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**CFA Practice Question**

Shaker Chin has an 11.000%, four year bond that is selling for a price of $98.432 and is currently yielding 11.50%. The table below shows how the price will vary given a 235 basis point change in market interest rates. Assuming the duration is 3.159 and the convexity is 12.592, what is the total estimated percentage price change based on a 235 BP market rate increase?

A. -7.0769%

B. -4.1071%

C. 7.7723%

**Explanation:**This answer requires candidates to recognize how to handle an interest rate decrease. The duration estimate is a negative adjustment while the positive convexity is a positive adjustment. The detailed solution follows.

Estimated change using duration = Approximate percentage price change = -duration * dy *100, since duration = 3.159 and dy = 0.0235

The estimated change associated with duration = -7.425%

Convexity adjustment = 1/2 * convexity measure * (dy)

^{2}* 100

Since convexity = 12.592, and (dy)

^{2}= (0.0235)

^{2}

The adjustment associated with convexity = +0.348%

Total estimated percentage price change = The estimated change associated with duration + estimated change associated with convexity = -7.425% + 0.348% =-7.0769%

Another simple solution is to take prices as given:

(91.466 - 98.432)/98.432 = - 0.070770 = -7.0770%.

However, it remains important to know how to derive the answer using duration and convexity.

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**User Contributed Comments**
3

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

rhardin |
I thought duration was not to be used for large rate shocks, and I thought 235 bps counted as large. So I was trying to avoid using duration. Are there times when I should avoid using duration? so when the rate change is large, use convexity as well. |

shiva5555 |
Is it normal for duration and convexity to move in opposite directions? |

Vlz2103 |
convexity always means adding to duration. duration can be positive (if interest rates decrease) or negative (if interest rates increase). |