CFA Practice Question

There are 266 practice questions for this study session.

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.

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).
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