Derive the probability distribution of the 1 year HPR on a 30 year US Treasury Bond with a coupon of 4.00% It has a par value of $100.00 The probability distribution of its YTM a year form now is given below. Th entire 4% coupon is paid at the end of the year rather than every 6 months. Economy Probability YTM Price Bppm 10.00% 6.00% $72.82 Normal 60.00% 5.00% $84.86 Recession 30.00% 4.00% $100.00 100.00% What is the capital gain, if any, for each state of the economy, where it is calculated as the difference between the market value and par value? a. -$17.18, -$14.14, $0.00 b. $27.18, $15.14, $0.00 c. -$21.78, -$11.54, $0.00 d. -$27.18, -$15.14, $0.00