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; or (ii) a three-year bond; The current yield curve tells you that the one-year, two-year, and three-year yields to maturity are 2.5 percent, 4 percent, and 2.7 percent, respectively. You expect that one-year interest rates will be 5 percent next year and 5 percent the year after that. Assuming annual compounding, compute the return on each of the two investments.

Expected return for (i) =  %

Expected return for (ii) =  %

Answer 1

The rate of return on each of the two investments is calculated as below:

Expected return for (i) = (1+One-Year Yield to Maturity)*(1+One-Year Interest Rate for Next Year)*(1+One-Year Interest Rate After Next Year) - 1

Here, = One Year-Yield to Maturity = 2.5%, One-Year Interest Rate for Next Year = 5% and One-Year Interest Rate After Next Year = 5%

Using these values in the above formula, we get,

Expected return for (i) = (1+2.5%)*(1+5%)*(1+5%) - 1 = 13.01%

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Expected return for (ii) = (1+Three-Year Yield to Maturity)^3 - 1

Here, Three-Year Yield to Maturity = 2.7%

Using this value in the above formula, we get,

Expected return for (ii) = (1+2.7%)^3 - 1= 8.32%

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Tabular Representation: