Term Structure of Interest Rates

The term structure of interest rates is the variation of the yield of bonds with similar risk profiles with the terms of those bonds. The yield curve is the relationship of the yield to maturity (YTM) of bonds to the time to maturity, or more accurately, to duration, which is sometimes referred to as the effective maturity. In most cases, bonds with longer maturities have higher yields. However, sometimes the yield curve becomes inverted, with short-term notes and bonds having higher yields than long-term bonds. Sometimes, the yield curve may even be flat, where the yield is the same regardless of the maturity. The actual shape of the yield curve depends on economic conditions, fiscal policies, expected forward rates, inflation, foreign exchange rates, foreign capital inflows and outflows, credit ratings of the bonds, tax policies, and the current state of the economy. The term structure of interest rates has 3 characteristics:

  1. The change in yields of different term bonds tends to move in the same direction.
  2. The yields on short-term bonds are more volatile than long-term bonds.
  3. The yields on long-term bonds tend to be higher than short-term bonds.

The expectations hypothesis has been advanced to explain the 1st 2 characteristics and the premium liquidity theory have been advanced to explain the last characteristic. The market segmentation theory explains the yield curve in terms of supply and demand within the individual segments.

Market Segmentation Theory

Because bonds and other debt instruments have set maturities, buyers and sellers of debt usually have preferred maturities. Bond buyers want maturities that will coincide with their liabilities or when they want the money, while bond issuers want maturities that will coincide with expected income streams. Market Segmentation Theory (MST) posits that the yield curve is determined by supply and demand for debt instruments of different maturities. Generally, the debt market is divided into 3 major categories in regard to maturities: short-term, intermediate-term, and long-term. The difference in the supply and demand in each market segment causes the difference in bond prices, and therefore, yields. There are many different factors that would cause differences in the supply and demand for bonds of a certain maturity, but much of that difference will depend on current interest rates and expected future interest rates. If current interest rates are high, then future rates will be expected to decline, thus increasing the demand for long-term bonds by investors who want to lock in high rates while decreasing the supply, since bond issuers do not want to be locked into high rates. Therefore, long-term interest rates will be lower than short-term rates. On the other hand, if current interest rates are low, then bond buyers will tend to avoid long-term bonds so that they are not locked into low rates, especially since bond prices will decline when interest rates rise, which will generally happen if interest rates are already low. On the other hand, borrowers generally want to lock in low rates, so the supply for long-term bonds will increase. Hence, a lower demand and a higher supply will cause long-term bond prices to fall, thereby increasing their yield.

Preferred Habitat Theory

Preferred Habitat Theory (PHT) is an extension of the market segmentation theory, in that it posits that lenders and borrowers will seek different maturities other than their preferred or usual maturities (their usual habitat) if the yield differential is favorable enough to them. For instance, if short-term rates are a lot lower than long-term rates, then bond issuers will issue more short-term bonds to take advantage of the lower rates even though they would prefer longer maturities to match their expected income streams; likewise, lenders will tend to buy long-term debt if the yield advantage is significant, even though carrying long-term debt has increased risks.

Expectations Hypothesis

There are several versions of the expectations hypothesis, but essentially, the expectations hypothesis (aka Pure Expectation Theory, Unbiased Expectations Theory) states that different term bonds can be viewed as a series of 1-period bonds, with yields of each period bond equal to the expected short-term interest rate for that period. For example, compare buying a 2-year bond with buying 2 1-year bonds sequentially. If the interest rate for the 1st year is 4% and the expected interest rate, which is often referred to as the forward rate, for the 2nd year is 6%, then one can be either buy a 1-year bond that yields 4%, then buy another bond yielding 6% after the 1st one matures for an average interest rate of 5% over the 2 years, or one can buy a 2-year bond yielding 5%—both options are equivalent: (4%+6%) / 2 = 5%. Hence, the sequential 1-year bonds are equivalent to the 2-year bond. (Actually, the geometric mean gives a slightly more accurate result, but the average is simpler to calculate and the argument is the same.)

Note that this relationship must hold in general, for if the sequential 1-year bonds yielded more or less than the equivalent long-term bond, then bond buyers would buy either one or the other, and there would be no market for the lesser yielding alternative. For instance, suppose the 2-year bond paid only 4.5% with the expected interest rates remaining the same. In the 1st year, the buyer of the 2-year bond would make more money than the 1st year bond, but he would lose more money in the 2nd year—earning only 4.5% in the 2nd year instead of 6% that he could have earned if he didn't tie up his money in the 2-year bond. Additionally, the price of the 2-year bond would decline in the secondary market, since bond prices move opposite to interest rates, so selling the bond before maturity would only decrease the bond's return.

Note, however, that expected future interest rates are just that – expected. There is no reason to believe that they will be the actual rates, especially for extended forecasts, but, nonetheless, the expected rates still influence present rates.

According to the expectations hypothesis, if future interest rates are expected to rise, then the yield curve slopes upward, with longer term bonds paying higher yields. However, if future interest rates are expected to decline, then this will cause long term bonds to have lower yields than short-term bonds, resulting in an inverted yield curve. The inverted yield curve often results when short-term interest rates are higher than historical averages, since there is a greater expectation that rates will decline, so long term bond issuers would be reluctant to issue bonds with higher rates when the expectation is that lower rates will prevail in the near future.

The expectations hypothesis helps to explain 2 of the 3 characteristics of the term structure of interest rates:

  1. The yield of bonds of different terms tend to move together.
  2. Short-term yields are more volatile than long-term yields.

However, the expectations hypothesis does not explain why the yields on long-term bonds are usually higher than short-term bonds. This could only be explained by the expectations hypothesis if the future interest rate was expected to continually rise, which isn't plausible nor has it been observed, except in certain brief periods.

Liquidity Premium Theory

The liquidity premium theory has been advanced to explain the 3rd characteristic of the term structure of interest rates: that bonds with longer maturities tend to have higher yields. Although illiquidity is a risk itself, subsumed under the liquidity premium theory are the other risks associated with long-term bonds: notably interest rate risk and inflation risk. Naturally, increased risks will lower demand for those bonds, thus increasing their yield. This increase in yield is the risk premium to compensate buyers of long-term bonds for their increased risk.

Liquidity is defined in terms of its marketability — the easier it is to sell a bond at its value in the secondary marketplace, the more liquid it will be, thus reducing liquidity risk. This explains why long-term Treasuries have such low yields, because they are the easiest to sell. Assets may be illiquid because they are riskier and/or because supply exceeds demand. Additionally, illiquid assets are more difficult to price, since previous sale prices may be stale or nonexistent.

A bond's yield can theoretically be divided into a risk-free yield and the risk premium. The risk-free yield is simply the yield calculated by the formula for the expectation hypothesis. The risk premium is the liquidity premium that increases with the term of the bond. Hence, the yield curve slopes upward, even if future interest rates are expected to remain flat or even decline a little, and so the liquidity premium theory of the term structure of interest rates explains the generally upward sloping yield curve for bonds of different maturities.

Liquidity Premium = Illiquid Bond YTM – Liquid Bond YTM

Besides liquidity, there are 2 other risks with holding bonds that increases with the term of the bond: inflation risk and interest rate risk. Both the inflation rate and the interest rate become more difficult to predict farther into the future. Inflation risk reduces the real return of the bond. Interest rate risk is the risk that bond prices will drop if interest rates rise, since there is an inverse relationship between bond prices and interest rates. Of course, interest rate risk is only a real risk if the bondholder wants to sell before maturity, but it is also an opportunity cost, since the long-term bondholder forfeits the higher interest that could be earned if the bondholder's money was not tied up in the bond. Therefore, a longer term bond must pay a higher risk premium to compensate the bondholder for the greater risk.

Other risks that will contribute to an upward sloping yield curve include both the credit risk and default risk of corporate bonds, since both increase with time. While it is generally accepted that there is no credit or default risk for Treasuries, most corporate bonds do have a credit rating that can change because of changing business or economic conditions, which, in turn, may increase default risk. Indeed, during recessions, the yield spread between Treasuries and corporate bonds increases, because of the increased credit risk during recessions, as can be seen in the graph below. This is often referred to as a flight to quality, such as occurred during the 2008 credit crisis, when interest rates on Treasury bills actually went negative — people were actually paying more for T-bills than they would receive at maturity!

Graph of long-term interest rates from 1996 to 2013 for conventional mortgages, corporate Aaa bonds, and 10-year Treasuries. The shaded portions represent recessions.
Graph of long-term interest rates from 1996 to 2013 for conventional mortgages, corporate Aaa bonds, and 10-year Treasuries.
Source: http://research.stlouisfed.org/publications/mt/page9.pdf

Another reason why bonds with longer maturities pay a higher yield is that most issuers would rather issue long-term bonds than a series of short-term bonds, since it costs money to issue bonds regardless of maturity, thus increasing the supply relative to demand.

Yield Curve Shifts

The yield curve shows how yield changes with time to maturity — it is a graphical representation of the term structure of interest rates. The general pattern is that shorter maturities have lower interest rates than longer maturities. The yield of a bond depends on the price of the bond, which in turn, depends on the supply and demand for a particular bond issue. Over time, supply and demand for particular maturity groups changes unevenly, so the yield curve shifts in different ways to reflect these differences. This article has already explained some of the hypotheses or theories to account for the yield curve and its changes, but regardless of the veracity of those explanations, the yield curve does shift in ways that are hard to predict, which lowers the effectiveness of bond strategies and makes it more difficult to analyze interest rate risk.

Although yield shifts are difficult to predict and to explain, they can be described. The yield curve is composed of a continuum of interest rates, so changes in the yield curve can be described as the type of shift that occurs. The types of yield curve shifts that regularly occur include parallel shifts, flattening shifts, twisted shifts, and shifts with humpedness.

Note that these yield curves are schematic: actual curves will be more wavy and tortuous in their details.
Diagrams of shifts in the yield curve: parallel shifts, flattening shifts, steepening shifts, twisted shifts, and humpedness or butterfly shifts.

A parallel shift is the simplest kind of shift in which short-, intermediate-, and long-term yields change by the same amount, either up or down. Some bond strategies, such as immunization, remain effective only if changes in the yield curve are parallel. A shift with a twist is one that involves either a flattening or an increasing curvature to the yield curve or it may involve a steepening of the curve where the yield spread becomes either wider or narrower as one progresses from shorter durations to longer durations. A yield shift with humpedness is one where the yields for intermediate durations changes by a different amount from either short- or long-term durations. Positive humpedness (aka positive butterfly) occurs when the intermediate-term yields are lower than either short- or long-term durations; negative humpedness (aka negative butterfly) is the inverse: short-term and long-term yields are lower than intermediate term yields.

There are different kinds of yield curves that are differentiated by the underlying security. So, for instance, there are yield curves for U.S. Treasuries, zero-coupon bonds, par value, euro securities, swaps, forward rates, and there are even curves for specific credit ratings, such as the BBB rated curve, and so on. Yield curves have several practical uses:

Because the yield curve is usually upward sloping, deviations from the normal yield curve will allow arbitrageurs to profit from the distortion in the yield curve by selling short bonds that are overpriced and buying bonds that are underpriced, so that when the yield curve reverts to normal, the arbitrageurs can earn a profit — this is referred to as yield-curve arbitrage. For instance, in 2000, the United States government decided to use some of its surplus to buy back 30-year Treasury bonds, which lowered their yields relative to 10 year Treasuries, so profits could be made by selling short the 30-year Treasuries and buying the underpriced 10-year bonds.

Inverted Yield Curve

This curve is also schematic. When the yield curve is inverted, long-terms rates are lower than short-term rates, which is the opposite of the usual case, which is why the curve is said to be inverted. This usually results when interest rates are high, but there is an expectation that they will be lower over the longer term, so there is a greater demand for the long-term bonds with a high-coupon rate to lock in the yield, thereby increasing their prices, which, of course, lowers their yield..
Inverted yield curve.

As already stated, short-term bonds may actually pay a higher yield than long-term bonds when short-term rates are expected to decline sharply. This was the situation in 1980-1982, when interest rates were much higher than normal. Because they were so high, it was expected that they would revert to the mean — decline to more normal values. Hence, no bond issuer is going to issue long-term bonds at a low price when they can fetch a higher price later, when interest rates are lower. Although long-term bond yields will be higher under a high interest rate environment than under low interest rates, long-term bonds will still be priced higher (lower yield) than short-term bonds in the secondary market, because investors will be willing to pay more for the longer-term bonds to lock in the higher yields over the long term to reduce their reinvestment risk and to earn a greater profit when interest rates decline, since bonds with longer durations rise more in price than bonds with shorter durations when interest rates decline.