Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 3.0% if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as shown in the table below. (Assume the entire 3.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)

Economy Probability YTM Price Capital Gain Coupon Interest HPR Boom 0.30 8.0 % % Normal Growth 0.40 6.0 % % Recession 0.30 5.0 % %