Derive the probability distribution of the one-year HPR on a 3-year U.S. Treasury bond with an 8% coupon (paid semiannually) if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows
Probability YTM
Boom 0.15 11%
Better than Normal 0.3 9.5%
Normal 0.2 7.8%
Recession 0.35 2%