According to the Expectations Theory, long-term rates are an average of investors’ expected future short term rates of interest.

According to this theory, if the yield curve is upward sloping, this indicates that investors expect short-term rates to be higher in the future. If the yield curve is downward sloping, this indicates that investors expect short-term rates to be lower in the future. If the yield curve is flat, this indicates that investors expect short-term rates to be unchanged in the future.

One of the key assumptions of the Expectations Theory is that investors do not have any preferences for bond maturities; they are indifferent between bonds of all maturities. This may be true for institutional investors but may not be true for retail investors. For example, an investor who needs to save for five years would be indifferent between:

§ Buying a five-year bond

§ Buying a ten-year bond and selling it after five years

§ Buying a thirty-year bond and selling it after five years

This is a bit too simplistic because it misses out the aspect of Yield to Call when there is an embedded call option in such bonds.

The following numerical example illustrates this idea. Suppose that the current one-year rate is 9% and the current two-year rate is 10%. According to the Expectations Theory, the fact that the two-year rate is higher than the one-year rate implies that investors expect the one-year rate to be higher next year.

This can be shown by computing the return to the following strategies:

§ Buying a two year bond

§ Buying a one-year bond and then reinvesting the proceeds in another one-year bond

If the investor buys the two-year bond, his return over the next two years will be:

(1 + 0.10)^{2} – 1 = 0.21 = 21%

In order for the investor to be indifferent between the two strategies, he must expect to earn the same return from both. In order for him to earn 21% by buying a one-year bond with a 9% rate and then reinvesting in another one-year bond, the expected rate paid by the second one-year bond must be:

(1 + 0.09)(1 + X) = (1.10)^{2}

(1 + X) = (1.10)^{2} / (1.09)

X = (1.10)^{2} / (1.09) – 1

X = 0.11 = 11%

This shows that if one year rates are 9% and two-year rates are 10%, then according to the Expectations Theory, investors expect the one-year rate to be 11% next year. When long-term rates exceed short-term rates, this indicates that investors expect future short-term rates to be greater than they are today. Equivalently, if long-term rates are below short-term rates, according to the Expectations Theory, investors expect short-term rates to be lower in the future than they are today.

Mary Josephanswered.According to the Expectations Theory, long-term rates are an average of investors’ expected future short term rates of interest.

According to this theory, if the yield curve is upward sloping, this indicates that investors expect short-term rates to be higher in the future. If the yield curve is downward sloping, this indicates that investors expect short-term rates to be lower in the future. If the yield curve is flat, this indicates that investors expect short-term rates to be unchanged in the future.

One of the key assumptions of the Expectations Theory is that investors do not have any preferences for bond maturities; they are indifferent between bonds of all maturities. This may be true for institutional investors but may not be true for retail investors. For example, an investor who needs to save for five years would be indifferent between:

§ Buying a five-year bond

§ Buying a ten-year bond and selling it after five years

§ Buying a thirty-year bond and selling it after five years

This is a bit too simplistic because it misses out the aspect of Yield to Call when there is an embedded call option in such bonds.

The following numerical example illustrates this idea. Suppose that the current one-year rate is 9% and the current two-year rate is 10%. According to the Expectations Theory, the fact that the two-year rate is higher than the one-year rate implies that investors expect the one-year rate to be higher next year.

This can be shown by computing the return to the following strategies:

§ Buying a two year bond

§ Buying a one-year bond and then reinvesting the proceeds in another one-year bond

If the investor buys the two-year bond, his return over the next two years will be:

(1 + 0.10)

^{2}– 1 = 0.21 = 21%In order for the investor to be indifferent between the two strategies, he must expect to earn the same return from both. In order for him to earn 21% by buying a one-year bond with a 9% rate and then reinvesting in another one-year bond, the expected rate paid by the second one-year bond must be:

(1 + 0.09)(1 + X) = (1.10)

^{2}(1 + X) = (1.10)

^{2}/ (1.09)X = (1.10)

^{2}/ (1.09) – 1X = 0.11 = 11%

This shows that if one year rates are 9% and two-year rates are 10%, then according to the Expectations Theory, investors expect the one-year rate to be 11% next year. When long-term rates exceed short-term rates, this indicates that investors expect future short-term rates to be greater than they are today. Equivalently, if long-term rates are below short-term rates, according to the Expectations Theory, investors expect short-term rates to belowerin the future than they are today.