Question

A pension fund has an average duration of its liabilities equal to 17 years. The fund is looking at 4-year maturity zero-coupon bonds and 4% yield perpetuities to immunize its interest rate risk. How much of its portfolio should it allocate to the zero-coupon bonds to immunize if there are no other assets funding the plan

Answer 1

40.91%

Step-by-step explanation:

Duration perpetuity = 1.04/4%

Duration perpetuity = 1.04/0.04

Duration perpetuity = 26 years

Now, 17 = (Wz)*4 + (1 - Wz)*26

17 = 4Wz + 26 - 26Wz

26Wz - 4Wz = 26 - 17

22Wz = 9

Wz = 9/22

Wz = 0.409091

Wz = 40.91%

So, 40.91% of its portfolio should be allocated to the zero-coupon bonds to immunize, if there are no other assets funding the plan.