Question

Please show me how to complete questions d,i, ii, iii and iv. e.f

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

The Ppresent value of this liability?   PV = 1227.12 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

e.   Which strategy (from parts c and d) would you recommend, based solely on price sensitivity?

f.    What additional factors might you want to consider before choosing between the two strategies?

Answer 1

a. Face Value = $ 1000

Coupon = 6.5%*1000 = 65

Price of bond = 65/(1+5%)+65/(1+5%)^2+..............+65/(1+5%)^28 + 1065/(1+5%)^29 = $ 1227.12

b. Duration = Time weighted PV of cashfows

=(1*65/(1+5%)+2*65/(1+5%)^2+..............+28*65/(1+5%)^28 + 29*1065/(1+5%)^29)/Price of Bond

= 15.12

c. For zero coupon bond, duration is equal to the maturity of bond

Lets weight for 8 year bond be W1

therefore weight for 30 year bond be 1-W1

W1*8+(1-W1)*30 = 15.12

22*W1 = 14.88

W1 = 0.6763 and W2 = 0.3237

Face value of bonds = 1000

Price of 8 years bond = 1000/(1+5%)^8 = $ 676.84

Price of 16 years bond = 1000/(1+5%)^30 = $ 231.38

e. Since the duration of both the strategy is same, so price sensitivity would also be same. Thus both the strategies are indifferent.

f. We need to determine the convexity of both the strategy to reach the final decision for investing