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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%

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