Suppose that the current YTM is 10% and assume semi-annual compounding. We have a liability to pay $10,000 in 3 years. In order to construct a hedged portfolio, we can use the bonds as follows:

Please show work.

We want to construct an asset portfolio by purchasing bond A and B in a way that the value and duration of the asset portfolio and the liability coincide (immunization). How many bonds do we need to buy? You do not need to consider convexity matching.

Bond The frequency of coupon payments Maturity (year) Coupon rate (%) Par value ($) YTM (%) A 2 12 100 10 semi-annual B 4 4 100 10 semi-annual Bond The frequency of coupon payments Maturity (year) Coupon rate (%) Par value ($) YTM (%) A 2 12 100 10 semi-annual B 4 4 100 10 semi-annual