You manage a pension fund where payouts are essentially going to resemble a leve

Question

You manage a pension fund where payouts are essentially going to resemble a level perpetuity of $2 million per year. At t = 0 the interest rate is two and a half percent per year (2 1/2 %). You plan to fully fund the obligation using 10-year and 30-year maturity zero-coupon Treasury Bonds. Short sale is allowed in both these bonds - important information as you answer part (a). At t=0 how much market value of each of the zeros will be necessary to fund the plan if you desire an immunized position? What must be the face value of the two zeroes to fund the plan?

Explanation / Answer

present value of Annuities = $ 2 Million / 0.025 = $80 Million

Duration = 1+y/ y = 1.025/0.025 = 41 Year

Let X = weight of 10 year zero bond

let X-1 = Weight of 30 year treasury bond

41 = 10 (x)+ 30 (1-x)

X = -0.55

X-1 = 1.55

( A)

Market value of 10 year bond will be = $ 80 M *0.55 = $ 44 m required to be short sale

Market value of 30 year bond = $ 80 M*1.55 = $ 124 M

(B)

Face value of 10 year bond = $ 44 M * (1.025)10

   = $ 56.32 M

Face value of 30 Year Bond = $ 124 M * (1.025 )30

   = $ 260 M

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