# How to Calculate Unbiased Expectations Theory

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From the mortgage banker to the stockbroker to the financial advisor, investors are forever reminded that interest rates will do what they do and we predict them at our financial peril. Of course, that cautious approach helps such professionals maintain their respective licenses. In fact, most everyone attempts to get a handle on the direction of rates as they plan for both the present and future.

One manner of gaining such insight is the unbiased expectations theory. Although it does not carry all the reliability of hard science, many bondholders find it a useful tool for understanding near-term rate activity.

## What Is Unbiased Expectations Theory?

Briefly, unbiased expectations theory, also known as expectations theory or pure expectations theory, looks at the long-term interest rates of bonds and other securities for clues as to where short-term rates will go. In other words, there is an inherent message about short-term interest rates in the rates of longer-term products.

In essence, a two-year bond's yield should be nearly equivalent to the combined returns of two consecutive one-year bonds. Although the two one-year bonds would ordinarily come with lower interest rates than their two-year counterpart, the unbiased expectations theory formula propounds that earnings would be very similar when all is said and done due to compounding interest.

## Calculating Unbiased Expectations Theory

An unbiased expectations theory calculator begins with the long-term rate, ​19 percent​ for example. Adding the whole number ​one​ to this rate gives a factor of ​1.19​. At this point, a pure expectations theory calculator will square that figure, e.g. ​1.19​ x ​1.19​ = ​1.42.

If the one-year bonds are listed at ​17​ percent each, add ​one​ and divide the squared two-year rate by that sum: ​1.42/1.17​ leaves us with a quotient of ​1.21​. Subtract the one for ​21​ percent. This is the predicted interest rate for a one-year bond.

With this information, an investor can determine whether the two successive one-year bonds are the best route to take.

## Is Expectations Theory Fool-Proof?

The unbiased expectations theory formula is by no means an ironclad prophecy as to what kind of financial fruit compounding interest will bear. There are times when this calculation overshoots and investors are left with a wrong prediction about the yield curve, i.e. an x-y axis line that represents where returns were and where they should be going.

In addition, in a sense, an unbiased expectations theory calculator is by definition blind to external factors that play on interest rates: Federal Reserve interventions, the rate of inflation and trends in economic growth. Variables like these affect rates and, by consequence, affect bond yields.

Read More:What Is the Federal Reserve?

## Predictive Alternatives to Unbiased Expectations

Another option for bondholders is to adopt the preferred habitat theory. This takes unbiased expectations to the next level, assuming that short-term bonds are preferable because they mature sooner, possibly precluding some risk.

Adherents to this theory assume shorter-term is better unless the longer-term bonds are of a significantly higher yield. This is the only reason an investor should opt for long-term and, hence, the reason long-term bonds carry higher yields. This is certainly a simpler approach than the unbiased expectations formula.

The liquidity premium, or preference, theory is similar in that it assumes investors prefer cash to the promise of interest payments and, since short-term bonds are easier to cash in for full value, they are to be favored. Any medium- or longer-term bonds must offset this disadvantage with higher yields. Whereas preferred habitat focuses on term length and maturity, liquidity premium centers on cash conversion.