Question

You have $1,000 to invest over an investment horizon of three years. The bond market offers various options. You can buy (i) a sequence of three one-year bonds; (ii) a three-year bond; or (iii) a two-year bond followed by a one-year bond. The current yield curve tells you that the one-year, two-year, and three-year yields to maturity are 3.5 percent, 4.0 percent, and 4.5 percent respectively. You expect that one-year interest rates will be 4 percent next year and 5 percent the year after that. Assuming annual compounding, compute the return on each of the three investments.
a. Expected return for (i)
b. Expected return for (ii)
c. Expected return for (iii)

Answer 1

Answer:

a) 13.02%

b) 14.12%

c) 13.57%

Explanation:

Given:

Yield to maturity for:

One year = 3.5%

Two year = 4.0%

Three year = 4.5%

Required:

Compute the return on investments

One year interest rate = 4%

Next year (2nd year) interest rate = 5%

a) For sequence of three one-year bonds:

1000 x (1+3.5%)(1+4%)(1+5%)

=1000 x 1.13022

= $1,130.25

Return =(1130.22/1000)-1 = 0.13022 = 13.02%

b) For a three-year bond; or

1000 x (1+4.5%)³

=1000 x 1.141166125

= $1,141.166

Return = (1,141.166/1000)-1 = 14.12%

c) For two-year bond followed by a one-year bond.

1000 x (1+4.0%)² (1+5%)

= 1000 x 1.13568

=$1,135.68

Return =(1135.68/1000)-1 = 13.568%