The Yield Curve

The yield to maturity of any bond is strongly tied to general conditions in the fixed-income securities market All yields tend to move together in this market. However, all bond yields are not exactly the same.

The variation in yields across bonds is explained in part by the fact that bonds have various quality ratings. A strong AAA-rated bond is likely to cost more (and hence have lower yield) than a bond with an identical promised income stream but having a B-quality rating. It is only natural that high quality is more expensive than low quality, However, quality alone does not fully explain the observed variations in bond yields.

Another factor that partially explains the differences in the yields of various bonds is the time to maturity. As a general rule, 'long" bonds (bonds with very distant maturity dates) tend to offer higher yields than "short" bonds of the same quality The situation is depicted in Figure 4 1. The curve featured in this figure is an example of a yield curve. It displays yield as a function of time to maturity The curve is constructed by plotting the yields of various available bonds of a given quality class Figure 4 1 shows the yields for various government securities as a function of the maturity date. Note that the yields trace out an essentially smooth curve, which rises gradually as the time to maturity increases. A rising curve is a "normally shaped" yield curve; this shape occurs most often However, the yield curve undulates around in time, somewhat like a branch in the wind, and can assume various other shapes If long bonds happen to have lower yields than short bonds, the result is said to be an inverted yield curve. The inverted shape tends to occur when short-term rates

4.2 THE TERM STRUCTURE 73

FIGURE 4.1 Yield curve. Yields are plotted as a function of maturity date The curve shown here is typical and has a normal upward slope Source: Treasury Bulletin, June 1995

95 97 99 01 03 05 07 09 1 1 13 15 17 19 21 23 25 Years increase rapidly, and investors believe that the rise is temporary, so that long-term rates remain near their previous levels.

When studying a particular bond, it is useful to determine its yield and maturity date and place it as a point on the yield curve for bonds in its risk class This will give a general indication of how it is priced relative to the overall market. If it is far from the curve, there is probably a reason, related to special situations or special features (such as call features of the bond or news affecting the potential solvency of the issuer)

The yield curve is helpful, but because it is a bit arbitrary, it does not provide a completely satisfactory explanation of yield differences. Why, for example, should the maturity date be used as the horizontal axis of the curve rather than, say, duration? A more basic theory is required, and such a theory is introduced in the next section

Term structure theory puts aside the notion of yield and instead focuses on pure interest rates. The theory is based on the observation that, in general, the interest rate charged (or paid) for money depends on the length of time that the money is held Your local bank, for example, is likely to offer you a higher rate of interest for deposits committed for 3 years than for demand deposits (which can be withdrawn at any time). This basic fact, that the interest rate charged depends on the length of time that the funds are held, is the basis of term structure theory. This chapter works out the details and implications of that fact.

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