1. You graduated from USF and got a job at MetLife pension department. Your supe
ID: 2655991 • Letter: 1
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1. You graduated from USF and got a job at MetLife pension department. Your supervisor needs your help with some of its liabilities and risk control. The pension fund has a seres of ?abilitics to bc paid to the pension plan beneficiaries: In 6 months: $2,000,000, In 1 ycar: $2,200,000, In 1.5 ycars: $2,500,000, In 2 years: $3,200,000, In 2.5 ycars: S3,700,000, In 3 years: $4,300,000, In 3.5 ycars: $4,700,000, In 4 years: $5,100,000. Your 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 different bonds: (1) a 1-year Trcasury Bill with a face value of $1,000 and no coupon, (2) a 2-ycar Trcasury note with a face value of $1,000 and an annual coupon rate of 1.5%, (3) a 3-year Treasury note with a face value of $1,000 and an annual coupon rate of 1.90%, and (4) a 5-year Treasury note with a face value of $1,000 and an annual coupon rate of 2.30%. All Treasury notes make 2 (seni-annual) coupon payments per year. The current yield on all bonds is 1.45%. Your supervisor wants you to find out how many of cach of these four Treasury bonds the fund should buy to fully fund the liability and be immunized against interest rate risk right now:Explanation / Answer
as we know that current yields 1.45 and as we know yield takes into account coupon payments also,so we can use that yield on an average basis for the coupon of all kinds of t-bills & notes so if we know that we will be needing the sum total of $17,700,000 till year 4 and we also know that yield is 1.45 then we can calculate by using the formulae FCF/1+R^T here we will take T=8 as in there are 8 outflows R=1.45 and FCF=17,700,000 which comes out to be 15,774,545.5112
after puting all the values in the formuale we know that we have to invest now $15774545 in bonds any bond having face value$1000 which means you have to buy bonds $15774
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