### CFA Practice Question

A bond's price increases by 1.25% of par when interest rates drop by 10 basis points (bp). Its price declines by 1.08% of par when rates increase by 10 bp. The current bond price is \$98.85 and the prevailing yield to maturity is 8%. What is the duration of this bond?
A. 10.93
B. 11.65
C. 11.79
Explanation: Duration is calculated by, ignoring the negative sign, D = (ΔP / P) x (1 / P)
ΔP is averaged for the up and the down move. In this case, Avg. ΔP = (1.25 + 1.08) / 2 = 1.165.
Thus, D = (1.165 / 98.85) x (1 / 0.001) = 11.79. One basis point equals 0.0001.

### User Contributed Comments11

User Comment
eddeb What about this method:

(100.085-97.78)/(2*98.85*0.001) = 11.65

Looks good to me.
jayjunk D = (delta P / P) x (1 / delta r)
not D = (delta P / P) x (1 / P)

At least that's what I think, correct me if I am wrong.
amak Read the question carefully, it is 1.25% of PAR, meaning 1.25% of \$100. So you must add \$1.25 to 98.85, NOT 1.0125x98.85
MUSK Good point amak, thanks
Kuki Price if yields decrease: 98.85+(1.25%*100)=100.10
Price if yields increase: 98.85-(1.08%*100)=97.77
Therefore Duration =
(100.10-97.77)/(2*98.85*0.001) = 11.79 (2 dp)
malawyer the PAR got me too, good and tricky question!
StanleyMo we are too tire to handle tricky questions after fighting war with 90 questions++ lol
cfahitman thanks amak! yours is straight to the point and explain the trick.

it said delta P is average = (1.25+1.08)/2... which confused me even more.

the trick is simply 1.25% of par, not of 98.85! we can use the same formula by doing difference between two prices: 101.25 and 98.92 to get the answer.
ddrmax tricky
mary11 man,they make easy questions confusing.
madelinee Arrrgggghhhhh PAR!!!
You need to log in first to add your comment.