In: Finance
The current yield curve for default-free zero-coupon bonds is as
follows:
Maturity (years) | YTM | |
1 | 9.4 | % |
2 | 10.4 | |
3 | 11.4 | |
a. What are the implied one-year forward rates?
(Do not round intermediate calculations.
Round your answers to 2 decimal places.)
b. Assume that the pure expectations hypothesis of
the term structure is correct. If market expectations are accurate,
what will the pure yield curve (that is, the yields to maturity on
one- and two-year zero-coupon bonds) be next year?
There will be a shift upwards in next year's curve.
There will be a shift downwards in next year's curve.
There will be no change in next year's curve.
c. What will be the yield to maturity on two-year
zeros? (Do not round intermediate calculations.
Round your answers to 2 decimal places.)
d. If you purchase a two-year zero-coupon bond
now, what is the expected total rate of return over the next year?
(Hint: Compute the current and expected future prices.)
Ignore taxes. (Do not round intermediate calculations.
Round your answer to 2 decimal places.)
e. If you purchase a three-year zero-coupon bond
now, what is the expected total rate of return over the next year?
(Hint: Compute the current and expected future prices.)
Ignore taxes. (Do not round intermediate calculations.
Round your answer to 2 decimal places.)
Part (a)
One year forward rate 1 year hence, = F1,2 = (1 + y2)2 / (1 + y1) - 1 = (1 + 10.4%)2 / (1 + 9.4%) - 1 = 11.41%
One year forward rate 2 year hence, = F2,3 = (1 + y3)3 / (1 + y2)2 - 1 = (1 + 11.4%)3 / (1 + 10.4%)2 - 1 = 13.43%
Part (b)
Under the assumption that the pure expectations hypothesis of the term structure is correct, spot rate = expected forward rate.
Hence, at the end of 1 year, 1 year spot rate will become same as F1,2 calculated above and 1 year forward rate, 1 year hence will be F2,3 calculated above. F1,2 > y2 and F2,3 > y3
hence, There will be a shift upwards in next year's curve.
Part (c)
The yield to maturity on two year zero will then be: (1 + y2 after 1 year)2 = (1 + y1 after 1 year) x (1 + F1,2 after 1 year)
= (1 + F1,2 current) x (1 + F2,3 current) = (1 + 11.41%) x (1 + 13.43%) = 1.2637
Hence, y2 after 1 year = 1.26371/2 - 1 = 12.41%
Part (d)
Price of two year Zero coupon bond now, P0 = 1000 / (1 + y2)2 = 1,000 / (1 + 10.4%)2 = 820.47
Price of two year Zero coupon bond one year later, P1 = 1000 / (1 + y1 after 1 year) = 1,000 / (1 + 11.41%) = 897.59
Hence, the expected total rate of return over the next year = P1 / P0 - 1 = 897.59 / 820.47 - 1 = 9.40%
Part (e)
Price of three year Zero coupon bond now, P0 = 1000 / (1 + y3)3 = 1,000 / (1 + 11.4%)3 = 723.34
Price of three year Zero coupon bond one year later, P1 = 1000 / (1 + y2 after 1 year)2 = 1,000 / (1 + 12.41%)2 = 791.34
Hence, the expected total rate of return over the next year = P1 / P0 - 1 = 791.34 / 723.34 - 1 = 9.40%