My pension plan will pay me $10,000 once a year for a 10-year period. The first payment come in at the end of 6th year from now. The pension fund wants to immunize its position. If the pension plan uses 5-year zero-coupon bond and 20-year zero coupon bond to construct the immunization position,what is the weight on the 5-year zero-coupon bond? Suppose the interest rate is 10%.

0.75163

Explanation:

So, we are given the following data or parameters or information which is going to help us in solving the question above;

=> Payment for the pension = $10,000 once a year for a 10-year period.

=> Time for the first payment = ''end of 6th year from now''.

=> Type of Pension plan for immunization = " 5-year zero-coupon bond and 20-year zero coupon bond to construct the immunization position''

=> Interest rate = 10%.

Therefore, the weight on the 5-year zero-coupon bond can be calculated as follows:

Duration = (Weight × 5) + [( 1 - weight) × 20].

=> 5b + 20 - 20b = 8.7255.

=> b = 0.75163.

Therefore, the weight on the 5-year zero-coupon bond is 0.75163.

The weight on the 20- year zero-coupon bond = 1 - 0.75163= 0.2884.