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# Bond Concepts

#### intuitive

##### New Member
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

#### ShaktiRathore

##### Well-Known Member
Subscriber
I would solve it as:
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 is this right
thanks

#### intuitive

##### New Member
Yes you are correct many thanks..

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Agreed except it looks like the answer should be effective duration = -9.425 years as the price is atypically an increasing function of the yield (negative duration). thanks,