A financial institution has an obligation to pay $10,000 at the end of each year for 5 years. The institution receives 10,00003|0.1 = 37908 in exchange for assuming this obligation. The only investments available to the institution are 1, 3, and 5-year zero coupon bonds, all yielding 10%. The institution develops an investment policy using the following reasoning: 

(i) The durations of the obligations are symmetrically spaced around the durations of the available investments. 

(ii) Thus, the money to be invested will be divided into thirds, so that $12,636 will be invested in each of the 1, 3, and 5-year zero coupon bonds. Verify that this investment strategy is not optimal under immunization theory, and develop a superior strategy.

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