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.
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 Comments 11
| 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!!! |