Question

Can you show me how to do questions d, i, ii, iii and iv .   

You have following liability: 29-year bond, 6.5% annual coupon, market interest rate is 5%.

a.   What is the present value of this liability?   PV = 1227.12

b.   What is the duration of this liability?    Duration = 15.12

d.   You want to consider immunizing the liability using 8-year and 30- year zero coupon-bonds.

i.   What are the investment weights needed for the two bonds?

ii.   What are the present values of the two bonds needed to immunize the liability?

iii.   What are the face values of the two bonds needed to immunize the liability?

iv.   Build a sensitivity table showing the results of changes in interest rates:

	Weight	3%	4%	5%	6%	7%
Liablility
Bond (8 yrs)
Bond (30 yrs)
Portfolio sum

Answer 1

Soln : Let w1 & w2 be the weight of the 8 year and 30 year bond , also, P1 & P2 be the PV values of the 2

When we do immunization that means the liabilities and assest value will be equal at the time of maturty or after completing the duration.

We can say that P1 +P2 = 1227.12

Also, the duration of the liabilities and asset should be same , for zero coupon bond the maturity is duration.

We can say that , w1*8 + w2*30 = 15.12

w1 = P1/1227.12 and w2 = 1-w1

w1*8 + 30-30w1 = 15.12, on calculation we get , w1 = 0.676 and w2 = 1-w1 = 0.324

P1 = 0.676*1227.12 = $830 and P2 = 0.324*1227.12 = $397.14

Let F1 and F2 be the value of face values of these bonds.

Liability bond face value is of $1000. So, Face value should be $1000 for these bonds.

d) Please refer the table :

Duration	19.1	17	15.12	13.46	12
	3%	4%	5%	6%	7%
Liablility	1490.20	1346.89	1227.12	1126.34	1041.00
Bond (8 yrs)	0.495	0.591	0.676	0.752	0.818
Bond (30 yrs)	0.505	0.409	0.324	0.248	0.182
Portfolio sum