Question

Assume you hold a 2-year coupon bond. You want to replace
this bond by a portfolio of bonds with the same market value
and $-Duration. How can you achieve this?

Answer 1

In order to replicate 2 year coupon bond with portfolio of bonds, I would create a portfolio having same future cashflows.

I would buy following bonds:

1 year zero coupon bond with maturity value equal to yearly coupon amount and

2 year zero coupon bond with maturity value equal to (yearly coupon + face value of 2 year coupon bond).

Market value of portfolio of above 2 bonds will be equal to market value of 2 year coupon bond

and $ duration of above portfolio will be same as $ duration of 2 year coupon bond.

Crux is to replicate future cashflows of 2 year coupon bond