Bond duration and convexity

Discussion in 'P1.T3. Financial Markets & Products (30%)' started by sleepybird, May 8, 2012.

1. sleepybirdActive Member

Hi David,
Why "short a coupon bond is equivalent to long effect duration and short effective convexity?" I think bonds have positive durations, so shorting bond = shorting duration?

Also, for the below question, why am I getting 2 different duration and convexity using different method? What did I do wrong?

What are the duration and convexity of a two-year bond that pays an annual coupon of 10% and whose current yield to maturity is 14%? Use 1,000 as the face value.

Method 1:
BV0​
BV+​
BV-​
N 2 2 2
PMT 100 100 100
I/Y 14% 15% 13%
FV 1,000 1,000 1,000
PV $934.13$918.71 \$949.96

Duration 1.6723 =(949.96-918.71)/(2*1%*934.13)
Convexity 4.3283 =(949.96+918.71-2*934.13)/(934.13*1%^2)

Method 2:
t CF PV Wt t*wt t^2*wt
1 100 87.71929825 0.093904448 0.093904448 0.093904448
2 1100 846.4142813 0.906095552 1.812191104 3.624382208
934.1335796​
1.000000​
1.906095552​
3.718286656
Duration
Convexity​

Thank you very much for your help.
Sleepybird

2. sleepybirdActive Member

Sorry the table was copied from excel. For method 2, using the weighted average of time method, I get duration of 1.9061 and convexity of 3.7183, which differ from duration of 1.6723 and convexity of 4.3283 calculated in method 1. Thanks.

3. KrivetkaNew Member

No one have ideas?
To calculate the price impact on a bond (currently priced 60.00) with modified duration of 5.7 and convexity 55.65 if the yield change in basis points is 23.

4. slActive Member

change in price = -price*mod.duration*change in yield