Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury

Question

Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 4.0% coupon if it is currently selling at par and the probability distribution of its yield to maturity a year from now is as follows: (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 "O" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "S" & "%" signs in your response.) Economy Boom Normal Growth Recession Probability YTM Price Capital Gain Coupon Interest HPR 0.35 11.0% 0.40 9.0% 0.25 70%

Explanation / Answer

Answer )

Price and one-year HPR for a 30-year U.S. Treasury bond , with 30-1= 29 years to maturity at year’s end.

Using the Present value discounting concept : Price = pv(rate,nper,pmt fv)

For Boom : Price = PV (rate,nper,pmt fv) : rate = 11%: nper (no of year left to maturity) = (30-1) = 29 : pmt (coupon) =4%*100 = 4 : fv (maturity value) = 100

i.e. Price = pv(11%,29,4,100) = $35.83

  Capital Gain = Price from 1 year now - current price = $35.83 - $100 = -$64.17 ( No capital gain)

Coupon rate = 4% fixed .

Returne from HRP = Capital gain + Coupon rate.

Using the above concept for others , the answer is in below table.

Economy Probability YTM Price Capital gain Coupon Interest HPR Boom 0.35 11% $35.83 ($64.17) 4 -60.17% Normal 0.4 9% $49.01 ($50.99) 4 -46.99% Recession 0.25 7% $63.17 ($36.83) 4 -32.83%

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