Suppose that a risk-neutral investor has a choice between buying a one-year bond

Question

Suppose that a risk-neutral investor has a choice between buying a one-year bond paying 4 percent today, a two-year bond paying 5 percent today, a three-year bond paying 5.3 percent today, or a four-year bond paying 5.8 percent today, if a one-year bond purchased one year from now is expected to have an interest rate of 5.5 percent, a one-year bond purchased two years from now is expected to have an interest rate of 6 percent, and a one-year bond purchased three years from now is expected to have an interest rate of 7 percent. If the investor has a 4 year time horizon, which combination would the investor buy?   To receive full credit, you must show all work.

Explanation / Answer

The investor has the following possible options and return in each case:

1. Buy four bond now = 5.8%
2. Buy three year bond now and one year bond three year from now = 5.3 + 7 + 12.3%
3. Buy two year bond now and one year bond two year from now and one year bond three year from now = 5 + 6 + 7 = 18%
4. One year bond now then one year bond after every year = 4 + 5.5 + 6 + 7 = 22.5%

Thus, Investor should purchase one year bond now, one year bond one year from now, one year bond two year from now and one year bond three year from now since it is giving maximum return, 22.5%.

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