Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 8% coupon if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows:

State of the Economy Probability YTM

Boom .20 11.0%

Normal growth .50 8.0

Recession .30 7.0

For simplicity, assume the entire 8% coupon is paid at the end of the year rather than every 6 months