# Bonds and Bond Valuation

## Using the Yield Curve


### Learning Outcomes

By the end of this section, you will be able to:
1. Use the yield curve to show the term structure of interest rates.
2. Describe and define changes in the yield curve shape.
3. Explain the importance of the yield curve shape.

### Term Structure of Interest Rates

The expected yields of various bonds across different maturity periods are referred to as the term structure of interest rates. This is because they represent interest rates for different periods of time, maturities, or terms.
When interest rate yields are plotted against their respective maturity periods and these plotted points are connected, the resulting line is called a yield curve. Essentially, the yield curve is a result of this plotting process and becomes a graphical representation of the term structure of interest rates. A yield curve will always be constructed by showing the value of yields (rates) on the y-axis and maturities or time periods on the x-axis (see ).
To create a useful graph of the yield curve, interest rate yields should be computed for all government bonds at all remaining times to maturity. For example, the yields on all government bonds with a single year remaining until maturity should be calculated. This value is then plotted on the y-axis against the one-year term on the x-axis. Similarly, yields on government bonds with two years remaining until maturity are calculated and plotted on the y-axis against two years on the x-axis, and so on, until a point of critical mass of information is reached and the resulting graph displays useful information.
The yield curve for government bonds is also known as the risk-free yield curve because these securities are thought of as safe investments that are not expected to fail or default and will in all likelihood repay or otherwise meet all financial obligations made through the bond issuance.
A normal yield curve slopes upward, with yield increasing as the term increases. This is because yields on fixed-income investments such as bonds will rise as maturity periods increase and produce greater levels of risk.
Corporate issuers of bonds will usually offer bond issues at higher yields that the government, which is understandable because they are potentially riskier for investors. Government securities are guaranteed by governments and have little to no chance of default or nonpayment. This is not the case for corporate bonds, where there is always a chance of default, though the likelihood of this occurring will vary by individual company or issuer as well as by bond type and term. We will discuss bond default and default risk next.

### Different Shapes of the Yield Curve

There are two important elements to any yield curve that will define its shape: its level and its slope. The level of a yield curve directly relates to the yield rates depicted on the y-axis of the graph (see ). The slope of the yield curve indicates the difference between yields on short-term and longer-term investments. The difference in yields is primarily due to investors’ expectations of the direction of interest rates in the economy and how the federal funds rate (referred to as cash rate in many countries) is uncertain and may differ significantly over time. As an example, yields on three-year bonds incorporate the expectations of investors on how bank rates might move over the next three years, combined with the uncertainty of those rates over the three-year period.
As we briefly discussed above, a positive or normal yield curve is indicative of the investment community’s requirements for higher rates of return as financial consideration for assuming the risk of entering into fixed-income investments, such as the purchase of bond issues. Typically, as a bond term increases, so will the potential interest rate risk to the bondholder. Therefore, bonds with longer terms will usually carry higher coupon rates to make returns greater for investors. Additionally, economists have come to believe that a steep positive yield curve is a sign that investors anticipate relatively high inflation in the future and thus higher interest rates accompanied by higher investment yields over shorter (inflationary) periods of time.
Normal yield curves are generally observed during periods of economic expansion, when growth and inflation are increasing. In any expansionary economy, there is a greater likelihood that future interest rates will be higher than current rates. This tends to occur because investors will anticipate the Fed or the central bank raising its short-term rates in response to higher inflation rates within the economy.
A flat shape for the yield curve occurs when there is not a great deal of difference between short-term and long-term yields (see ). A flat curve is usually not long lasting and is often observed when the curve is transitioning between a normal and an inverted shape, or vice versa.
A flat yield curve has also been observed as a result of low interest rate levels or some types of unconventional monetary policy.

### Why Is the Yield Curve Important?

Market technicians, brokers, and investment analysts will study the yield curve in great detail by keeping track of its many changes and movements. This is because of the overall importance of the yield curve as an economic indicator and how it can be representative of the ideas, attitudes, and bond market expectations of individuals as well as large institutional investors that exert significant influence on investment markets and the economy as a whole.

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When interest rate yields are plotted against their respective maturity periods and these plotted points are connected, the resulting line is called the yield curve. The yield curve is a graphical representation of the term structure of interest rates. A yield curve always shows the value of yields (rates) on the y-axis and maturities or time periods on the x-axis.

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