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According to the expectations theory, this implies that a 2-year Treasury note purchased
today should yield 7.25 percent. Similarly, if 10-year bonds yield 9 percent today, and if 5-year bonds are expected to yield 7.5 percent 10 years from now, then investors should expect to earn 9 percent for 10 years and 7.5 percent for 5 years, for an average return of 8.5 percent over the next 15 years:

9% + 9% +…+9%+7.5%+…+7.5% = 10(9%) + 5(7.5%) = 8.5%
15                                        15

Consequently, a 15-year bond should yield this same return, 8.5 percent.

To understand the logic behind this averaging process, ask yourself what would happen if long-term yields were not an average of expected short-term yields. For example, suppose 2-year bonds yielded only 7 percent, not the 7.25 percent calculated above. Bond traders would be able to earn a pro?t by adopting the following trading strategy:

1. Borrow money for two years at a cost of 7 percent.
2. Invest the money in a series of 1-year bonds. The expected return over the 2-year period would be (7.0 + 7.5)/2 = 7.25%.

In this case, bond traders would rush to borrow money (demand funds) in the 2- year market and invest (or supply funds) in the 1-year market. Recall from Figure 1-3 that an increase in the demand for funds raises interest rates, whereas an increase in the supply of funds reduces interest rates. Therefore, bond traders’ actions would push up the 2-year yield but reduce the yield on 1-year bonds. The net effect would be to bring about a market equilibrium in which 2-year rates were a weighted average of expected future 1-year rates.

Taken From : Five-Minute MBA – Corporate Finance

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