2010 garp practise question : Q15

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Q. 15 the table below gives the closing prices and yields of a particular liquid bonds over past few weeks:
Day price yield
Mon 106.3 4.25%
Tue 105.8 4.20%
Wed 106.1 4.23%
What is the approx duration of the bond?
Ans.b
106.3-105.8/106.3/.0005=9.4
106.3-106.1/106.3/.0002=9.4

My doubt is which formula is used here
Duration formula is P(y0 – delta y) − P(y0 + delta y)/(2delta y)P0

But here we have not been given the change in yield. And its not consistent between mon and tues & tues and wed.So how did the answer map with the formula above. Or is there any other formula used. Please guide.
Waiting for your response
Snigdha

 

[David Harper CFA FRM]

Hi snigdha,

We have paid member discussion on this here. The days don't matter, think of them as three points on a scatter plot (unfortunately the question is flawed for an incorrect P/Y implying negative duration, but ignoring that...)

This modified (effective) duration is best understood as a function of the slope of the tangent line.
Specifically: Duration = - slope * 1/price. And slope is rise/run, so this function is:
Duration = - (change in price/change in rates)*1/P, where slope = rise/run = change in price/change in rates
… viewed this way, you can see the only requirement is that we are consistent in numerator and denominator; i.e., your formula assumes a symmetrical shock: Price [Y0 - S] - Price [Y0 + S], where the total yield change, which must MATCH, is given in the denominator as Y0 + S - [Y0 - S] = 2S.
... but in the question above, we do not need the deltaY as 2*deltaY is just mean to get us (yield+) - (yield-) which we can get directly above with 4.25% - 4.20%.

David