Question

Consider an insurance company that needs to pay £10 million in years 1, 2 and 3 from now. The term structure is flat at r=3% per year and only shifts in a parallel way (that is, the whole term structure shifts by some Dr). There are zero-coupon bonds maturing in years 1 and 2, respectively, and a three-year bond with a 10% coupon rate. All bonds have face value £100. The company wants to buy these bonds to perfectly immunize its liabilities so that the cash flows generated by the portfolio of bonds perfectly match the cash flows of its liabilities. How many units of each bond does the company need to buy? The company has £29 million in cash. Is this money enough to achieve perfect immunization?

Answer 1

SOLUTION :

1) ZERO COUPON BOND

IT IS BOND WHICH IS ISSUED AT DISCOUNT AND MATURED IN ITS FACE VALUE(PAR VALUE) AND IS NOT PAYING INTEREST DURING ITS TERM

HENCE THERE IS ONLY 2 CASH FLOW ONE AT THE TIME OF INVESTMENT (OUTFLOW ) AND SECOND AT THE TIME OF MATURITY OF BOND (INFLOW)

2)How many units of each bond does the company need to buy

FACE VALUE OF ALL BONDS ARE  £100

CASHFLOW REQUIRED AT THE END OF EACH YEAR £10 MILLION

HENCE NO OF BONDS REQUIRED TO BE PURCHASED OF EACH TYPE WILL BE

= £10 MILLION / FACE VALUE OF BOND

= 10,000,000 /100

=100000 BONDS

3) INVESTMENT IN EACH BOND

VALUE TO TOTAL INVESTMENT IS 28286000 WHICH IS LESS THAN 29 MILLIONS

HENCE THE COMPANY HAVE ENOUGH MONEY TO ACHIEVE PERFECT IMMUNIZATION