Question

a pension fund has an average duration of its liabilities equal to 15 years. the fund is looking at 8-year maturity zero-coupon bonds yield perpetuities to immunize its interest rate risk how much of its portfolio should it allocate to the zero-coupon bonds to immmunize if there are no other assets funding the plan

Answer 1

a = 27.6%

Step-by-step explanation:

The computation of the allocation of zero coupon bonds is shown below:

But before that we need to determine the following calculations

Duration of perpetuity is

= 1.06 ÷ .0.06

= 17.67 years

Now the equation should be

Let us assume the allocation of zero coupon bond be a

15 years = a × 8 + (1 - a) × 17.67

15 years = 8a + 17.67 - 17.67a

-2.67 = -9.67a

a = 27.6%