A pension fund has a liability of $100 million due in 10 years. The expected annual return on the assets is 8%. The standard deviation of the returns is 12%. The duration of the liabilities is 12 years. The pension fund wants to immunize its liabilities by matching the duration of its assets with the duration of its liabilities. How much should the pension fund invest in bonds that have a duration of 12 years and a yield to maturity of 6% to immunize its liabilities?

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