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 "O" 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 HPR 0.30 8.0 % $ Boom Normal Growth Price Capital Gain Coupon Interest 21.89 $ (78.11) $ 3.00 3.00 (75.11) % % 0.40 0.30 6.0 % 5.0 % Recession 3.00 %