Term Structure Theory

We’ll explain each of the theories of the term structure of interest rates, paying particular attention to the implications of each theory for the shape of the yield curve and the interpretation of forward rates.

Unbiased Expectations Theory

Under the unbiased expectations theory or the pure expectations theory, we hypothesize that it is investors’ expectations that determine the shape of the interest rate term structure.

Specifically, this theory suggests that forward rates are solely a function of expected future spot rates, and that every maturity strategy has the same expected return over a given investment horizon. In other words, long term interest rates equal the mean of future expected short term rates. This implies that an investor should earn the same return by investing in a five year bond or by investing in a three year bond and then a two year bond after the three year bond matures.

Similarly, an investor with a three year investment horizon would be indifferent between investing in a three year bond or in a five year bond that will be sold two years prior to maturity. The underlying principle behind the pure expectations theory is risk neutrality: Investors don’t demand a risk premium for maturity strategies that differ from their investment horizon.

For example, suppose the one year spot rate is 5% and the two year spot rate is 7%. Under the unbiased expectations theory, the one year forward rate in one year must be 9% because investing for two years at 7% yields approximately the same annual return as investing for the first year at 5% and the second year at 9%. In other words, the two year rate of 7% is the average of the expected future one year rates of 5% and 9%.

This is shown in Figure 23.3.

Figure 23.3: Spot and Future Rates

Notice that in this example, because short term rates are expected to rise (from 5% to 9%), the yield curve will be upward sloping.

Therefore, the implications for the shape of the yield curve under the pure expectations theory are:

If the yield curve is upward sloping, short term rates are expected to rise. If the curve is downward sloping, short term rates are expected to fall.

A flat yield curve implies that the market expects short term rates to remain constant.

Local Expectations Theory

The local expectations theory is similar to the unbiased expectations theory with one major difference: the local expectations theory preserves the risk neutrality assumption only for short holding periods. In other words, over longer periods, risk premiums should exist. This implies that over short time periods, every bond (even long maturity risky bonds) should earn the risk free rate.

The local expectations theory can be shown not to hold because the short holding period returns of long maturity bonds can be shown to be higher than short holding period returns on short maturity bonds due to liquidity premiums and hedging concerns.

Liquidity Preference Theory

The liquidity preference theory of the term structure addresses the shortcomings of the pure expectations theory by proposing that forward rates reflect investors’ expectations of future spot rates, plus a liquidity premium to compensate investors for exposure to interest rate risk. Furthermore, the theory suggests that this liquidity premium is positively related to maturity: a 25 year bond should have a larger liquidity premium than a five year bond.

Thus, the liquidity preference theory states that forward rates are biased estimates of the market’s expectation of future rates because they include a liquidity premium. Therefore, a positive sloping yield curve may indicate that either: (1) the market expects future interest rates to rise or (2) rates are expected to remain constant (or even fall), but the addition of the liquidity premium results in a positive slope. A downward sloping yield curve indicates steeply falling short term rates according to the liquidity preference theory.

The size of the liquidity premiums need not be constant over time. They may be larger during periods of greater economic uncertainty when risk aversion among investors is higher.

Segmented Markets Theory

Under the segmented markets theory, yields are not determined by liquidity premiums and expected spot rates. Rather, the shape of the yield curve is determined by the preferences of borrowers and lenders, which drives the balance between supply of and demand for loans of different maturities. This is called the segmented markets theory because the theory suggests that the yield at each maturity is determined independently of the yields at other maturities; we can think of each maturity to be essentially unrelated to other maturities.

The segmented markets theory supposes that various market participants only deal in securities of a particular maturity because they are prevented from operating at different maturities. For example, pension plans and insurance companies primarily purchase long maturity bonds for asset liability matching reasons and are unlikely to participate in the market for short term funds.

Preferred Habitat Theory

The preferred habitat theory also proposes that forward rates represent expected future spot rates plus a premium, but it does not support the view that this premium is directly related to maturity.

Instead, the preferred habitat theory suggests that the existence of an imbalance between the supply and demand for funds in a given maturity range will induce lenders and borrowers to shift from their preferred habitats (maturity range) to one that has the opposite imbalance. However, to entice investors to do so, the investors must be offered an incentive to compensate for the exposure to price and/or reinvestment rate risk in the less than preferred habitat. Borrowers require cost savings (i.e., lower yields) and lenders require a yield premium (i.e., higher yields) to move out of their preferred habitats.

Under this theory, premiums are related to supply and demand for funds at various maturities. Unlike the liquidity preference theory, under the preferred habitat theory a 10 year bond might have a higher or lower risk premium than the 25 year bond. It also means that the preferred habitat theory can be used to explain almost any yield curve shape.