Question: A pension fund must make two fixed payments (2 liabilities): a first payment of $400 due in 10 years and a second payment of $1200

A pension fund must make two fixed payments (2 liabilities): a first payment of $400 due in 10 years and a second payment of $1200 due in 20 years. The current market interest rate is 4% at all maturities. The fund has $1,000 available to invest today. The fund can allocate its assets between 10-year zero-coupon notes and 30-year zero-coupon bonds. Each bond and note has a face value of $1. The fund wants to stabilize its equity/assets ratio. What is the initial equity value of the fund?

What is the duration of liabilities?

What fraction of the market value of assets should be invested in the 30-year bond?

How many 10-year notes does the fund own? Round to an integer.

Right after the fund is set up, the market yields jump from 4% to 5%. What is the new equity value of the fund?

After the yield jump, what should be the new target for the market value weight of 30-year bonds in the portfolio?

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