Reconsider the same series of liabilities as in Problem $7.$ Suppose that the company wishes to construct a portfolio of assets to cover this series of liabilities, such that it is fully immunized against interest rate over the entire

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four year timeframe. Further suppose that the company has available eight Treasury Strips that mature in each of the eight periods. Treasury strips have no intermediate coupons $($i$.$e$.,$ their annual coupon rate is $0\mathrm{.}00\%)$ and they just pay a single cash flow on the maturity date. The current yield on all bonds is $3\mathrm{.}17\%.$ How many of each of these eight Treasury strips should the pension fund buy in order to fully fund the liability and be fully immunized against interest rate risk over the entire four year timeframe?

Suppose that a pension fund has a series of liabilities to be paid every six months to the pension plan beneficiaries: $$4,500,000,$$$5,100,000,$ $$5,600,000,$$$6,300,000,$$$6,800,000,$$$7,200,000,$$$7,900,000,$ and $$8,600,000.$ The company wishes to construct a portfolio of assets to cover this series of liabilities, such that it is immunized against interest rate risk right now. The company is considering investing in four bonds: $(1)$ a $1-$year Treasury bond with a face value of $$1,000$ and an annual coupon rate of $1\mathrm{.}50\%,(2)$ a $2-$year Treasury bond with a face value of $$1,000$ and an annual coupon rate of $2\mathrm{.}70\%,(3)$ a $3-$year Treasury bond with a face value of $$1,000$ and an annual coupon rate of $2\mathrm{.}90\%,$ and $(4)$ a $4-$year Treasury bond with a face value of $$1,000$ and an annual coupon rate of $3\mathrm{.}20\%.$ All four bonds make $2($semi$-$annual$)$ coupon payments per year. Thus they have $2$ periods, $4$ periods, $6$ periods, and $8$ periods until maturity, respectively. The current yield on all bonds is $3\mathrm{.}17\%.$ How many of each of these four Treasury bonds should the pension fund buy in order to fully fund the liability and be immunized against interest rate risk right now?