- 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

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**CFA Practice Question**

Jackie Gold owned a bond that had a modified duration of 19.400. If the bond had a annual coupon of 19.00%, and a yield to maturity of 8.50%, what is the change in bond price given a change in yield of - 290 basis points?

A. 33.756%

B. -14.741%

C. 56.260%

**Explanation:**Candidates, beware of extraneous information and possible traps set for you! Modified duration estimates the percentage change in bond price with a change in yield and is a very simple computation. You do not need to make the Macaulay adjustment (i.e., (Macaulay duration)/(1+YTM)) since the modified duration is already provided. This calculation is very straightforward; however, do not forget to adjust for the " - "sign at the beginning of the formula. Remember that bond prices and interest rates move in an inverse manner. Consequently as interest rates decrease, bond prices decrease (and vice versa).

The formula for a bond with a Modified duration is: % dP = - Modified Duration * di

dP/P * 100 = - Dmod * di

Where dP = change in price for the bond, - Dmod = the modified duration for the bond, di = the yield change in basis points divided by 100, P = beginning price for the bond

% dP = -19.400 * -2.90 = 56.260%

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**User Contributed Comments**
3

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

savita |
I thought that duration was a good measure only for small interest rate changes (up to 100 basis point). This rate change is signficantly higher. |

wink44 |
I agree, wouldn't you need to apply a convexity adjustment for a rate change of this magnitude? |

achu |
in real life, yes, but with no convexity option provided and 'none of the above' not an option, this answer was the 'best'. |