Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 4.0% if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as shown in the table below. (Assume the entire 4.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)
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| Economy | Probability | YTM | Price | Capital Gain | Coupon Interest | HPR |
| Boom | 0.25 | 10% | $43.78 | -56.22% | 4.00% | -52.22% |
| Normal Growth | 0.5 | 9% | $49.01 | -50.99% | 4.00% | -46.99% |
| Recession | 0.25 | 8% | $55.37 | -44.63% | 4.00% | -40.63% |
Calculate Bond Price using PV function on a calculator or excel
I/Y = 10%, 9% or 8%, N = 29, PMT = 4% x 100 = 4, FV = 100 => Compute PV to get the above prices.
Capital Gains = Price / 100 - 1
Coupon = 4 / 100 = 4%
HPR = Capital Gains + Coupon
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