Why Bonds With Different Maturities Have Different Interest Rates
In this paper, I will discuss why bonds with different maturities can have different interest rates. I will do so by explaining the importance of understanding the term structure, as well as the three theories that support the term structure; the expectations theory, the segmented markets theory, and the liquidity premium theory.
Term Structure According to Hubbard and O’Brien, the term structure “is the relationship among the interest rates on bonds that are otherwise similar but have different maturities.” Term structure is most commonly analyzed by looking at the Treasury yield curve, which is the relationship of interest rates on Treasury bonds with different maturities on a particular day. Yields generally tend to move in line with maturity, producing an upward sloping yield curve or a “normal yield curve.” Rarely, however, the yields on the long-term treasuries fall below the yields of short-term treasuries. This creates an inverted yield curve. According to a class lecture, six times when the yield curve became inverted, there was an economic recession. Wheelock and Wohar believe that term structure plays an important role in an economy because it “has been found useful for forecasting such variables as output growth, inflation, industrial production, consumption, and recessions.”
The Expectations Theory According to Hubbard and O’Brien, the expectations theory “holds that the interest rate on a long-term bond is an average of the interest rates investors expect on short-term bonds over the lifetime of the bond.” As an example, assume that one-year interest rates over the next five years are 3%, 4%, 5%, 6% and 7%. The interest rate on a two-year bond would be calculated as
3%+4%2=3.5%.
The interest rate on a four-year bond would be calculated as
3%+4%+5%+6%4=4.5%.
As previously stated, long-term rates are an average of the expectations of future short-term rates. Therefore, it is safe to say that interest rates of different maturities will move together. If the current short-term rate changes, it will have little impact on a long-term rate. Wheelock and Wohar suggest that the expectations theory “of the term structure is the foundation of many explanations of the term spread’s usefulness in forecasting output growth and recessions.”
Segmented Markets Theory The segmented markets theory suggests that there is no relationship between short-term and long-term bonds and that the interest rates are only determined by the supply and demand for bonds. This means that bonds of different maturities cannot be substitutes for each other, opposite of what the expectations theory suggests. Lower inflation and lower risk are associated with short-term bonds, suggesting that segmented markets theory would predict that higher yields would be associated with long-term bonds and lower yields associated with short-term bonds, producing an upward sloping yield curve or normal yield curve.
Liquidity Premium Theory Like the expectations theory, the liquidity premium theory suggests that the interest rate on a long-term bond is an average of the interest rates investors expect on short-term bonds over the lifetime of the long-term bond, however, unlike the expectations theory, there must be the addition of a term premium. A term premium is additional interest, or compensation that investors require for taking the risk of buying long-term bonds. According to Wheelock and Wohar, “term premium explains why the yield curve usually slopes upward—that is, why the yields on long-term securities usually exceed those on short-term securities.” Risk increases as maturity increases, so the term premium must increase along with it. As an example, assume that one-year interest rates over the next five years are 2%, 3%, 4%, 5% and 6%. Also assume that term premiums for one-year to five-year bonds are 1%, 1.25%, 1.50%, 1.75% and 2%. The interest rate on a two-year bond would be calculated as
2%+3%2+1%=3.5%.
The interest rate on a four-year bond would be calculated as
2%+3%+4%+5%4+1.75%=5.25%.
The liquidity premium theory, like the expectations theory, predicts that interest rates of different maturities will move together. In addition, long-term rates will hardly be affected by changes to the current short-term rate. Term structure plays an important role in an economy as it helps to forecast output growth and recessions. Although the expectations theory, the segmented markets theory, and the liquidity premium theory help explain term structure and provide explanations to why bonds with different maturities have different interest rates, there are a few drawbacks. The expectations theory fails to explain why the yield curve is usually normal and the segmented markets theory fails to explain why the yield curve might become inverted. The liquidity premium theory, combining elements from the other theories, fully explains the importance and all facts of term structure.

Works Cited
Hubbard, R., & O'Brien, A. (2014). The Risk Structure and Term Structure of Interest Rates. In Money, Banking, and the Financial System (Second ed., p. 39). Pearson Education.
Wheelock, D., & Wohar, M. (2009). Can the Term Spread Predict Output Growth and Recessions? A Survey of the Literature. Federal Reserve Bank of St. Louis Review, September/October(Part 1), 419-440.