Question

Consider a self-financed convexity trade.

Three zero couple bonds:

i. 2Y zero at 1.60%; ii. 10Y zero at 1.85%; iii. 30Y zero at 2.30%

a. Calculate duration and convexity for all three

Answer 1

For a zero coupon bond,

Duration of the bond equals its years to maturity and its convexity is square of the years to maturity.

i). For 2Y zero at 1.60%

Years to maturity t = 2 years

So duration t = 2 years

& Convexity = t^2 = 2^2 = 4

ii). For 10Y zero at 1.85%

Years to maturity t = 10 years

So duration t = 10 years

& Convexity = t^2 = 10^2 = 100

iii).30Y zero at 2.30%

Years to maturity t = 30 years

So duration t = 30 years

& Convexity = t^2 = 30^2 = 900