# Expectations Theory

## What is the 'Expectations Theory'

The Expectations Theory – also known as the Unbiased Expectations Theory – states that long-term interest rates hold a forecast for short-term interest rates in the future. The theory postulates that an investor earns the same amount of interest by investing in a one-year bond in the present and rolling the investment into a different one-year bond after one year as compared to purchasing a two-year bond in the present.

## BREAKING DOWN 'Expectations Theory'

In some instances, the expectations theory is utilized as an explanation for the yield curve. However, the theory has been shown to be inaccurate in execution, because interest rates typically stay flat when the yield curve is normal. Essentially, the expectations theory is known to over-estimate future short-term interest rates.

## Example

Consider that the present bond market provides investors with a two-year bond that has an interest rate of 20% and a one-year bond with an interest rate of 18%. The expectations theory can be utilized to forecast the interest rate for the one-year bond in one year. The first step of the calculation is to add one to the two-year bond’s interest rate. In this example, the result is 1.2, or 120%.

The next step is to square the result; 1.2 squared results in 1.44. This number is then divided by the current one-year interest rate plus one. This means that 1.44 is divided by 1.18 to equal 1.22. Subtracting one from that sum is the final step and results in a predicted one-year bond interest rate of 22% for the following year.

In this example, the investor, theoretically, is earning an equivalent return to the present interest rate of a two-year bond. If the investor chooses to invest in a one-year bond at 18%, he has to hope for the bond yield to increase to 22% for the following year’s one-year bond.

## Preferred Habitat Theory

The preferred habitat theory – another term-structure theory – is an expansion of the expectations theory and is used to explain why longer-term bonds typically pay out higher interest than two shorter-term bonds that, added together, result in the same maturity. The theory states that investors have a preference for short-term bonds over long-term bonds, unless that latter pays a risk premium. When comparing the preferred habitat theory to the expectations theory, the difference is that the former assumes investors are concerned with maturity as well as yield, while the expectations theory assumes that investors are only concerned with yield.