Term Structure of Interest Rates

The term structure of interest rates is the collection of interest rates for bonds that differ only in their length to maturity. For instance, a Treasury bond with 3 years to maturity may have an interest rate of 4%, while a treasury bond with 10 years to maturity may have an interest rate of 7 %. What accounts for this?

The Liquidity Premium Theory says that there are two elements to the story. First, long-term interest rates are the average of expected one-year rates. For instance, if interest rates on one-year bonds, over the next five years, are expected to be 3%, 4%, 5%, 6%, and 7%, the interest rate on a five-year bond is predicted to be 5%.

Why is this the case? Suppose it was not. If the five-year bond rate was only 3%, I could earn a greater expected return over the five years by purchasing a one-year bond this year, a one-year bond next year, etc. until I reached five years. Doing so would give me an average return of 5% over the five years, which is greater than holding the 3% bond. Suppose instead that the five-year bond rate was 7%. In this case, holding the five-year bond gives me a higher expected rate of return than purchasing 5 one-year bonds.

The first part of the Liquidity Premium Theory is essentially an arbitrage condition: if the long-term rates were not equal to the average of short-term rates, buyers would purchase whichever gave the greatest return. This act would tend to lower the return on the 'high-return' option, and raise the return on the 'low-return' option. Very soon, we'd expect interest rates to become equal. Thus, the arbitrageur guarantees the arbitrage condition!

The second element to the story is the assertion that people prefer bonds with shorter maturities. In particular, people prefer bonds with shorter maturities, since the price risk is reduced. If this is so, the above arbitrage condition won't hold exactly. Instead, it may be possible for the rate on a long-term bond to be consistently higher than the average of expected short rates. This is because people must be paid a 'term' or 'liquidity' premium to be willing to hold the longer-term bond.

In our above example, the five-year bond rate may persist at 7%, despite the fact that the average expected short-term rate is 5% if bond holders require a 2% term premium to hold the longer-term bonds.

We can put both elements into the formal Liquidity Premium Theory:

(long-term interest rate) =
(average expected one-year rates) + (liquidity or term premium)

where the average expected one-year rates are the rates during the period of the long-term bond.