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**Risk and term structure of interest rates**

Fundamentals of Finance – Lecture 5

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**Risk Structure of Interest Rates**

Bonds with the same maturity have different interest rates due to: Default risk Liquidity Tax considerations In our supply and demand analysis of interest-rate behavior, we examined the determination of just one interest rate. Yet we saw earlier that there are enormous numbers of bonds on which the interest rates can and do differ. Now, we complete the interest-rate picture by examining the relationship of the various interest rates to one another. Understanding why they differ from bond to bond can help businesses, banks, insurance companies, and private investors decide which bonds to purchase as investments and which ones to sell. We first look at why bonds with the same term to maturity have different interest rates. The relationship among these interest rates is called the risk structure of interest rates, although risk, liquidity, and income tax rules all play a role in determining the risk structure. A bond’s term to maturity also affects its interest rate, and the relationship among interest rates on bonds with different terms to maturity is called the term structure of interest rates. In this lecture we will examine the sources and causes of fluctuations in interest rates relative to one another and look at a number of theories that explain these fluctuations.

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**Long-Term Bond Yields, 1919–2011**

This Figure shows the yields to maturity for several categories of long-term bonds from 1919 to It shows us two important features of interest-rate behavior for bonds of the same maturity: Interest rates on different categories of bonds differ from one another in any given year, and the spread (or difference) between the interest rates varies over time. The interest rates on municipal bonds, for example, are above those on U.S. government (Treasury) bonds in the late 1930s but lower thereafter. In addition, the spread between the interest rates on Baa corporate bonds (riskier than Aaa corporate bonds) and U.S. government bonds is very large during the Great Depression years 1930–1933, is smaller during the 1940s–1960s, and then widens again afterwards. We can observe similar patterns during the last financial crisis that started in What factors are responsible for these phenomena? Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics

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**Risk Structure of Interest Rates (cont’d)**

Default risk: probability that the issuer of the bond is unable or unwilling to make interest payments or pay off the face value Treasury bonds are considered default free (government can raise taxes). Risk premium: the spread between the interest rates on bonds with default risk and the interest rates on (same maturity) Treasury bonds Default risk: One attribute of a bond that influences its interest rate is its risk of default, which occurs when the issuer of the bond is unable or unwilling to make interest payments when promised or pay off the face value when the bond matures. A corporation suffering big losses might be more likely to suspend interest payments on its bonds. The default risk on its bonds would therefore be quite high. By contrast, Treasury bonds have usually been considered to have no default risk because the government can always increase taxes to pay off its obligations. Bonds like these with no default risk are called default-free bonds. (However, during the budget negotiations in Congress in 1995 and 1996, the Republicans threatened to let Treasury bonds default, and this had an impact on the bond market, as one application following this section indicates.) The spread between the interest rates on bonds with default risk and default-free bonds, called the risk premium, indicates how much additional interest people must earn in order to be willing to hold that risky bond. Our supply and demand analysis of the bond market can be used to explain why a bond with default risk always has a positive risk premium and why the higher the default risk is, the larger the risk premium will be.

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**Response to an Increase in Default Risk on Corporate Bonds**

To examine the effect of default risk on interest rates, let us look at the supply and demand diagrams for the default-free (T-bonds) and corporate long-term bond markets. To make the diagrams somewhat easier to read, let’s assume that initially corporate bonds have the same default risk as T-bonds. In this case, these two bonds have the same attributes (identical risk and maturity); their equilibrium prices and interest rates will initially be equal (Pc1= PT1 and i c1= i T1 ), and the risk premium on corporate bonds (i c1 - i T1 ) will be zero. If the possibility of a default increases because a corporation begins to suffer large losses, the default risk on corporate bonds will increase, and the expected return on these bonds will decrease. In addition, the corporate bond’s return will be more uncertain as well. The theory of asset demand predicts that because the expected return on the corporate bond falls relative to the expected return on the default-free Treasury bond while its relative riskiness rises, the corporate bond is less desirable (holding everything else equal), and demand for it will fall. The demand curve for corporate bonds in panel (a) then shifts to the left, from Dc1 to Dc2. At the same time, the expected return on default-free T-bonds increases relative to the expected return on corporate bonds, while their relative riskiness declines. The Treasury bonds thus become more desirable, and demand rises, as shown in panel (b) by the rightward shift in the demand curve for these bonds from DT1 to DT2. As we can see in the Figure, the equilibrium price for corporate bonds falls from P c1 to P c2, and since the bond price is negatively related to the interest rate, the equilibrium interest rate on corporate bonds rises. At the same time, however, the equilibrium price for the Treasury bonds rises from P T1 to P T2, and the equilibrium interest rate falls from i T1 to i T2. The spread between the interest rates on corporate and default-free bonds—that is, the risk premium on corporate bonds—has risen from zero to i c 2 - i T2. We can now conclude that a bond with default risk will always have a positive risk premium, and an increase in its default risk will raise the risk premium.

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**Analysis of the Increase in Default Risk on Corporate Bonds**

Corporate Bond Market 1. Re on corporate bonds , Dc , Dc shifts left 2. Risk of corporate bonds , Dc , Dc shifts left 3. Pc , ic Government Bond Market 4. Relative Re on Government bonds , DT , DT shifts right 5. Relative risk of Government bonds , DT , DT shifts right 6. PT , iT Outcome: Risk premium, ic – iT, rises

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**Bond Ratings by Moody’s, Standard and Poor’s, and Fitch**

Because default risk is so important to the size of the risk premium, purchasers of bonds need to know whether a corporation is likely to default on its bonds. Rating agencies provide default risk information by rating the quality of corporate and municipal bonds in terms of the probability of default. The ratings and their description are contained in next slide. Bonds with relatively low risk of default are called investment-grade securities and have a rating of Baa (or BBB) and above. Bonds with ratings below Baa (or BBB) have higher default risk and have been aptly dubbed speculative-grade or junk bonds. Because these bonds always have higher interest rates than investment-grade securities, they are also referred to as high-yield bonds. Next let’s look back at Figure 1 and see if we can explain the relationship between interest rates on corporate and Treasury bonds. Corporate bonds always have higher interest rates than Treasury bonds because they always have some risk of default, whereas Treasury bonds do not. Because Baa-rated corporate bonds have a greater default risk than the higher-rated Aaa bonds, their risk premium is greater, and the Baa rate therefore always exceeds the Aaa rate. We can use the same analysis to explain the huge jump in the risk premium on Baa corporate bond rates during the Great Depression years 1930–1933 and after The depression period saw a very high rate of business failures and defaults. As we would expect, these factors led to a substantial increase in default risk for bonds issued by vulnerable corporations, and the risk premium for Baa bonds reached unprecedentedly high levels.

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**Risk Structure of Interest Rates (cont’d)**

Liquidity: the relative ease with which an asset can be converted into cash Cost of selling a bond Number of buyers/sellers in a bond market Income tax considerations Interest payments on municipal bonds are exempt from federal income taxes. Another attribute of a bond that influences its interest rate is its liquidity. As we learned before, a liquid asset is one that can be quickly and cheaply converted into cash if the need arises. The more liquid an asset is, the more desirable it is (holding everything else constant). Treasury bonds are the most liquid of all long-term bonds, because they are so widely traded that they are the easiest to sell quickly and the cost of selling them is low. Corporate bonds are not as liquid, because fewer bonds for any one corporation are traded; thus it can be costly to sell these bonds in an emergency, because it might be hard to find buyers quickly. We can use the same supply and demand analysis with the same figure that was used to analyze the effect of default risk in order to capture the liquidity risk.

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**Interest Rates on Municipal and Treasury Bonds**

Returning to Figure 1, we are still left with one puzzle—the behavior of municipal bond rates. Municipal bonds are certainly not default-free. Also, municipal bonds are not as liquid as Treasury bonds. Why is it, then, that these bonds have had lower interest rates than Treasury bonds for at least 40 years ? The explanation lies in the fact that interest payments on municipal bonds are exempt from income taxes and thus one clearly earns more on a municipal bond after taxes, so he will be willing to hold the riskier and less liquid municipal bond even though it has a lower interest rate than the Treasury bond - a factor that has the same effect on the demand for municipal bonds as an increase in their expected return. Another way of understanding why municipal bonds have lower interest rates than Treasury bonds is to use the supply and demand analysis displayed in the Figure. As before, we assume that municipal and Treasury bonds have identical attributes and so have the same bond prices and interest rates as drawn in the figure: P m1 P T1 and i m1 i T1. Once the municipal bonds are given a tax advantage that raises their after-tax expected return relative to Treasury bonds and makes them more desirable, demand for them rises, and their demand curve shifts to the right, from Dm1 to Dm2. The result is that their equilibrium bond price rises from Pm1 to P m2, and their equilibrium interest rate falls from i m 1 to i m2. By contrast, Treasury bonds have now become less desirable relative to municipal bonds; demand for Treasury bonds decreases, and DT 1 shifts to DT 2. The Treasury bond price falls from P T1 to P T2, and the interest rate rises from i T1 to i T2. The resulting lower interest rates for municipal bonds and higher interest rates for Treasury bonds explains why municipal bonds can have interest rates below those of Treasury bonds.

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**Tax Advantages of Municipal Bonds**

Municipal Bond Market 1. Tax exemption raises relative RETe on municipal bonds, Dm , Dm shifts right 2. Pm , im Treasury Bond Market 1. Relative RETe on Treasury bonds , DT , DT shifts left 2. PT , iT Outcome: im < iT This slide just explains once again what we talked about To summarize: The risk structure of interest rates (the relationship among interest rates on bonds with the same maturity) is explained by three factors: default risk, liquidity, and the income tax treatment of the bond’s interest payments. As a bond’s default risk increases, the risk premium on that bond (the spread between its interest rate and the interest rate on a default-free Treasury bond) rises. The greater liquidity of Treasury bonds also explains why their interest rates are lower than interest rates on less liquid bonds. If a bond has a favorable tax treatment, as do municipal bonds, whose interest payments are exempt from federal income taxes, its interest rate will be lower.

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**Term Structure of Interest Rates**

Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different. We have seen how risk, liquidity, and tax considerations (collectively embedded in the risk structure) can influence interest rates. Another factor that influences the interest rate on a bond is its term to maturity: Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different.

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**Term Structure of Interest Rates (cont’d)**

Yield curve: a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations Upward-sloping: long-term rates are above short-term rates Flat: short- and long-term rates are the same Inverted: long-term rates are below short-term rates

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Yield Curves A plot of the yields on bonds with differing terms to maturity but the same risk, liquidity, and tax considerations is called a yield curve, and it describes the term structure of interest rates for particular types of bonds, such as government bonds. Yield curves can be classified as upward-sloping, flat, and downward-sloping (the last sort is often referred to as an inverted yield curve). When yield curves slope upward the long-term interest rates are above the short-term interest rates; when yield curves are flat, short- and long-term interest rates are the same; and when yield curves are inverted, long-term interest rates are below short-term interest rates. Yield curves can also have more complicated shapes in which they first slope up and then down, or vice versa. Why do we usually see upward slopes of the yield curve but sometimes other shapes?

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**Movements over Time of Interest Rates on U. S**

Movements over Time of Interest Rates on U.S. Government Bonds with Different Maturities Sources: Federal Reserve

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**Facts that the Theory of the Term Structure of Interest Rates Must Explain**

Interest rates on bonds of different maturities move together over time. When short-term interest rates are low, yield curves are more likely to have an upward slope; when short-term rates are high, yield curves are more likely to slope downward and be inverted. Yield curves almost always slope upward.

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**Three Theories to Explain the Three Facts**

Expectations theory: explains the first two facts but not the third. Segmented markets theory: explains fact three but not the first two. Liquidity premium theory: combines the two theories to explain all three facts. Three theories have been put forward to explain the term structure of interest rates; that is, the relationship among interest rates on bonds of different maturities reflected in yield curve patterns: (1) the expectations theory, (2) the segmented markets theory, and (3) the liquidity premium theory. The expectations theory does a good job of explaining the first two facts, but not the third. The segmented markets theory can explain fact 3 but not the other two facts, which are well explained by the expectations theory. Because each theory explains facts that the other cannot, a natural way to seek a better understanding of the term structure is to combine features of both theories, which leads us to the liquidity premium theory, which can explain all three facts. If the liquidity premium theory does a better job of explaining the facts and is hence the most widely accepted theory, why do we spend time discussing the other two theories? There are two reasons. First, the ideas in these two theories provide the groundwork for the liquidity premium theory. Second, it is important to see how economists modify theories to improve them when they find that the predicted results are inconsistent with the empirical evidence.

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Expectations Theory Bond holders consider bonds with different maturities to be perfect substitutes. The interest rate on a long-term bond will equal an average of the short-term interest rates that people expect to occur over the life of the long-term bond. Buyers of bonds do not prefer bonds of one maturity over another; they will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity. The expectations theory of the term structure states the following commonsense proposition: The interest rate on a long-term bond will equal an average of short-term interest rates that people expect to occur over the life of the long-term bond. For example, if people expect that short-term interest rates will be 10% on average over the coming five years, the expectations theory predicts that the interest rate on bonds with five years to maturity will be 10% too. If short-term interest rates were expected to rise even higher after this five-year period so that the average short-term interest rate over the coming 20 years is 11%, then the interest rate on 20-year bonds would equal 11% and would be higher than the interest rate on five-year bonds. We can see that the explanation provided by the expectations theory for why interest rates on bonds of different maturities differ is that short-term interest rates are expected to have different values at future dates. The key assumption behind this theory is that buyers of bonds do not prefer bonds of one maturity over another, so they will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity. Bonds that have this characteristic are said to be perfect substitutes. What this means in practice is that if bonds with different maturities are perfect substitutes, the expected return on these bonds must be equal.

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**Expectations Hypothesis**

Key Assumption: Bonds of different maturities are perfect substitutes Implication: RETe on bonds of different maturities are equal Investment strategies for two-period horizon 1. Buy $1 of one-year bond and when it matures buy another one-year bond 2. Buy $1 of two-year bond and hold it. To see how the assumption that bonds with different maturities are perfect substitutes leads to the expectations theory, let us consider the following two investment strategies: 1. Purchase a one-year bond, and when it matures in one year, purchase another one-year bond. 2. Purchase a two-year bond and hold it until maturity. Because both strategies must have the same expected return if people are holding both one- and two-year bonds, the interest rate on the two-year bond must equal the average of the two one-year interest rates. For example, let’s say that the current interest rate on the one-year bond is 9% and you expect the interest rate on the one-year bond next year to be 11%. If you pursue the first strategy of buying the two one-year bonds, the expected return over the two years will average out to be (9% + 11%)/2 10% per year. You will be willing to hold both the one- and two-year bonds only if the expected return per year of the two-year bond equals this. Therefore, the interest rate on the two year bond must equal 10%, the average interest rate on the two one-year bonds.

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**Expected return from strategy 2**

(1 + i2t)(1 + i2t) – (i2t) + (i2t)2 – 1 = 1 1 Since (i2t)2 is extremely small, expected return is approximately 2(i2t)

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**Expected Return from Strategy 1**

(1 + it)(1 + iet+1) – it + iet+1 + it(iet+1) – 1 = 1 1 Since it(iet+1) is also extremely small, expected return is approximately it + iet+1 From implication above expected returns of two strategies are equal: Therefore 2(i2t) = it + iet+1 Solving for i2t i2t = 2

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**Expected Return from Strategy 1 cont’d**

More generally for n-period bond: it + iet+1 + iet iet+(n–1) int = n In words: Interest rate on long bond = average short rates expected to occur over life of long bond Numerical example: One-year interest rate over the next five years 5%, 6%, 7%, 8% and 9%: Interest rate on two-year bond: (5% + 6%)/2 = 5.5% Interest rate for five-year bond: (5% + 6% + 7% + 8% + 9%)/5 = 7% Interest rate for one to five year bonds: 5%, 5.5%, 6%, 6.5% and 7%. The expectations theory is an elegant theory that provides an explanation of why the term structure of interest rates (as represented by yield curves) changes at different times. When the yield curve is upward-sloping, the expectations theory suggests that short-term interest rates are expected to rise in the future, as we have seen in our numerical example. In this situation, in which the long-term rate is currently above the short-term rate, the average of future short-term rates is expected to be higher than the current short-term rate, which can occur only if short-term interest rates are expected to rise. This is what we see in our numerical example. When the yield curve is inverted (slopes downward), the average of future short-term interest rates is expected to be below the current short-term rate, implying that short-term interest rates are expected to fall, on average, in the future. Only when the yield curve is flat does the expectations theory suggest that short-term interest rates are not expected to change, on average, in the future.

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**Expectations Hypothesis and Term Structure Facts**

Explains why yield curve has different slopes: 1. When short rates expected to rise in future, average of future short rates = int is above today’s short rate: therefore yield curve is upward sloping 2. When short rates expected to stay same in future, average of future short rates are same as today’s, and yield curve is flat 3. Only when short rates expected to fall will yield curve be downward sloping Expectations Hypothesis explains Fact 1 that short and long rates move together 1. Short rate rises are persistent 2. If it today, iet+1, iet+2 etc. average of future rates int 3. Therefore: it int , i.e., short and long rates move together The expectations theory is an attractive theory because it provides a simple explanation of the behavior of the term structure, but unfortunately it has a major shortcoming: It cannot explain fact 3, which says that yield curves usually slope upward. The typical upward slope of yield curves implies that short-term interest rates are usually expected to rise in the future. In practice, short-term interest rates are just as likely to fall as they are to rise, and so the expectations theory suggests that the typical yield curve should be flat rather than upward-sloping.

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**Expectations Hypothesis and Term Structure Facts cont’d**

Explains Fact 2 that yield curves tend to have steep slope when short rates are low and downward slope when short rates are high 1. When short rates are low, they are expected to rise to normal level, and long rate = average of future short rates will be well above today’s short rate: yield curve will have steep upward slope 2. When short rates are high, they will be expected to fall in future, and long rate will be below current short rate: yield curve will have downward slope Doesn’t explain Fact 3 that yield curve usually has upward slope Short rates as likely to fall in future as rise, so average of future short rates will not usually be higher than current short rate: therefore, yield curve will not usually slope upward.

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**Segmented Markets Theory**

Key Assumption: Bonds of different maturities are not substitutes at all Implication: Markets are completely segmented: interest rate at each maturity determined separately Explains Fact 3 that yield curve is usually upward sloping People typically prefer short holding periods and thus have higher demand for short-term bonds, which have higher price and lower interest rates than long bonds Does not explain Fact 1 or Fact 2 because assumes long and short rates determined independently As the name suggests, the segmented markets theory of the term structure sees markets for different-maturity bonds as completely separate and segmented. The interest rate for each bond with a different maturity is then determined by the supply of and demand for that bond with no effects from expected returns on other bonds with other maturities. The key assumption in the segmented markets theory is that bonds of different maturities are not substitutes at all, so the expected return from holding a bond of one maturity has no effect on the demand for a bond of another maturity. This theory of the term structure is at the opposite extreme to the expectations theory, which assumes that bonds of different maturities are perfect substitutes. The argument for why bonds of different maturities are not substitutes is that investors have strong preferences for bonds of one maturity but not for another, so they will be concerned with the expected returns only for bonds of the maturity they prefer. This might occur because they have a particular holding period in mind, and if they match the maturity of the bond to the desired holding period, they can obtain a certain return with no risk at all. In the segmented markets theory, differing yield curve patterns are accounted for by supply and demand differences associated with bonds of different maturities. If, as seems sensible, investors have short desired holding periods and generally prefer bonds with shorter maturities that have less interest-rate risk, the segmented markets theory can explain fact 3 that yield curves typically slope upward. Because in the typical situation the demand for long-term bonds is relatively lower than that for short-term bonds, long-term bonds will have lower prices and higher interest rates, and hence the yield curve will typically slope upward.

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**Liquidity Premium (Preferred Habitat) Theories**

Key Assumption: Bonds of different maturities are substitutes, but are not perfect substitutes Implication: Modifies Expectations Theory with features of Segmented Markets Theory Investors prefer short rather than long bonds must be paid positive liquidity (term) premium, lnt, to hold long-term bonds. Results in following modification of Expectations Theory it + iet+1 + iet iet+(n–1) int = lnt n The liquidity premium theory of the term structure states that the interest rate on a long-term bond will equal an average of short-term interest rates expected to occur over the life of the long-term bond plus a liquidity premium (also referred to as a term premium) that responds to supply and demand conditions for that bond. The liquidity premium theory’s key assumption is that bonds of different maturities are substitutes, which means that the expected return on one bond does influence the expected return on a bond of a different maturity, but it allows investors to prefer one bond maturity over another. In other words, bonds of different maturities are assumed to be substitutes but not perfect substitutes. Investors tend to prefer shorter term bonds because these bonds bear less interest-rate risk. For these reasons, investors must be offered a positive liquidity premium to induce them to hold longer term bonds. Such an outcome would modify the expectations theory by adding a positive liquidity premium to the equation that describes the relationship between long and short-term interest rates. The liquidity premium theory is thus written as the above formula.

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**Preferred Habitat Theory**

Investors have a preference for bonds of one maturity over another. They will be willing to buy bonds of different maturities only if they earn a somewhat higher expected return. Investors are likely to prefer short-term bonds over longer-term bonds. Closely related to the liquidity premium theory is the preferred habitat theory, which takes a somewhat less direct approach to modifying the expectations hypothesis but comes up with a similar conclusion. It assumes that investors have a preference for bonds of one maturity over another, a particular bond maturity (preferred habitat) in which they prefer to invest. Because they prefer bonds of one maturity over another they will be willing to buy bonds that do not have the preferred maturity only if they earn a somewhat higher expected return. Because investors are likely to prefer the habitat of short-term bonds over that of longer-term bonds, they are willing to hold long-term bonds only if they have higher expected returns. This reasoning leads to the same Equation implied by the liquidity premium theory with a term premium that typically rises with maturity.

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**The Relationship Between the Liquidity Premium (Preferred Habitat) and Expectations Theory**

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Numerical Example 1. One-year interest rate over the next five years: 5%, 6%, 7%, 8% and 9% 2. Investors’ preferences for holding short-term bonds, liquidity premiums for one to five-year bonds: 0%, 0.25%, 0.5%, 0.75% and 1.0%. Interest rate on the two-year bond: (5% + 6%)/ % = 5.75% Interest rate on the five-year bond: (5% + 6% + 7% + 8% + 9%)/ % = 8% Interest rates on one to five-year bonds: 5%, 5.75%, 6.5%, 7.25% and 8%. Comparing with those for the expectations theory, liquidity premium (preferred habitat) theories produce yield curves more steeply upward sloped The relationship between the expectations theory and the liquidity premiums and preferred habitat theories is shown in Figure 5. There we see that because the liquidity premium is always positive and typically grows as the term to maturity increases, the yield curve implied by the liquidity premium theory is always above the yield curve implied by the expectations theory and generally has a steeper slope. A simple numerical example similar to the one we used for the expectations hypothesis further clarifies what the liquidity premium and preferred habitat theories in Equation 3 are saying. Again suppose that the one-year interest rate over the next five years is expected to be 5, 6, 7, 8, and 9%, while investors’ preferences for holding short-term bonds means that the liquidity premiums for one- to five-year bonds are 0, 0.25, 0.5, 0.75, and 1.0%, respectively. Equation 3 then indicates that the interest rate on the two-year bond would be:

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**Liquidity Premium and Preferred Habitat Theories (cont’d)**

Interest rates on different maturity bonds move together over time, as explained by the first term in the equation. Yield curves tend to slope upward when short-term rates are low and to be inverted when short-term rates are high, as explained by the liquidity premium term in the first case and by a low expected average in the second case. Yield curves typically slope upward, as explained by a larger liquidity premium as the term to maturity lengthens. The liquidity premium and preferred habitat theories explain fact 3 that yield curves typically slope upward by recognizing that the liquidity premium rises with a bond’s maturity because of investors’ preferences for short-term bonds. Even if short-term interest rates are expected to stay the same on average in the future, long-term interest rates will be above short-term interest rates, and yield curves will typically slope upward. How can the liquidity premium and preferred habitat theories explain the occasional appearance of inverted yield curves if the liquidity premium is positive? It must be that at times short-term interest rates are expected to fall so much in the future that the average of the expected short-term rates is well below the current short-term rate. Even when the positive liquidity premium is added to this average, the resulting long-term rate will still be below the current short-term interest rate.

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Yield Curves and the Market’s Expectations of Future Short-Term Interest Rates According to the Liquidity Premium (Preferred Habitat) Theory A particularly attractive feature of the liquidity premium and preferred habitat theories is that they tell you what the market is predicting about future short-term interest rates just from the slope of the yield curve. A steeply rising yield curve, as in panel (a) of the Figure indicates that short-term interest rates are expected to rise in the future. A moderately steep yield curve, as in panel (b), indicates that short-term interest rates are not expected to rise or fall much in the future. A flat yield curve, as in panel (c), indicates that short-term rates are expected to fall moderately in the future. Finally, an inverted yield curve, as in panel (d), indicates that short-term interest rates are expected to fall sharply in the future.

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The Risk and Term Structure of Interest Rates

The Risk and Term Structure of Interest Rates

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