A pension fund has an average duration of its liabilities equal to 15 years. The fund is looking at 5-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?

The 52 of its portfolio should be allocated to the zero-coupon bonds to immunie if there are no other assets funding the plan.

Explanation:

the duration of the perpetuity = (1+YTM) / YTM

= (1+0.04) / 0.04

= 26 years

the weights of the bonds = w

5*w + 26 * (1-w) = 15

5*w + 26 - 26*w = 15

21*w = 11

w = 0.52

Therefore, The 52 of its portfolio should be allocated to the zero-coupon bonds to immunie if there are no other assets funding the plan.