### CFA Practice Question

There are 266 practice questions for this study session.

### CFA Practice Question

A 6% coupon bond with semi-annual coupons has a convexity (in years) of 120, sells for 80% of par, and is priced at a yield to maturity of 8%. If the ytm increases to 9.5%, the predicted contribution to the percentage change in price, due to convexity, would be ______.

A. 1.08%
B. 1.35%
C. 2.7%

User Comment
virginia How do you compute it?
Aimy The answer should be 13.5 percent.
kevin Come on Aimy, the total change is only 1.5%!
(estim convexity on seminann.basis)(delta r^2)x100
=60(0.015)^2(100)
=1.35
mm04 Where is the 60 from? I never see convexity adjusted for semi-annual?
stefdunk convexity is 120, but the bond has a semi-annual coupon, therefore adjust 120/2=60
natali if convexity is adjusted for semi-annual, shouldn't the change in yield also be adjusted - 0.015/2?
tengo If you calculate the convexity for a 20bp shock you get about 84 not 120. I do not know what a convexity of 120 measured in years is sinc econvexity it has totally different units that a duration. the answer appaear to be 2.7%. There are no sample problems were the convexity is ever divided by 2 for a semi annual pay bond!!
tanyak so are we dividing annual convexity by 2 or not???
thekapila nopes convexity is not adjusted for semiannual basis.
mountaingoat appears change in yld is not adjusted semi-annual only convexity. when you calculate convexity the change in yield is not divided by 2.
MFTIOA This problem is flawed: if the annual convexity is 120, the semi-annual convexity should be n^2 (n = number of payments), or 2^2=4 times as much, or 480.
sam95 No the problem is not flawed.
2x [(120)(0.015/2)^2x100] =1.35
don't forget to change the yld in to semi annual and then after using the formula change it back to the annual to get the % change in price annually.
panvino I also agree with Tengo - I calculated the convexity and got 84, though I got 1.89 for convexity adjustment.
rocyang sam95: since convexity adjustment from calculation is given in decimal, the end result 1.35 should stand for 135% change!
Jurrens Rocyang: that's not factoring convexity which causes the curvature in the yield/price relationship. Good question to exemplify this extreme adjustment
dipu617 Thanks to sam95.
@Gina : convexity doesn't change to semi-annual, rather change in interest rate is semi-annual....
The solution provided by sam95 is correct. :-)
johntan1979 No no no no no... it is NEVER stated in the question that the change in YTM is semi-annual... We always assume the basis point change, which, in this case, is 150 basis points or in decimals, 0.015.

2.7% is the right answer, not half of that.
gill15 Sometimes I read these posts and I think i'm wrong when I'm right. Listen to Johntan...

When you change the basis points you are changing the ANNUAL yield up and down. Do NOT do any other way.
Callie2 Hmmm..I thought this was a pretty straight forward question.

Convexity Adj = est. convexity * (change in r)^2 * 100

= 120*(.015)^2*100
=2.7
CJPerugini Convexity Effect = 0.5*Annual Convexity*(Change in YTM)^2

=0.5*120*(0.015^2)
=0.0135
CJPerugini To prove this we can also calculate the effect on price based on a semi-annual basis, where Semi-Annual Convexity = Annual Convexity * 2^2

=0.5*120*4*(0.0075^2)
=0.0135
sarasyed5 where does the 0.015 come from?