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Shaker Chin has an 11.000%, 4 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 6.296, what is the total estimated percentage price change based on a 235 BP market rate increase?
Correct Answer: A
This answer requires candidates to recognize how to handle an interest rate decrease. The duration estimate is a negative 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 = The estimated change associated with duration = -7.425% Convexity adjustment = convexity measure * (dy)2 * 100 Since convexity = 6.296, 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, you'd better understand how to derive the answer using duration and convexity!