Derive the probability distribution of the one-year HPR on a 30-year U.S. Treasury bond with an 8% coupon if it is currently selling at par and the rob ability 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 six months.