Question

1.     The following is a list of prices for zero-coupon bonds of various maturities. Calculate the yields to maturity of each bond and the implied sequence of forward rates.

maturity years: Price of bond

1 943.40

2 898.47

3 847.62

4 792.16

2.    [Chapter 15] The current yield curve for default-free zero-coupon bonds is as follows:

Maturity (Years): YTM%

1 10%

2 11%

3 12%

a.      What are the implied 1-year forward rates?

b.     Assume that the pure expectations hypothesis of the term structure is correct. If market expectations are accurate, what will be the pure yield curve (that is, the yields to maturity on 1- and 2-year zero coupon bonds) next year?

c.      If you purchase a 2-year zero-coupon bond now, what is the expected total rate of return over the next year? What if you purchase a 3-year zero-coupon bond?

d.     What should be the current price of a 3-year maturity bond with a 12% coupon rate paid annually? If you purchased it at that price, what would your total expected rate of return be over the next year (coupon plus price change)?

Answer 1

1. Present Value of zero coupon bond = PV

Par Value of the bond = FV

Number of Years to maturity = n

Let Yield to Maturity be r

Hence, PV = FV/(1+r)ⁿ

=> r = (FV/PV)^1/n - 1

For Maturity = 1 year, PV = 953.40, FV = 1000

r = (FV/PV)^1/n - 1 = (1000/953.40)^1/1 - 1 = 0.0489 or 4.89%

For Maturity = 2 year, PV = 898.47, FV = 1000

r = (FV/PV)^1/n - 1 = (1000/898.47)^1/2 - 1 = 0.0550 or 5.50%

For Maturity = 3 year, PV = 847.62, FV = 1000

r = (FV/PV)^1/n - 1 = (1000/847.62)^1/3 - 1 = 0.0567 or 5.67%

For Maturity = 4 year, PV = 792.16, FV = 1000

r = (FV/PV)^1/n - 1 = (1000/792.16)^1/4 - 1 = 0.060 or 6.00%