You observe the spot rates for various time-to-maturity. Please provide four deci- Year 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Spot Rate (%) 5.00 5.75 5.90 6.35 6.79 7.38 8.17 8.92 9.61 10.36 mal accuracy to all your computations. (a) What should be the fair price of a 7% coupon rate three-year semi-annual coupon-bond with face value of $1000 be? (6pts) (b) If this bond is selling at $1000, is there arbitrage assuming there are no transaction costs whatsoever? Describe how you would take advantage of an arbitrage opportunity if there is indeed one? Construct a portfolio to answer this question and discuss also how much you be making from this transaction. (4pts) (c) What are the 12-month-interval and 24-month-interval forward rates for a contract starting exactly at the beginning of the third year? (6pts) (d) A pension fund manager knows that the following liabilities must be satisfied: Suppose that the pension fund manager want to invest today a lumpsum of money that will satisfy this liability stream. How much must he invest today to meet this liability stream in the future? Discuss the portfolio that he should build to meet this liability. (6pts) You observe the spot rates for various time-to-maturity. Please provide four deci- Year 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Spot Rate (%) 5.00 5.75 5.90 6.35 6.79 7.38 8.17 8.92 9.61 10.36 mal accuracy to all your computations. (a) What should be the fair price of a 7% coupon rate three-year semi-annual coupon-bond with face value of $1000 be? (6pts) (b) If this bond is selling at $1000, is there arbitrage assuming there are no transaction costs whatsoever? Describe how you would take advantage of an arbitrage opportunity if there is indeed one? Construct a portfolio to answer this question and discuss also how much you be making from this transaction. (4pts) (c) What are the 12-month-interval and 24-month-interval forward rates for a contract starting exactly at the beginning of the third year? (6pts) (d) A pension fund manager knows that the following liabilities must be satisfied: Suppose that the pension fund manager want to invest today a lumpsum of money that will satisfy this liability stream. How much must he invest today to meet this liability stream in the future? Discuss the portfolio that he should build to meet this liability. (6pts)