economics_of_money_banking__financial_markets

Liquidity

Income Tax

Considerations

Another attribute of a bond that influences its interest rate is its liquidity. As we learned in Chapter 4, 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). U.S. 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.

How does the reduced liquidity of the corporate bonds affect their interest rates relative to the interest rate on Treasury bonds? We can use supply and demand analysis with the same figure that was used to analyze the effect of default risk, Figure 2, to show that the lower liquidity of corporate bonds relative to Treasury bonds increases the spread between the interest rates on these two bonds. Let us start the analysis by assuming that initially corporate and Treasury bonds are equally liquid and all their other attributes are the same. As shown in Figure 2, their equilibrium prices and interest rates will initially be equal: P c1 P T1 and i c1 i T1. If the corporate bond becomes less liquid than the Treasury bond because it is less widely traded, then (as the theory of asset demand indicates) its demand will fall, shifting its demand curve from D c1 to D c2 as in panel (a). The Treasury bond now becomes relatively more liquid in comparison with the corporate bond, so its demand curve shifts rightward from D T1 to D T2 as in panel (b). The shifts in the curves in Figure 2 show that the price of the less liquid corporate bond falls and its interest rate rises, while the price of the more liquid Treasury bond rises and its interest rate falls.

The result is that the spread between the interest rates on the two bond types has risen. Therefore, the differences between interest rates on corporate bonds and Treasury bonds (that is, the risk premiums) reflect not only the corporate bondÕs default risk but its liquidity, too. This is why a risk premium is more accurately a Òrisk and liquidity premium,Ó but convention dictates that it is called a risk premium.

Returning to Figure 1, we are still left with one puzzleÑthe behavior of municipal bond rates. Municipal bonds are certainly not default-free: State and local governments have defaulted on the municipal bonds they have issued in the past, particularly during the Great Depression and even more recently in the case of Orange County, California, in 1994 (more on this in Chapter 13). Also, municipal bonds are not as liquid as U.S. Treasury bonds.

Why is it, then, that these bonds have had lower interest rates than U.S. Treasury bonds for at least 40 years, as indicated in Figure 1? The explanation lies in the fact that interest payments on municipal bonds are exempt from federal income taxes, a factor that has the same effect on the demand for municipal bonds as an increase in their expected return.

Let us imagine that you have a high enough income to put you in the 35% income tax bracket, where for every extra dollar of income you have to pay 35 cents to the government. If you own a $1,000-face-value U.S. Treasury bond that sells for $1,000 and has a coupon payment of $100, you get to keep only $65 of the payment after taxes. Although the bond has a 10% interest rate, you actually earn only 6.5% after taxes.

Suppose, however, that you put your savings into a $1,000-face-value municipal bond that sells for $1,000 and pays only $80 in coupon payments. Its interest rate is only 8%, but because it is a tax-exempt security, you pay no taxes on the $80 coupon payment, so you earn 8% after taxes. Clearly, you earn more on the municipal bond

Quantity of Municipal Bonds

(a) Market for municipal bonds

F I G U R E 3 Interest Rates on Municipal and Treasury Bonds

P T1 i T1

P T2 i T2

DT

DT2 1

Quantity of Treasury Bonds

(b) Market for Treasury bonds

Summary

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 bondÕs interest payments. As a bondÕs 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.

The Wall Street Journal publishes a daily plot of the yield curves for Treasury securities, an example of which is presented here. It is typically found on page 2 of the ÒMoney and InvestingÓ section.

The numbers on the vertical axis indicate the interest rate for the Treasury security, with the maturity given by the numbers on the horizontal axis. For example, the yield curve marked ÒYesterdayÓ indicates that the interest rate on the three-month Treasury bill yesterday was 1.25%, while the one-year bill had an interest rate of 1.35% and the ten-year bond had an interest rate of 4.0%. As you can see, the yield curves in the plot have the typical upward slope.

Source: Wall Street Journal, Wednesday, January 22, 2003, p. C2.

Treasury Yield Curve

Yield to maturity of current bills, notes and bonds.

5.0%

Yesterday

1 month ago

1 year ago

4.0

3.0

2.0

1.0

Source: Reuters

www.ratecurve.com/yc2.html

Check out todayÕs yield curve.

upward slopes of the yield curve as in the ÒFollowing the Financial NewsÓ box but sometimes other shapes?

Besides explaining why yield curves take on different shapes at different times, a good theory of the term structure of interest rates must explain the following three important empirical facts:

1.As we see in Figure 4, interest rates on bonds of different maturities move together over time.

2.When short-term interest rates are low, yield curves are more likely to have an upward slope; when short-term interest rates are high, yield curves are more likely to slope downward and be inverted.

3.Yield curves almost always slope upward, as in the ÒFollowing the Financial NewsÓ box.

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, each of which is described in the following sections. The expectations theory does a good job of explaining the first two facts on our list, 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

Expectations

Theory

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.

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.

Segmented

Markets Theory

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.

The expectations theory also explains fact 1 that interest rates on bonds with different maturities move together over time. Historically, short-term interest rates have had the characteristic that if they increase today, they will tend to be higher in the future. Hence a rise in short-term rates will raise peopleÕs expectations of future shortterm rates. Because long-term rates are the average of expected future short-term rates, a rise in short-term rates will also raise long-term rates, causing shortand longterm rates to move together.

The expectations theory also explains fact 2 that yield curves tend to have an upward slope when short-term interest rates are low and are inverted when shortterm rates are high. When short-term rates are low, people generally expect them to rise to some normal level in the future, and the average of future expected short-term rates is high relative to the current short-term rate. Therefore, long-term interest rates will be substantially above current short-term rates, and the yield curve would then have an upward slope. Conversely, if short-term rates are high, people usually expect them to come back down. Long-term rates would then drop below short-term rates because the average of expected future short-term rates would be below current shortterm rates and the yield curve would slope downward and become inverted.4

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.

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

4The expectations theory explains another important fact about the relationship between short-term and long-term interest rates. As you can see in Figure 4, short-term interest rates are more volatile than long-term rates. If interest rates are mean-revertingÑthat is, if they tend to head back down after they are at unusually high levels or go back up when they are at unusually low levelsÑthen an average of these short-term rates must necessarily have lower volatility than the short-term rates themselves. Because the expectations theory suggests that the long-term rate will be an average of future short-term rates, it implies that the long-term rate will have lower volatility than short-term rates.

Liquidity

Premium and

Preferred Habitat

Theories

if they match the maturity of the bond to the desired holding period, they can obtain a certain return with no risk at all.5 (We have seen in Chapter 4 that if the term to maturity equals the holding period, the return is known for certain because it equals the yield exactly, and there is no interest-rate risk.) For example, people who have a short holding period would prefer to hold short-term bonds. Conversely, if you were putting funds away for your young child to go to college, your desired holding period might be much longer, and you would want to hold longer-term bonds.

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 shortterm bonds, long-term bonds will have lower prices and higher interest rates, and hence the yield curve will typically slope upward.

Although the segmented markets theory can explain why yield curves usually tend to slope upward, it has a major flaw in that it cannot explain facts 1 and 2. Because it views the market for bonds of different maturities as completely segmented, there is no reason for a rise in interest rates on a bond of one maturity to affect the interest rate on a bond of another maturity. Therefore, it cannot explain why interest rates on bonds of different maturities tend to move together (fact 1). Second, because it is not clear how demand and supply for shortversus long-term bonds change with the level of short-term interest rates, the theory cannot explain why yield curves tend to slope upward when short-term interest rates are low and to be inverted when short-term interest rates are high (fact 2).

Because each of our two theories explains empirical facts that the other cannot, a logical step is to combine the theories, which leads us to the liquidity premium theory.

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 theoryÕs 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 shorterterm 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 longerterm bonds. Such an outcome would modify the expectations theory by adding a positive liquidity premium to the equation that describes the relationship between longand short-term interest rates. The liquidity premium theory is thus written as:

5The statement that there is no uncertainty about the return if the term to maturity equals the holding period is literally true only for a discount bond. For a coupon bond with a long holding period, there is some risk because coupon payments must be reinvested before the bond matures. Our analysis here is thus being conducted for discount bonds. However, the gist of the analysis remains the same for coupon bonds because the amount of this risk from reinvestment is small when coupon bonds have the same term to maturity as the holding period.