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 immunise its interest rate risk. How much of its portfolio should it allocate to the zero coupon bonds to immunise if there are no other assets funding the plan?

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Quizplus · Accepted Answer

To immunize the interest rate risk, the fund should match the duration of its assets to the duration of its liabilities. The duration of a zero-coupon bond is equal to its maturity, which is 5 years. The duration of a perpetuity is 1/yield, which is 1/0.04 = 25 years. Using the formula for duration matching: (Weight of zero-coupon bonds * Duration of zero-coupon bonds) + (Weight of perpetuities * Duration of perpetuities) = Duration of liabilities. Solving: (W * 5) + ((1-W) * 25) = 15, gives W = 0.52 or 52%.

A Pension Fund Has an Average Duration of Its Liabilities