# How to Calculate Unbiased Expectations Theory

by C. Taylor

Unbiased expectations theory predicts future short-term interest rates based on the assumption that long-term interest rates are indicators for the future. This calculation applies to securities with set interest levels, such as government bonds. A common example is deciding between one 2-year bond or two 1-year successive bonds. A 2-year bond usually offers a higher interest rate than a 1-year bond, which means the obvious choice would be the 2-year bond. However, unbiased expectations theory allows you to predict the interest rate of the second 1-year bond that allows an equivalent investment.

Add one to the 2-year bond's interest rate. As an example, if the 2-year bond offered a 10 percent interest rate, you would add one, which results in 1.10.

Square this figure. In the example, you would then have 1.21.

Divide this figure by the first 1-year interest rate, plus one. In the example, if the first year's 1-year interest rate was 9 percent, so you would divide 1.21 by 1.09 to get 1.11.

Subtract one from this figure to calculate the 1-year bond's interest rate in the second year. In the example, the second 1-year interest rate would need to be 0.111, or 11.1 percent, to offer an equivalent investment between one 2-year bond and two 1-year successive bonds.