PROBLEM 3.1. Consider the following two bonds: (1) Bond 1 has maturity in one year and a 2% coupon rate. (2) Bond 2 has maturity in two years and a 4% coupon rate. Both bonds have a face-value equal to SEK 1000; the coupon payments are due at the end of each year, and the first payment on each bond is dues in one year from today. The current one year- and two year-rates of interest are equal to 2.5% and to 3.5%, respectively.

3.1.1. Provide the current market prices of the two bonds. What is the yield to maturity on (i) Bond 1, (ii) Bond 2?

3.1.2. Provide the current slopes of the two bonds.

3.1.3. We believe that the yield curve is going to become flatter very soon, due to a relative drop in the long term-rates, compared to the one year-rate; we are however uncertain about the direction of possible changes the overall level of the rates - namely about the size and/or the direction of the possible shifts of the curve. How can we refer to the slopes of the two bonds to create a portfolio that would yield a profit, if our beliefs were correct, and that would not be substantially exposed to the risk of shifts of the yield curve? You can refer your answer to a position of arbitrary absolute value in one of the two bonds.

3.1.4. Suppose that immediately after that we construct our portfolio, the one and the two-year rate of interest both drop to the level of 2%. Show that the portfolio constructed in does indeed allow us to realise a gain, in this scenario?

3.1.5. What would be our profit or loss if the one and the two year-rates dropped to 2% and to 2.5%, respectively