1. The yield curve is flat and the spot interest rate is r-5%. The market has pure discount bonds (zero coupon) with a notional of 10000 and expiration in 1, 2, 3 and 4 years, respectively. A firm has to make front to the following payments: i. 50.000 in one year, ii. 100.000 in two years, and iii. 500.000 in three years. With this information: a. Calculate the value, duration and convexity of this firm's liabilities (assume that the IRR is 5%). b. Suppose that the interest rate increases 0.5% and calculate the approximate change in the price of the four bonds and the firm's liabilities in both cases, use only duration). c. Combine the bonds with maturity in one and three years (and only these two) to construct a portfolio that has approximately the same price as the liabilities, both before and after the 0.5% increase of interest rates. d. Using as many bonds as necessary of the four available in the market) construct a portfolio that perfectly replicates the firm's liabilities. 1. The yield curve is flat and the spot interest rate is r-5%. The market has pure discount bonds (zero coupon) with a notional of 10000 and expiration in 1, 2, 3 and 4 years, respectively. A firm has to make front to the following payments: i. 50.000 in one year, ii. 100.000 in two years, and iii. 500.000 in three years. With this information: a. Calculate the value, duration and convexity of this firm's liabilities (assume that the IRR is 5%). b. Suppose that the interest rate increases 0.5% and calculate the approximate change in the price of the four bonds and the firm's liabilities in both cases, use only duration). c. Combine the bonds with maturity in one and three years (and only these two) to construct a portfolio that has approximately the same price as the liabilities, both before and after the 0.5% increase of interest rates. d. Using as many bonds as necessary of the four available in the market) construct a portfolio that perfectly replicates the firm's liabilities