A pension plan will have a cash outflow in 3 years. They can invest in 2 year bonds with duration of 1.7 years and 4 year bonds with a duration of 3.5 years. To immunize the portfolio, the proportion invested in the 4 year bonds should be

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Quizplus · Accepted Answer

To immunize the portfolio against interest rate changes, the duration of the portfolio must match the duration of the liability. Here, the liability has a duration of 3 years. Using the formula for portfolio duration, which is the weighted average of the durations of the individual investments, we can set up the equation: 1.7(1-x) + 3.5x = 3, where x is the proportion invested in the 4-year bonds. Solving for x gives us 0.72 or 72%.

A Pension Plan Will Have a Cash Outflow in 3