 # Duration

A bond has a duration of 10, a yield to maturity of 9% and a price of \$103. Which of the following could be the exact new price of the bond, if its yield to maturity increases to 10%? A. 92.65 B. 92.70 C. 92.75 D. 113.30

B? % change = -duration * % increase in ytm % change = -10 * 1 = -10% 103 * -10% = -10.3 103 - 10.3 = 92.70 Is that right?

b?

Well apparently, (and I’m so annoyed about getting this wrong): C Price change due to duration is –10 × 0.01% × \$103 = –\$10.30, giving a price of \$92.70. However, the exact new price must be slightly higher than this, due to convexity !!!

sre you telling me C is the right answer?? that is stupid only because they are saying what is the exact new price not a possible new price

Yep, that stupid question cost me half a percent!

I went for C as well (only because B was too obvious)…but its an incorrect question…are we supposed to just assume that its a straight bond, last I checked MBS & ABS markets are equally huge, and they all have -ve convexity. The answer could be A as well

no… bpp… so i’m hoping cfa would not have such a controversial question… here’s another question: If a bond has a yield to maturity of 8% and a flat yield of 9%, which of the following is most likely to be its coupon? A. 7% B. 8% C. 9% D. 10%

D

what is flat yield? Is it something we apply on bread??? Never heard the term yet.

wow…I have no clue how to approach this…I will go out on a limb and guess B: 8%

i assumed it was the yield that the bond would offer from inception till maturity

FY = coupon rate/price

Discount Bond: CRCY>YTM Par = CR = CY = YTM

This flat yield is called Current yield elsewhere Given that 8/.09 = Price ==> SO price = 88.88 So we just know it is a discount bond. So Coupon has to be less than YTM. So 7% is your answer. With 8% it would be par. With 9 or 10 % as coupon, bond would be a premium bond. CP

I think the ans. should be D… this is a premium bond… If our CY is greater than YTM then the Coupon Rate has got to be greater than current yield…

I think C N=1, I/Y=8,FV=100, if PMT=9 then PV=-100.9 9/100.9=8.92% Edit: just to follow up, if N=10, and PMT=10, then I get 8.8% CY. So D may be the right answer as well. I think it would truly depend on the character of the bond.

what is wrong with my answer? 8/P = .09 (current yield definition) so P=88.88 gives you it is a discount bond… so YTM > Coupon, and that is satisfied only by 7, If it had been a premium bond, two of the answers 9 and 10% would come up as choices, and in the absence of the term of the bond, we cannot go down to one answer. CP

cpk123 Wrote: ------------------------------------------------------- > what is wrong with my answer? > > 8/P = .09 > > (current yield definition) > > so P=88.88 > > gives you it is a discount bond… > > so YTM > Coupon, and that is satisfied only by 7, > > If it had been a premium bond, two of the answers > 9 and 10% would come up as choices, and in the > absence of the term of the bond, we cannot go down > to one answer. > > CP Aren’t you using a coupon of 8 to calculate price initially, which would imply par bond, and not a CY=.09?