# Duration: 4Years a little more or a little less

I was out of time whe I got into thatone… I know that I did it wrong if I answered plain 4Years. Do you remember thisone?

Yes! I had finished the test 28 minutes early and the proctor didn’t let me leave so I just sat there thinking about the amount of drinking I’d be doing later that night when it came to me; I got the last answer wrong! I went back and changed it to less than 4%…I remember it asked what the price change would be if the yield increased by 200 bps given a duration of 4.

Less than.

Hi, Did that question tell you the convexity or was it just based on yield change…I can’t remember? Thanks.

it didn’t say anything about convexity and it was an option free bond…i calculated duration and put 4

Straight up 4

You have to take convexity into consideration, if the price moved on a straight line then it would be 4 but the price moves along an arc and is less than 4.

It would be very close to 4 had it only changed by 100 or less than 100 bps, but when you have anything greater you need to adjust for convexity.

Duration is an approximation, i.e. it is a straight line when the actual price change is convex. For a large BP change, it is always be less than for a yield increase and more than for a yield decrease. The answer was less than in this case.

Yup. I remember that beauty. Straight from Schweser as well. Less than, FTW.

Now this has me thinking. Isn’t the % change is price formula equal to: -De*change in r + C*change in r^2 If the rate goes up the price should decrease by -4 * .02 + the effect of convexity. That would be -.08 + what ever effect convexity has which was not indicated. Was this possibly one of the tricky CFAI questions as the choices were greater than 4%, %4 and less than %4. With that said -8% is still less than %4! Any thoughts???

Now this has me thinking. Isn’t the % change is price formula equal to: -De*change in r + C*change in r^2 If the rate goes up the price should decrease by -4 * .02 + the effect of convexity. That would be -.08 + what ever effect convexity has which was not indicated. Was this possibly one of the tricky CFAI questions as the choices were greater than 4%, 4% and less than 4%. With that said -8% is still less than 4%! Any thoughts???

I chose flat (absolute) 4%. It is just the reason being there was not convexity measure given. And as you know… that duration is a linear measure (straight line) and convexity measure adjusts for the convexity of the curve. Without convexity given, we would not know where the increase or decrease would be greater or less than 4 %. Moreover, I came across a similar question in the Schweser Q-Bank and the correct answer was an absolute number and not the greater or lesser than x number. Hope this helps…

Wow, I guess it all depends on the answers they gave you. I don’t remember this question very well. Does anyone remember the possible anwers exactly. If the answers were something like, price change of 4% little less than 4% little more than 4% based on the info from Conquistador07 ((200bp move)) everyone on this thread got it wrong. Everyone skipped over the 200bp move, me included most likely. And I bet they did this because there was a similar question in the Schweser Q-bank. Nice catch dubpg47

I think wording was: An increase of more than 4% An increase of 4% An increase of less than 4% However, with that said I am not 100% sure. Bottom line is a 200bp rate increase would produce a DECREASE in price.

less than 4 more than 4 exactly 4 this is what I remember…

dubpg47 Wrote: ------------------------------------------------------- > I think wording was: > > An increase of more than 4% > An increase of 4% > An increase of less than 4% > > However, with that said I am not 100% sure. > Bottom line is a 200bp rate increase would produce > a DECREASE in price. dubpg47, Do you think the possible answer were more like badem’s and the question asked what would be the % decrease in price? Because I don’t think they would ask you about an increase in yield and give you answers of “increases”. BTW, I’m pretty sure the answer was not 4 flat. Duration is the first derivative of the price-yield curve. As long as there are no options in the bond, any tangent line on the curve will never be above the curve. So basically, duration WILL ALWAYS underestimate your predicted bond price. 1 bp - 500bp, increase or decrease in yield, in theory it doesn’t matter.

spunboy, I honestly can’t remember the wording, what I wrote earlier is what I thought. Does anyone else remember?

A few points as I see it. - There was a 200 bp change in the yield -For large bp changes, duration is a crap measure, hence why the convexity adjustment is necessary -Just because convexity isn’t given, doesn’t mean it doesn’t exist -It is an option free bond, so therefore convexity is always positive -It was an increase in yield of 200 bp, that means a decrease in price -Duration is -4, but convexity is positive by rule -Therefore the actual price change will be less than 4%. -It isn’t necessary for the CFA to trick us as the latest posts are thinking. Just look- using the question honestly is sparking a huge debate.

Convexity is much more sensitive to falling rates. Not sure.but it seems like this was an increase in rates according to the question…and with that being said…wouldnt the tangent line be much more flat and closer to the approximate for duration at that level of increase. Not sure if I articulated that correctly, but it seems there is less difference in regards to convexity when rates are increasing compared to when rates are falling due to price sensitivity.