961 = 0.440, D2 = 8.047
- w3 = $1,378,586/$9,609,961 = 0.144, D3 = 9.168

The portfolio's duration is: 0.416 (3.861) + 0.440 (8.047) + 0.144 (9.168) = 6.47.

A portfolio duration of 6.47 means that for a 100 basis point change in the yield for each of the three bonds, the market value of the portfolio will change by approximately 6.47%. Keep in mind that the yield for each of the three bonds must change by 100 basis points for the duration measure to be useful. This is a critical assumption and its importance cannot be overemphasized.

**Learning Outcome Statements**

CFA® 2021 Level I Curriculum, 2021, Volume 5, Reading 46

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**User Contributed Comments**
9

User |
Comment |
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WaheedAbbasKhan |
can anyone help? what does this mean? "10% 5-year 100.0000 10 $4 million $4,000,000 3.861" 10% copuon - 5Year Maturity - FV100 - next? |

zackychoo |
10 is 10%, the interest rate. $4 mill is the total par val of the bonds $4,000,000 is the total market value of the bonds, which is equal to par value because coupon rate is equal to interest rate. 3.861 is the duration. |

papajeff |
This is hands down the shittiest part of the whole course. |

johntan1979 |
Nah... this is an easy piece of shit. Econ is the worst, whether micro or macro. |

gill15 |
This is easy crap. Problem is i think nobody reads the notes as we're nearing the end of lessons.... Accounting ---- by far the worst and most boring --- Taxes still scare me.. |

ldfrench |
This sections sucks. Accounting sucks too. |

farhan92 |
eco is fun -except the global eco! Fixed income is just shitty |

sandra1010 |
Can someone help? How did you get the market value of 4,231,375? |

bemccall95 |
sandra1010 you do the par value of 5,000,000 times the discount value of 0.846275 to get the market value |

I passed! I did not get a chance to tell you before the exam - but your site was excellent. I will definitely take it next year for Level II.