### CFA Practice Question

There are 266 practice questions for this study session.

### CFA Practice Question

The estimated duration of a bond will ______ if one uses 50 basis points to estimate duration rather than 25 basis points.

A. change to a lower number
B. change to a new value, but one cannot tell which direction
C. not change in value
D. change to a higher number

The straight line that is tangent to the curved line remains the same for small or large yield changes.

User Comment
sharapov A mathematically correct answer is B. Approximated value of a derivative always depends on the step.
gaur strictly speaking there is no way that a duration calculated with 25 bp and 50 bp will be the same. however, duration is an appro measure and the questions asks for the "estimated".
NinaB This is because it is small changes, if it was from 25 to 250 bps the estimation would change and be far from the actual price change. If we are investigating an option free bond the actual price curve is always above to the estimated price curve, and tangent in the original price.
achu I expect a clearer question on the actual exam! B sounded good. All of these durations calculated are estimates by this formula; and they would differ.
steved333 the question is asking about the estimated duration, and since any yield change of <=50bp in either direction is going to be negligible to the point that the estimate will be the same. I think that the point is that 100bp spread is the general rule. You're not going to get much more accurate than that.
sam95 There will be a small difference which will be due to error.The point to be noted is this that in smaller changes of bps we will be dividing by smaller number 25bps where as for larger changes like 50bp we will have a larger denominator. Don't forget we have in the formula 2xVox %bp(.005 &.0025 as bps)as the denominator.
johnowens in the exam they will expect a certain amount of common sense and familiarity with the basic concepts. C is correct. B would be technically pedantic and irrelevant.
dah62 C is correct because the 25bp difference will affect both the numerator and the denominator and will therefore not affect the result.
dmfcrowe There is no difference, duration is a linear measure.
Kashi2010 A 'grey' question.. If one was entirely mathematically correct the answer would be D.

Due to the convexity of a bonds price, the larger the 'step' in yield you use, the longer you are extrapolating the error and, therefore, the more you will OVERestimate the duration. Hence a larger step (50bp vs 25bp) would cause you the duration to change to a higher number.

For example using the parameters in the last questions, changing your bp move from 50bp to 100bp in the calculation caused the (rounded) duration to change from 7.49 to 7.50.

Of course due to positive convexity the duration will generally slightly underestimate price changes for decreasing yield, and overestimate price changes for increasing yield, hence it is an APPROXIMATE measure.
cbeliveau @Kashi2010, I was thinking the same way in terms of convexity and also picked D. I agree with the logic.
johntan1979 For those who argued that the answer is wrong, you obviously missed the meaning of the question.

When you want to estimate the duration, it doesn't matter whether you use 50 basis, 25 basis... you still end up with the same estimation. Better still, try to do this with the previous question. Are you going to get a duration different than 7.5 if you used different basis to estimate/calculate?
SKIA johntan1979 is right - create an example and plug it in, for small changes the duration is the same.
Shaan23 I do agree its a small change but what constitutes a small change...if its not it would be answer D --- Duration would increase

Think of the formula say for a 1000BP change... The Price increase due to a yield decrease(1000bp) will be much greater then the price decrease when the yield increases(1000bp) so the numerator of duration is increasing at a an increasing rate.