Question

Suppose you purchase a

3030​-year,

​zero-coupon bond with a yield to maturity of

6.2 %6.2%.

You hold the bond for five years before selling it.

a. If the​ bond's yield to maturity is

6.2 %6.2%

when you sell​ it, what is the annualized rate of return of your​ investment?

b. If the​ bond's yield to maturity is

7.2 %7.2%

when you sell​ it, what is the annualized rate of return of your​ investment?

c. If the​ bond's yield to maturity is

5.2 %5.2%

when you sell​ it, what is the annualized rate of return of your​ investment?

d. Even if a bond has no chance of​ default, is your investment risk free if you plan to sell it before it​ matures? Explain.

Answer 1

Current Bond Price = FV / (1 + r)^n = 1000 / (1 + 6.2%)^30 = $164.54

a) If the yield to maturity after 5 years is same as 6.2%, then your annualized rate of return = 6.2%

b) If YTM = 7.2%, Bond Price = 1000 / (1 + 7.2%)^25 = $175.85

=> Annualized rate of return = (175.85 / 164.54)^(1/5) - 1 = 1.34%

c) If YTM = 5.2%, then Bond Price = 1000 / 1.052^25 = $281.58

=> Annualized rate of return = (281.58 / 164.54)^(1/5) - 1 = 11.34%

d) If you plan to sell the bond before expiry, your returns are likely to be different than the yield to maturity when you bought the bonds. Interest rates change over a period of time which leads to different rate of returns before maturity.