Problem 5-8 Derive the probability distribution of the 1-year HPR on a 30-year U
ID: 2819006 • Letter: P
Question
Problem 5-8
Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 3.0% 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 3.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.)
Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an 3.0% 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 3.0% coupon is paid at the end of the year rather than every 6 months. Assume a par value of $100.) (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.)
Explanation / Answer
Normal Growth
Price = pv(rate,nper,pmt fv)
Price = pv(rate,nper,pmt fv)
Price = pv(rate,nper,pmt fv)
nper (no of year left to maturity) = (30-1) = 29
nper (no of year left to maturity) = (30-1) = 29
nper (no of year left to maturity) = (30-1) = 29
pmt (coupon) = 3%*100 = 3
pmt (coupon) = 3%*100 = 3
pmt (coupon) = 3%*100 = 3
fv (maturity value) = 100
fv (maturity value) = 100
fv (maturity value) = 100
Price = pv(7%,29,3,100)
Price = pv(6%,29,3,100)
Price = pv(5%,29,3,100)
Capital Gain = Price from 1 year now - current price
Capital Gain = Price from 1 year now - current price
Capital Gain = Price from 1 year now - current price
Capital Gain = 50.89 - 100
Capital Gain = 59.23 - 100
Capital Gain = 69.72 - 100
Capital Gain = -49.11
Capital Gain = -40.77
Capital Gain = -30.28
Coupon Interest = 100*3%
Coupon Interest = 100*3%
Coupon Interest = 100*3%
Coupon Interest = 3
Coupon Interest = 3
Coupon Interest = 3
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (3 -49.11)/100
HPR = (3 -40.77)/100
HPR = (3 -30.28)/100
BoomNormal Growth
RecessionPrice = pv(rate,nper,pmt fv)
Price = pv(rate,nper,pmt fv)
Price = pv(rate,nper,pmt fv)
rate = 7% rate = 6% rate = 5%nper (no of year left to maturity) = (30-1) = 29
nper (no of year left to maturity) = (30-1) = 29
nper (no of year left to maturity) = (30-1) = 29
pmt (coupon) = 3%*100 = 3
pmt (coupon) = 3%*100 = 3
pmt (coupon) = 3%*100 = 3
fv (maturity value) = 100
fv (maturity value) = 100
fv (maturity value) = 100
Price = pv(7%,29,3,100)
Price = pv(6%,29,3,100)
Price = pv(5%,29,3,100)
Price = $ 50.89 Price = $ 59.23 Price = $ 69.72Capital Gain = Price from 1 year now - current price
Capital Gain = Price from 1 year now - current price
Capital Gain = Price from 1 year now - current price
Capital Gain = 50.89 - 100
Capital Gain = 59.23 - 100
Capital Gain = 69.72 - 100
Capital Gain = -49.11
Capital Gain = -40.77
Capital Gain = -30.28
Coupon Interest = 100*3%
Coupon Interest = 100*3%
Coupon Interest = 100*3%
Coupon Interest = 3
Coupon Interest = 3
Coupon Interest = 3
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (Coupon Interest + Capital Gain )/Purchase Price
HPR = (3 -49.11)/100
HPR = (3 -40.77)/100
HPR = (3 -30.28)/100
HPR = -46.11% HPR = -37.77% HPR = -27.28% Economy Probability YTM Price Capital Gain Coupon Interest HPR Boom 0.30 7% 50.89 -49.11 3 -46.11% Normal Growth 0.60 6% 59.23 -40.77 3 -37.77% Recession 0.10 5% 69.72 -30.28 3 -27.28%Related Questions
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