Modified Duration

[itimi]

Hi David,

Pls help with this. I got Duration 2.62 and Modified Duration 2.50 but the answer given is 2.62 for Modified Duration.

Suppose the face value of a three-year option-free bond is USD 1,000 and the annual coupon is 10%. The current yield to maturity is 5%. What is the Modified Duration of this bond?

a. 2.62
b. 2.85
c. 3.00
d. 2.75

 

[David Harper CFA FRM]

Hi uloyok,

I get (with Excel, if you don't mind)
Price @ 5% = =-PV(5%,3,10%*1000,1000) = $1,136.16
Price @ 4.9% = =-PV(4.9%,3,10%*1000,1000) = $1,139.15; arbitrarily using 10 bps shock
Price @ 5.1% = =-PV(5.1%,3,10%*1000,1000) = $1,133.19

rise/run (slope of the tangent line; aka, dollar duration) = (1,139.15 - 1,133.19)/(5.1% - 4.9%) = $2,978.4, such that
mod duration = dollar duration / price = $2,978.4/$1,136.16 = 2.62145. Mac duration = 2.62145 * (1+5%/1) = 2.7523

Thanks, David

 

[itimi]

Thanks.