# 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