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Derive the porbability distribution of the 1 year HPR on a 30 year US Treasury bond with an 8% coupon if it is currently selling

Derive the porbability distribution of the 1 year HPR on a 30 year US 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 Economy Boom Probability .20 YTM .11

State of Economy Normal Probability .50 YTM .08

State of Economy Bust Probability .30 YTM .07

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