Apension 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.

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