How to Calculate Unbiased Expectations Theory

by C. Taylor, studioD

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.

About the Author

C. Taylor embarked on a professional writing career in 2009 and frequently writes about technology, science, business, finance, martial arts and the great outdoors. He writes for both online and offline publications, including the Journal of Asian Martial Arts, Samsung, Radio Shack, Motley Fool, Chron, Synonym and more. He received a Master of Science degree in wildlife biology from Clemson University and a Bachelor of Arts in biological sciences at College of Charleston. He also holds minors in statistics, physics and visual arts.

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