Consider a Treasury coupon bond with maturity 18 months, and maturity value $100,000, trading at par. Consider now two other Treasury coupon bonds, with maturity 12 months and 30 months, respectively, also trading at par. Assume a flat yield curve, with y2(Coupon) = y3(Coupon) = y4(Coupon) = 2%. Construct a barbell portfolio of the second two bonds, with the same modified duration and price of the first bond. Specifically, compute: 1. the portfolio weights of the two bonds in the barbell; 2. the maturity values of the two bonds in the barbell. Calculate the prices of the first bond and of the barbell portfolio, under the following two scenarios (use present values): 1. all interest rates immediately decrease by 50 basis points; 2. the yield curve changes in a non-parallel fashion: y2(Coupon)= y2(Coupon)50 basis points, y3(Coupon)= y3(Coupon), and y4(Coupon)= y4(Coupon) + 50 basis points.