A company has a liability of $10,00,000 in three years time and wants to hedge this liability with the followins semiannual bonds:

Maturity	Face Value	Coupon	Yield
2	100,000	5%	4.8%
5	100,000	6%	5.0%
10	100,000	7%	5.2%

The semiannually compounded 3 year rate is 5%. The company wants to hedge this liability by constructing a portfolio that is duration and convexity neutral.

a) By differentiating the present valu of the liability with respect to the 3-year semiannual rate, show that the modified duration and convexity of the liability are

,

b) By computing the present values, durations, and convexities, determine the three equations that must be satisfied by the weights w2, w5 and w10 of the 2,5 and 10 year bonds respectively.

c) Express the equations in the matrix form:

And solve for w1,w2 and w3 d) Using the weights obtained in part (c), compute the corresponding units n2,n5 and n10 of the bonds required for the hedge. Can anyone help me solve this? Thanks

DL 3/(1 0.025) DL 3/(1 0.025)