CHAPTER 1
The Yield Curve

The main measure of return associated with holding bonds is the yield to maturity (YTM) or gross redemption yield (GRY). In developed markets there is usually a large number of bonds trading at one time, at different yields and with varying terms to maturity. Investors and traders frequently examine the relationship between the yields on bonds that are in the same class. Plotting yields of bonds that differ only in their term to maturity produces the yield curve. The yield curve is an important indicator and knowledge source of the state of a debt capital market.1 It is sometimes referred to as the term structure of interest rates, but strictly speaking this is not correct, as this expression should be reserved for the zero‐coupon yield curve only. We shall examine this in detail later.

Much of the analysis and pricing activity that takes place in the bond markets revolves around the yield curve. The yield curve describes the relationship between a particular redemption yield and a bond's maturity. We should be aware that the GRY of a bond is only ever the actual yield one receives during the period one holds the bond if certain specific, and generally unrealistic, conditions are met. However, we will leave the discussion of this for later.

Plotting the yields of bonds along the maturity term structure will give us our yield curve. It is very important that only bonds from the same class of issuer or with the same degree of liquidity are used when plotting the yield curve. For example, a curve may be constructed for UK gilts or for AA‐rated sterling Eurobonds, but not a mixture of both, because gilts and Eurobonds are bonds from different class issuers. The primary yield curve in any domestic capital market is the government bond yield curve, so for example, in the US market it is the US Treasury yield curve. With the advent of the euro currency in 11 (ultimately 19) countries of the European Union, in theory any euro‐currency government bond can be used to plot a default‐free euro yield curve. In practice, only bonds from the same government are used, as for various reasons different bonds within euro‐currency countries trade at different yields. Outside the government, bond markets yield curves are plotted for Eurobonds, money market instruments, off‐balance sheet instruments, in fact virtually all debt market instruments. Therefore it is always important to remember to compare like‐for‐like when analysing yield curves across markets.

In this chapter, we look at the yield to maturity yield curve as well as other types of yield curves that may be constructed. We also consider how to derive spot and forward yields from a current redemption yield curve. The main emphasis though, is on interpreting the shape of the yield curve, and explaining why it assumes the shapes it does. Later in the book we examine more advanced techniques for fitting, analysing, and interpreting the yield curve.

First though, we introduce the yield curve for beginners, of course experienced practitioners and graduate students may skip this part.

THE YIELD CURVE FOR BEGINNERS

This section is a summary of the importance and application of the yield curve. It was originally written with private investors in mind, so market practitioners may wish to skip this part.

What is the Yield Curve?

The yield curve is a graph that plots the yield of various bonds against their term to maturity. In other words, it is a snapshot of the current level of yields in the market. It is not an historical graph, that is, it does not show the level of yields over time. That would be an historical price (or yield) chart.

Yield curves are like football … it is very easy to grasp the basics, but difficult to become expert at (to continue the football analogy, akin to being good enough to play on a Sunday‐morning park football team and being good enough to play on a team that included David Beckham, Steven Gerrard, and Michael Owen). Let us imagine that we looked up gilt yields in the Financial Times on a day in August 2002 and saw the following:

Table 1.1 shows the yields for gilts of 1‐, 2‐, 5‐, 10‐, 15‐, 20‐, and 30‐year maturity. (The 8% 2021 gilt is slightly under 20 years maturity but it will do for our purposes – there is no gilt that matures in 2022 at the time we are looking at this.)

TABLE 1.1 Gilt yields

We open up Microsoft Excel3 and write down two columns, one for “maturity” and one for “yield”. The years to maturity column forms the x‐axis of the graph, while the yield forms the y‐axis. Then we use the Excel “chart wizard” and it plots our graph for us! The result is as shown in Figure 1.1.

FIGURE 1.1 Creating a yield curve in Excel.

This curve looks about right. Intuitively, we expect that yields increase the greater the maturity. If we lend one person an amount of money for one year and another person the same amount of money for 10 years, we would not charge them both the same rate of interest (assuming both had the same credit risk) – we would most likely charge a higher rate to the 10‐year borrower, for two reasons:

1. inflation will erode the value of the loan over the longer term, and;
2. while the longer‐dated borrower may be the same credit quality as the short‐dated borrower, there are other risks. For example, the long‐dated borrower may not be around in 10 years' time. Therefore, as a lender, we need a higher return to compensate for the greater risk the further out into the future we lend money.

So this gives us the positively sloping yield curve we see in Figure 1.1. However, if that is the case, why does the curve not continue to slope upwards, all the way to the 30‐year mark? The rate of upward movement declines after the five‐year mark, and then actually decreases to the 30‐year point. This is a peculiarity of many markets – the 30‐year bond, commonly called the long bond, is usually in such great demand among institutional investors, such as pension funds, that this demand outstrips supply. As a result, the price of this bond is forced upwards, and this moves the yield down to below what it should be.

Constructing a yield curve in the wholesale markets is a little more involved than what we have described above, and a ever‐so‐slightly complicated branch of mathematics is employed to derive the models used to fit yield curves. We consider this in later chapters.

Using the Yield Curve

The yield curve tells us where the bond market is trading now. It also implies the level of trading for the future, or at least what the market thinks will be happening in the future. In other words, it is a good indicator of the future level of the market. It is also a much more reliable indicator than any other used by private investors, and we can prove this empirically.

Let us consider the main uses of the yield curve. All participants in the debt capital markets have an interest in the current shape and level of the yield curve, as well as what this information implies for the future. The main uses are introduced below:

• Setting the yield for all debt market instruments. The yield curve essentially fixes the cost of money over the maturity term structure. The yields of government bonds from the shortest‐maturity instrument to the longest set the benchmark for yields for all other debt instruments in the market, around which all debt instruments are analysed. Issuers of debt (and their underwriting banks) therefore use the yield curve to price bonds and all other debt instruments. Generally the zero‐coupon yield curve is used to price new issue securities, rather than the redemption yield curve.
• Acting as an indicator of future yield levels. As we discuss later in this chapter, the yield curve assumes certain shapes in response to market expectations of the future interest rates. Bond market participants analyse the present shape of the yield curve in an effort to determine the implications regarding the future direction of market interest rates. This is perhaps one of the most important functions of the yield curve, and it is as much an art as a science. The yield curve is scrutinised for its information content, not just by bond traders and fund managers, but also by corporate financiers as part of project appraisal. Central banks and government treasury departments also analyse the yield curve for its information content, not just regarding forward interest rates, but also with regard to expected inflation levels.
• Measuring and comparing returns across the maturity spectrum. Portfolio managers use the yield curve to assess the relative value of investments across the maturity spectrum. The yield curve indicates the returns that are available at different maturity points and is...