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.

As given data including the expected interest rates and the yields to maturity (YTM in abbreviation) of three options, as well as the assumption of annual compounding, we can calculate the expected return on an investment horizon of 3 years for each case as follow:

(a): Three one-year bonds with YTM year 1: 3.5%; year 2: 4.0%; year 3: 5.0%. Therefore, we would have the expected return based on annual compounding like this:

(1.035) *(1.04) *(1.05) – 1 = 13.02%

(b): Similarly, a three-year bond with YTM: 4.5% would have the expected return as below:

(1.045)3 * 1 = 14.12%

(c): Likewise, the third option containing a two-year bond with YTM 4.0% for the first two year and one-year bond with YTM 5% for the last year, would have the expected return as follows:

(1.04)2 * (1.05) – 1 = 13.57%

Explanation:

To discuss and choose which option is the optimal choice in this situation, we can examine two theories that can help us make a decision in investing short-term or long-term bonds, which are the expectation theory and the preferred habitat theory.

At first, looking at the result, we can easily see the option (b) that has the highest expected return. Depending on the expectation theory, we would like to choose (b) because this theory assumes that investors are only concerned with YTM.

However, the expectation theory doesn’t take into account fundamental macroeconomic factors driving long-term bond yields such as inflation risk or interest-rate risk that lead to requiring compensation for these additional risks, which is why longer-term bonds generally have higher yields than would be suggested by the preferred habitat theory.

Besides, to select an investment strategy, an investor’s investment horizon is also important. Someone who wants to decrease outside forces like macroeconomic risks, tend to choose option (a), whilst those who have a three-year horizon given initially would probably choose (b) or (c). However, option (b) has a higher return than (c), option (b) is the most optimal choice.

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