Question

Suppose you buy a five-year zero-coupon Treasury bond for $800 per $1000 face
value. Answer the following questions:
(a) What is the yield to maturity (annual compounding) on the bond?
(b) Suppose you buy the bond. Immediately after you buy it, the yield to maturity
on comparable zeros increases to 7% and remains there. Calculate your annual
return (holding period yield) if you sell the bond after one year.
(c) Assume yields to maturity on comparable bonds remain at 7%. Instead of
selling the bond after 1 year, as in (b), now you sell the bond after two years.
Calculate your annual return.
(d) Suppose after 3 years, the yield to maturity on similar zeros declines to 3%.
Calculate the annual return if you sell the bond at that time.
(e) If yield remains at 3%, calculate your annual return if you sell the bond after
four years.
(f) Calculate the annual return if you sell the bond after five years.
(g) What explains the relationship between annual returns calculated in (b) through
(f) and the yield to maturity in (a)?

Answer 1

a) Yield to maturity is 4.564%
You can get this using a financial calculator or by solving the equation
800= 1000/(1+r)^5.
b)763.90 is the new price so your holding period return is 763.90-800/800= -4.51%.
c) 816.30 is the new price so your annual return is 16.30/800 for the two years or 2.04%. Annualized it would be 1.02% per year.
d) 942.60 so total yield would be 142.60/800 or 17.825%. Divide this by 3 to get 5.94% per year.
e) 970.87 so total yield would be 170.87/800= 21.36%. Divide by 4 to get 5.34% annually.
f)1000-800/800=25% or 5% per year.
The difference in yields is due to time to maturity and market rates for comparable securities.