- CFA Exams
- CFA Level I Exam
- Topic 6. Fixed Income
- Learning Module 46. Understanding Fixed-Income Risk and Return
- Subject 4. Bond Portfolio Duration

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**CFA Practice Question**

A portfolio consists of two bonds:

Bond A | 10 years | 8% | 6.7 | 60%

Bond B | 7 years | 5.2% | 3.9 | 40%

Bond | Maturity | Coupon | Duration | Proportion in Portfolio

Bond A | 10 years | 8% | 6.7 | 60%

Bond B | 7 years | 5.2% | 3.9 | 40%

If there is an upward parallel shift in yields by 61 basis points, what will be the percentage change in the portfolio value?

A. -5.58%

B. -3.4%

C. 3.4%

**Explanation:**Portfolio Duration = w

_{A}D

_{A}+ w

_{B}D

_{B}= 0.6*6.7 + 0.4 * 3.9 = 5.58

Percentage change = %Δ = -5.58 x (0.0061) = -3.4%

Note that we can only use this computation if there is a parallel change in yields for all the bonds.

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**User Contributed Comments**
6

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

lazio |
what then, if the yield shifts for the individual bonds are different? |

Xocrevilo |
I presume that would impact convexity, thus the "change in price equation" would need to include convexity. However, as convexity is not provided here, and is impossible to calculate from the data given, the price change (i.e. % change in portfolio value) is simply negative portfolio duration times basis point change. |

staudinger |
an upward shift means that i have to multiply the portfolio duration with -1? yes, required yield increases so the value decreases. |

zzhumanov |
how you calculate 0.0061 ? |

Dragonrana |
zzhumanov : 100 bps =0.01 or 1%, then 61 basis points = 0.0061 |

epfrndz |
@Lazio: if the shift is not parallel, you must compute that change in value from basis point change for every bond. Example: Bond A's yield goes up by 15 basis points. Bond B's yield goes up by 7 basis points. (In this example bond A's yield is rising faster) Bond A change in value = Duration x -(Basis Point change) = 6.7 x -0.15 = -1.01 Bond B change in value = = 3.9 x -0.07 = -0.27 Then multiply by their weights in the portfolio: = (60% x -1.01) + (40% x -0.27) = -0.71 Given this example of a non parallel shift in the curve, the portfolio's value should drop approximately by -0.71%. |