Question

Problem 5-8 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.) Answer is complete but not entirely correct. Economy Price HPR Boom Probability 0.25 0.50 0.25 YTM 10.0 90 $ Capital Gain (60.55) (50.99) 136.83) R 39.45 49.01 63.17 $ $ S Normal Growth Recession Coupon Interest 4.00 400 4.00 (56.55) % (46.99) % (32.83) 3 % 80 $

Answer 1

A Economy B C Probability YTM D Price E Capital Gain F Coupon Interest 1 HPR 2 Boom 3 Normal Growth 0.25 10% $43.78 -$56.22 $ 0.50 9% $49.01 -$50.99 $ 0.25 8% $55.37 -$44.63 $ 4.0 -52.22% 4.0 -46.99% 4.0 -40.63% 4 Recession

Price HPR A B C E F 1 Economy Probability YTM Capital Gain Coupon Interest 2 Boom 10.25 0.1 =PV(C2,29,4,100,0)*-1 =+D2-1004 =(F2+E2)/100 3 Normal Growth 0.5 0.09 =+D3-100 =F2 =(F3+E3)/100 4 Recession -1-B2-B30.08 =PV(C4,29,4,100,0)*-1 =+D4-100 =F3 =(F4+E4)/100

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