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 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. Instructions: Enter your responses rounded to the nearest two decimal places. Expected return for (i) = ___% Expected return for (ii) =____ % Expected return for (iii) =____ %

Answer 1

i) Calculating expected return for sequence of three one year bonds

We will invest the amount in sequence of these three one year bonds with following YTMs

YTM of one year bond = 3.5%

Expected YTM of one year bond after one year from now = One year forward rate one year from now = 4%

Expected YTM of one year bond after two years from now = One year forward rate two years from now = 5%

We know

Expected return from investment in sequence of three one year bonds = (1+YTM of one year bond)(1+Expected YTM of one year bond after one year from now)(1+Expected YTM of one year bond after two years from now) - 1 = (1+3.5%)(1+4%)(1+5%) - 1 = 1.035 x 1.04 x 1.05 - 1 = 1.13022 - 1 = 0.13022 = 13.022% = 13.02% (rounded to two decimal places)

Expected return for (i) = 13.02%

ii)   YTM of three year bond = 4.5%

Expected return for a three year bond = (1+YTM of three year bond)³ - 1 = (1+4.5%)³ - 1 = (1.045)³ - 1 = 1.14116612 - 1 = 0.14116612 = 14.116612% = 14.12% (rounded to two decimal places)

Hence Expected return for (ii) = 14.12%

iii) YTM of two year bond = 4%

Expected YTM of one year bond after two years from now = one year forward rate two years from now = 5%

Expected return from two year bond followed by one year bond = (1+YTM of two year bond)² (1+ Expected YTM of one year bond after two years from now) - 1 = (1+4%)² (1+5%) - 1 = (1.04)² (1.05) - 1 = 1.0816 x 1.05 - 1 = 1.13568 - 1 = 0.13568 = 13.568% = 13.57% (rounded to two decimal places)

Expected return for (iii) = 13.57%