Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury
ID: 2383182 • Letter: D
Question
Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 3.5% 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 3.5% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.)
Economy Probability YTM Price Capital Gain Coupon Interest HPR Boom 0.25 12.0 % $ $ $ % Normal Growth 0.40 10.0 % $ $ $ % Recession 0.35 9.0 % $ $ $ %Explanation / Answer
Boom
Price = pv(rate,nper,pmt fv)
rate = 12%
nper (no of year left to maturity) = (30-1) = 29
pmt (coupon) = 3.5%*100 = 3.5
fv (maturity value) = 100
Price = pv(12%,29,3.5,100)
Price = $ 31.81
Capital Gain = Price from 1 year now - current price
Capital Gain = 31.81 - 100
Capital Gain = -68.19
Coupon Interest = 100*3.5%
Coupon Interest = 3.5
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (3.5 + -68.19)/100
HPR = -64.69%
Normal Growth
Price = pv(rate,nper,pmt fv)
rate = 10%
nper (no of year left to maturity) = (30-1) = 29
pmt (coupon) = 3.5%*100 = 3.5
fv (maturity value) = 100
Price = pv(10%,29,3.5,100)
Price = $ 39.10
Capital Gain = Price from 1 year now - current price
Capital Gain = 39.10 - 100
Capital Gain = -60.90
Coupon Interest = 100*3.5%
Coupon Interest = 3.5
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (3.5 -60.90)/100
HPR = -57.40%
Recession
Price = pv(rate,nper,pmt fv)
rate = 9%
nper (no of year left to maturity) = (30-1) = 29
pmt (coupon) = 3.5%*100 = 3.5
fv (maturity value) = 100
Price = pv(9%,29,3.5,100)
Price = $ 43.91
Capital Gain = Price from 1 year now - current price
Capital Gain = 43.91 - 100
Capital Gain = -56.09
Coupon Interest = 100*3.5%
Coupon Interest = 3.5
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (3.5 -56.09)/100
HPR = -52.59%
Economy Probability YTM Price Capital Gain Coupon Interest HPR Boom 0.25 12% 31.81 -68.19 3.50 -64.69% Normal Growth 0.4 10% 39.10 -60.90 3.50 -57.40% Recession 0.35 9% 43.91 -56.09 3.50 -52.59%Related Questions
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