In: Finance
Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with a coupon of 3.5% 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 3.5% 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.)
economy | probabilty | ytm (%) | price | capital gain | coupon interest | HPR |
boom | .25 | 9 | ||||
normal | .50 | 7 | ||||
recession | .25 | 6 |
You will need to use a financial calculator
Boom Case
N = 29 years(After 1 year, it will be a bond with 29 years remaining for maturity
I/Y = YTM = 9%
PMT = 3.5%*100 = 3.5 (the coupon payment)
FV = 100
To find the price, you will need to calculate the Present Value using a calculator. Plugging in these values, we get PV = 43.90944. Ignore the negative sign if any
Capital gain = ending value - beginning value
= 43.909 - 100
= -56.09056
Coupon interest = 3.5%*100 = 3.5
HPR = (Capital Gain + Coupon interest)/Beginning value
= (-56.09056+3.5)/100
= -52.59%
Normal Case
N = 29 years(After 1 year, it will be a bond with 29 years remaining for maturity)
I/Y = YTM = 7%
PMT = 3.5%*100 = 3.5 (the coupon payment)
FV = 100
To find the price, you will need to calculate the Present Value using a calculator. Plugging in these values, we get PV = 57.02814 = 57.03. Ignore the negative sign if any
Capital gain = ending value - beginning value
= 57.02814 - 100
= -42.97
Coupon interest = 3.5%*100 = 3.5
HPR = (Capital Gain + Coupon interest)/Beginning value
= (-42.97+3.5)/100
= -39.47%
Boom Case
N = 29 years(After 1 year, it will be a bond with 29 years remaining for maturity)
I/Y = YTM = 6%
PMT = 3.5%*100 = 3.5 (the coupon payment)
FV = 100
To find the price, you will need to calculate the Present Value using a calculator. Plugging in these values, we get PV = 66.0232 = 66.02. Ignore the negative sign if any
Capital gain = ending value - beginning value
=66.0232 - 100
= -33.9768 = -33.98
Coupon interest = 3.5%*100 = 3.5
HPR = (Capital Gain + Coupon interest)/Beginning value
= (-33.98+3.5)/100
= -30.48%