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 $100.) (Leave no cells blank - be certain to enter "0" wherever required. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "$" & "%" signs in your response.)

Economy	Probability	YTM	Price	Capital Gains	Coupon Interest	HPR
Boom	0.30	10.0%
Normal Growth	.0.40	8.0%
Recession	0.30	6.0%

Please fill in the rest.

Answer 1

The calculation is shown below:

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 concept of Present value discounting :

Price = pv(rate,nper,pmt fv)

For Boom : Price = PV (rate,nper,pmt fv) : rate = 10%: nper (no of year left to maturity) = (30-1) = 29 : pmt (coupon) =4%*100 = 4 : fv (maturity value) = 100

Price = pv(10%,29,4,100) = $43.78

Capital Gain = Price from 1 year now - current price =$43.78 - $100 = -$56.22 ( No capital gain)

Coupon rate = 4% fixed .

Returne from HRP = Capital gain + Coupon rate.

For normal growth

Price = PV (rate,nper,pmt fv) : rate = 8%: nper (no of year left to maturity) = (30-1) = 29 : pmt (coupon) =4%*100 = 4 : fv (maturity value) = 100

Price = pv(8%,29,4,100) = $55.37

Capital Gain = Price from 1 year now - current price =$55.37  - $100 = -$44.63 ( No capital gain)

Coupon rate = 4% fixed .

for recession

Price = PV (rate,nper,pmt fv) : rate = 10%: nper (no of year left to maturity) = (30-1) = 29 : pmt (coupon) =4%*100 = 4 : fv (maturity value) = 100

Price = pv(6%,29,4,100) = $72.82

Capital Gain = Price from 1 year now - current price =$72.82 - $100 = -$27.18( No capital gain)

Coupon rate = 4% fixed .

Economy	Probability	YTM	Price	Capital gain	Coupon Interest	HPR
Boom	0.30	10%	$43.78	($56.22)	4	-52.22%
Normal	0.40	8%	$55.37	($44.63)	4	-40.63%
Recession	0.30	6%	$72.82	($27.18)	4	-23.18%