# Lesson 6: Risk Structure and Term Structure of Interest Rates

Upon completion of this lesson, you should be able to do the following:

• Identify how risk of default, liquidity, information costs, and taxes cause interest rates to differ among different markets for financial securities.
• Explain the term structure of interest rates.
• Describe the yield curve.
• identify the three theories that explain the characteristics of the yield curve.

## Introduction

This lesson examines the relationships among many different interest rates and the term structure of interest rates. From the last lesson, the assumption was made that there was only one interest rate. However, there are many interest rates. There are four factors that cause interest rates to differ.

## Differences in Interest Rates

1. Default risk the possibility a borrower will not pay back the principal and/or interest on the loans. For example, the U.S. government bonds have little risk of default (called default-risk-free instruments), because the government can raise taxes, "print money," or issue new debt, when it gets into financial trouble. Business corporations have some risk of default. The business can bankrupt and not be able to pay off its debt. The difference between the interest rate on the U.S. government bonds and corporate bonds is called the default risk premium. The risk premium is the additional interest investors must earn in order to hold a "risky" bond and the risk premium is always positive.

Private firms such as Standard & Poor's Corporation and Moody's Investor Service determine the size of the default risk of corporations. These companies calculate a single statistic, called the bond rating. The bond rating is based on a corporation's net worth, cash flow, and ability to meet its debt obligations.

Start the model with government and corporate bonds that have zero risk. Bond prices and interest rates are the same for both markets. Corporations have financial trouble, so investors think there is a risk of default. Some investors demand less corporate bonds (demand curve shifts left), and invest in government bonds. The government bonds are considered default-free and the demand curve shifts right.

Government Bonds Corporate Bonds

The first thing you notice is the government bonds increase in price, while the price of corporate bonds fall. The market interest rate always go in the opposite direction of the price of bonds. When government bond prices increases, the market interest rates decrease. The corporate bond prices decrease, causing the market interest rate to increase. The difference between the government bond and corporate bond interest rates is the risk premium. As the default risk increases, then the risk premium increases too. During recessions, when some businesses start failing, the default risk increases, so the risk premium increases, and the difference between government and corporate interest rates increase too.

2. Liquidity - U.S. government securities are the most liquid and widely traded, so they are the easiest to buy and sell. Corporate bonds are not as liquid and not as widely traded, so there could be difficulties in quickly selling them. This model is very similar to the risk of default model that was depicted above. Start the model with the same liquidity in the government bond and corporate bond markets.

Government Bonds Corporate Bonds

The secondary markets become stronger for government bonds, so liquidity increases for these securities. The investors are attracted to the government bonds, because they are more liquid and demand increases (demand curve shifts to the right). Investors decrease their trading of corporate bonds, because they are less liquid, causing the demand curve to shift left. The government bond prices increase, causing the interest rate for government bonds to decrease. The corporate bond prices decrease, causing the market interest rate for corporate bonds to increase. The difference between the two interest rates reflect the degree of liquidity. However it is still called a risk premium.

3. Information costs - the more time and money to acquire information on securities imposes high information costs. These costs are included in the interest rate and are the cost of borrowing. For example, U.S. government securities are well known and have the lowest information costs out of all securities. Large corporations are well-known and have low information costs. The information costs for new and small companies are high and therefore, these companies will pay a higher interest rate when they borrow funds. Using a model to demonstrate this, start the model for high and low-information-cost bond markets with the same level of information. The liquidity and risk of default for these two markets are the same.

Low-Information-Cost Bond Market High-Information-Cost Bond Market

The costs of acquiring information increases, causing investors to be attracted to the low-information-cost bonds. The demand increases for low-information-cost bonds, causing the market price to increases and market interest rate to decrease. The high-information-cost bonds are not as attractive as an investment, so investors buy less bonds, causing bond prices to decrease and interest rates to increase. Therefore, low-information-cost bonds have a lower interest rate.

4. Taxes - U.S. government bonds have lower risk of default and higher liquidity than municipal bonds (state and local government bonds). For the last 50 years, the interest rates of municipal bonds have been lower than U.S. government bonds. The reason is the interest earned on municipal bonds are exempt from U.S. government taxes, while U.S. government securities are taxed. If you bought municipal bonds, you would earn less interest than U.S. government securities. However, you pay no taxes, which compensates you for the higher risk and lower liquidity. Using the same model as the default risk and liquidity models, start the model that both the municipal bond and non-municipal bond markets are subjected to income taxes. The default risk, liquidity, and information costs are equivalent for both markets.

Municipal Bonds Non-Municipal Bonds

The government passes laws that exempt municipal bonds from taxation. Investors are attracted to municipal bonds and demand increases, causing the market price to increases and market interest rate to decrease. The non-municipal bonds are not as attractive as an investment, so investors buy less bonds, causing bond prices to decrease and interest rates to increase. Therefore, municipal bonds have a lower interest rate.

## Term Structure of Interest Rates

If securities have the same risk, same liquidity, same information costs, and same taxes, the interest rates will differ by the maturity, which is called the term structure of interest rates. The term structure of interest rates is usually defined by U.S. securities, because the U.S. government issues a variety of securities with maturities ranging from 15 days to 30 years. No other finance company or business comes close to issuing a wide range of securities that differ by maturity.

Term Structure of Interest Rates
U.S. Government Securities
July 31, 2000
 1-month T-bill 6.07% 3-month T-bill 6.27% 5-year T-note 6.16% 30 year T-bond 5.79%

Source: Federal Reserve

 Economists usually plot U.S. government securities by the market interest rates and maturity. The graph is called a yield curve. The yield curve can be upward sloping, flat, or downward sloping. There are two characteristics of yield curves. The yield curve is usually upward sloping. Long-term securities (e.g. T-bonds) have higher interest rates than short-term securities (T-bills). All interest rates tend to move together, so the yield curve can shift up or down.

Three theories have been proposed to explain why the yield curve has these two characteristics.

1. Segmented markets theory - U.S. government securities are broken down into specific and separate markets based on maturities. The interest rate is determined by supply and demand in each market. One group of investors will only invest in T-bonds, while another group will invest only in T-bills. The yield curve usually slopes upward, because people prefer to hold short-term bonds rather than long-term bonds. This theory has one problem. If the markets of different maturities are completely separated and independent, a change in short-term interest rates will have no effect on long-term ones. This theory cannot explain why short-term and long-term interest rates move together, causing the yield curve to shift.

2. Expectations theory - investors view all securities that have the same liquidity, risk, information costs, and taxes as perfect substitutes. The interest rate on a long-term bond will equal the average of short-term interest rates that people expect to occur over the life of the security. For example, the current market interest rate on a one-year bond is 9%. You expect the interest rate to increase to 11% next year, so when you buy another one-year bond next year, the average interest rate you expect to earn is 11%. If you decide to hold a two-year bond, the interest rate must be 10%, because the interest rate will be 9% for the first year and you believe interest rates will increase to 11% for the second year. The average interest rate for these two year is 10%. If investors expect that short-term interest rates will increase, then the yield curve has a positive slope. If investors expect that short-term interest rates will decrease, then the yield curve has a negative slope. If investors expect that short-term interest rates will not change, then the yield curve is flat. The expectations theory explains well why short-term and long-term interest rates move together, but there is one problem. The yield curve usually has a positive slope, indicating that investors think short-term interest rates will increase, but the short-term interest rate could as likely decrease or increase.

3. Preferred habitat theory - this theory is the most widely accepted and combines the expectations theory and segment markets theory together. This theory can explain why the yield curve is usually upward sloping. Investors prefer to hold short-term bonds (preferred habitat) with a low expected return, but will hold long-term bonds if they are paid a term premium (i.e. higher interest rate). The term premium causes the yield curve tends to be upward sloping. This theory can explain why long and short-term interest rates move together The interest rates on a long-term bond will equal the average of short-term interest rates expected to occur over the life of the long-term bond (plus the term premium). If investors expect that short-term interest rates will increase, then the yield curve has a positive slope. If investors expect that short-term interest rates will decrease, then the yield curve has a negative slope. If investors expect that short-term interest rates will rise or fall very little, then the yield curve can still be upward sloping, because the term premium is high enough to cancel the effect of changing interest rates.

The yield curve is a useful indicator of economic activity. When a yield curve is downward sloping, specifically a three-month T-Bill has a higher interest rate than a 10-year T-bond, a recession usually occurs one year later.