## Bond Duration

darshit.sr
Posts: 7
Joined: Fri May 17, 2013 5:53 pm

### Bond Duration

Following are the closing price (P) and yields(Y) of a particular liquid bond over the past few days:
Monday: P= 106.3 Y= 4.25%
Tuesday: P= 105.8 Y= 4.20%
Wednesday: P= 106.1 Y= 4.23%
What is the approximate duration of the bond?
A 18.8
B 9.4
C. 4.7
D 1.9

Answer given is B 9.4
but applying formula of Effective duration: BV(-Y) - BV(+Y)/ 2*BV*change in yield my anwer comes to 4.7.
Can you please explain why correct answer is 9.4
Source: FRM practice exams 2010

pradeeppdy
Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### Bond Duration

Take the wednesday price as base price,
P(y)=P(y=4.23%)=106.1,P(y+)=P(4.23%+.02%=4.25%)=106.3,P(y-)=P(4.23%-.03%=4.2%)=105.8,
Now duration is the average of the 1/P(y)[P(y)-P(y+)/y-y(+)] and1/P(y)[ P(y)-P(y-)/y-y(-)]{duration is % change in price w.r.t %change in yield take average of the % swings both ways to get an approximate duration]
Duration=.5*(1/P(y))*[P(y)-P(y+)/y-y(+) +P(y)-P(y-)/y-y(-)]
P(y)-P(y+)/y-y(+) =106.1-106.3/4.23%-4.25%=.2/.02%=1000
P(y)-P(y-)/y-y(-)=106.1-105.8/4.23%-4.2%=.3/.0003=1000
duration=.5*[1/106.1]*[1000+1000]=1000/106.1= 9.4

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