Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a 4.0% coupon 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 4.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) Note: 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 Boom Normal Growth Recession Probability YTM Price 0.25 10.0 % $ Capital Gain 43.44 $ (56.56) $ Coupon HPR Interest 4.00 0.50 9.0 % (52.56) % % 0.25 8.0 % %