An investor has immunized a stream of liabilities using the three bonds

shown in table below? The two liabilities that need to be paid are A$1m

and A$2m in year 1 and year 2. The classical immunization was based on

a yield to maturity of 9%. Show that if the yields increased by 0.5% the

portfolio of bonds will need to be rebalanced to maintain a duration

match with the liabilities

Bonds Macaulay'sDuration Weights Price Coupon Interest

90daybill($100Par) 0.25years $97.87 0%

1yearbond($100Par) 1year 0.5 $100.92 10%

5yearbond($100Par) 4.19years $111.67 12%